Asas D'Alembert - Wikipedia bahasa Indonesia, ensiklopedia bebas

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value="Istimewa:Pencarian"> <input class="search skin-minerva-search-trigger" id="searchInput" type="search" name="search" placeholder="Telusuri Wikipedia" aria-label="Telusuri Wikipedia" autocapitalize="sentences" title="Cari di Wikipedia [f]" accesskey="f"> </div><button id="searchIcon" class="cdx-button cdx-button--size-large cdx-button--icon-only cdx-button--weight-quiet skin-minerva-search-trigger"> Cari </button> </form> <nav class="minerva-user-navigation" aria-label="Navigasi pengguna"> </nav> </div> </header> <main id="content" class="mw-body"> <div class="banner-container"> <div id="siteNotice"></div> </div> <div class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading">Asas D'Alembert</h1> <div class="tagline"></div> </div> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"><a role="button" 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href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> Sunting </a></li> </ul> </nav> <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"> <script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script> <div class="mw-content-ltr mw-parser-output" lang="id" dir="ltr"> <section class="mf-section-0" id="mf-section-0"> Asas d'Alembert, juga dikenal sebagai asas Lagrange-d'Alembert, adalah pernyataan hukum gerak klasik yang mendasar. Dinamakan sesuai dengan penemunya, fisikawan dan matematikawan Prancis <a href="https://id-m-wikipedia-org.translate.goog/wiki/Jean_le_Rond_d%27Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Jean le Rond d'Alembert">Jean le Rond d'Alembert</a>, dan matematikawan Prancis-Italia <a href="https://id-m-wikipedia-org.translate.goog/wiki/Joseph-Louis_de_Lagrange?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Joseph-Louis de Lagrange">Joseph Louis de Lagrange.</a> Asas d'Alembert menggeneralisasi <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerja_maya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerja maya">prinsip kerja maya</a> dari sistem <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Statis&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Statis (halaman belum tersedia)">statis</a> ke <a href="https://id-m-wikipedia-org.translate.goog/wiki/Dinamis?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-disambig" title="Dinamis">dinamis</a> dengan memperkenalkan gaya inersia, dimana jika ditambahkan pada gaya yang diterapkan dalam suatu sistem akan menghasilkan keseimbangan dinamis.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:0-1">[1]</a><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-2">[2]</a> Asas d'Alembert dapat diterapkan dalam kasus kendala kinematik yang bergantung pada kecepatan.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:0-1">[1]</a>:92 Asas ini tidak berlaku untuk perpindahan yang tidak dapat dipulihkan, seperti <a href="https://id-m-wikipedia-org.translate.goog/wiki/Gesekan?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Gesekan">gesekan</a> geser, dan diperlukan spesifikasi yang lebih umum tentang ketidakberubahan.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-3">[3]</a><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:1-4">[4]</a> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="id" dir="ltr"> <h2 id="mw-toc-heading">Daftar isi</h2><label class="toctogglelabel" for="toctogglecheckbox"></label> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Pernyataan_asas">1 Pernyataan asas</a></li> <li class="toclevel-1 tocsection-2"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Turunan">2 Turunan</a> <ul> <li class="toclevel-2 tocsection-3"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kasus_umum_dengan_massa_variabel">2.1 Kasus umum dengan massa variabel</a></li> <li class="toclevel-2 tocsection-4"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kasus_khusus_dengan_massa_konstan">2.2 Kasus khusus dengan massa konstan</a></li> </ul></li> <li class="toclevel-1 tocsection-5"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Gaya_inersia_asas_d'Alembert">3 Gaya inersia asas d'Alembert</a></li> <li class="toclevel-1 tocsection-6"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Ekuilibrium_dinamis">4 Ekuilibrium dinamis</a></li> <li class="toclevel-1 tocsection-7"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Formulasi_menggunakan_Lagrangian">5 Formulasi menggunakan Lagrangian</a></li> <li class="toclevel-1 tocsection-8"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Generalisasi_untuk_termodinamika">6 Generalisasi untuk termodinamika</a></li> <li class="toclevel-1 tocsection-9"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Referensi">7 Referensi</a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <h2 id="Pernyataan_asas">Pernyataan asas</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Pernyataan asas" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> Asas ini menyatakan bahwa jumlah perbedaan antara <a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_(fisika)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya (fisika)">gaya</a> yang bekerja pada sistem partikel masif dan <a href="https://id-m-wikipedia-org.translate.goog/wiki/Turunan_waktu?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Turunan waktu">turunan waktu</a> dari <a href="https://id-m-wikipedia-org.translate.goog/wiki/Momentum?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Momentum">momentum</a> sistem itu sendiri yang diproyeksikan ke <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Perpindahan_maya&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Perpindahan maya (halaman belum tersedia)">perpindahan maya</a> apa pun yang konsisten dengan batasan sistem adalah nol. Dengan demikian, dalam notasi matematika, prinsip d'Alembert dituliskan sebagai berikut. <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}{\dot {\mathbf {v} }}_{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <mo stretchy="false"> ( </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> m </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}{\dot {\mathbf {v} }}_{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9ddcfebd252a92f0a8d875c0bd829af4e2fb9e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.319ex; height:5.509ex;" alt="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}{\dot {\mathbf {v} }}_{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 32.319ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9ddcfebd252a92f0a8d875c0bd829af4e2fb9e3" data-alt="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}{\dot {\mathbf {v} }}_{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dimana: <ul> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah sebuah bilangan bulat yang digunakan untuk mengindikasikan (melalui subskrip) sebuah variabel yang berhubungan dengan partikel tertentu di dalam sistem,</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.482ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.482ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" data-alt="{\displaystyle \mathbf {F} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah total gaya yang diberikan (tidak termasuk gaya pembatas) pada partikel ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> ,</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.84ex; height:2.009ex;" alt="{\displaystyle m_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.84ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" data-alt="{\displaystyle m_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah massa partikel ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> ,</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {v} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51747274b58895dd357bb270ba1b5cb71e4fa355" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.211ex; height:2.009ex;" alt="{\displaystyle \mathbf {v} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.211ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51747274b58895dd357bb270ba1b5cb71e4fa355" data-alt="{\displaystyle \mathbf {v} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah kecepatan partikel ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> ,</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta \mathbf {r} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta \mathbf {r} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.95ex; height:2.676ex;" alt="{\displaystyle \delta \mathbf {r} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.95ex;height: 2.676ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" data-alt="{\displaystyle \delta \mathbf {r} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah perpindahan maya partikel ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , konsisten dengan batasan.</li> </ul> Notasi titik Newton digunakan untuk merepresentasikan turunan terhadap waktu. Persamaan di atas sering disebut asas d'Alembert, tetapi pertama kali ditulis dalam bentuk variasi ini oleh <a href="https://id-m-wikipedia-org.translate.goog/wiki/Joseph-Louis_de_Lagrange?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Joseph-Louis de Lagrange">Joseph Louis de Lagrange</a>. Kontribusi d'Alembert adalah untuk menunjukkan bahwa dalam totalitas sistem dinamis, gaya pembatas menghilang. Artinya, gaya umum <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Q} _{j}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> Q </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {Q} _{j}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f00b18e86dfa7c5aab74007ab36cca660a8ba6a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.918ex; height:3.009ex;" alt="{\displaystyle \mathbf {Q} _{j}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.918ex;height: 3.009ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f00b18e86dfa7c5aab74007ab36cca660a8ba6a7" data-alt="{\displaystyle \mathbf {Q} _{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  tidak perlu menyertakan gaya pembatas. Ini setara dengan yang agak lebih rumit yaitu <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_Gauss_tentang_batasan_terkecil&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Asas Gauss tentang batasan terkecil (halaman belum tersedia)">asas Gauss tentang batasan terkecil</a>. </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <h2 id="Turunan">Turunan</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Turunan" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <div class="mw-heading mw-heading3"> <h3 id="Kasus_umum_dengan_massa_variabel">Kasus umum dengan massa variabel</h3> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Kasus umum dengan massa variabel" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> Pernyataan umum asas d'Alembert menyebutkan "<a href="https://id-m-wikipedia-org.translate.goog/wiki/Turunan_waktu?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Turunan waktu">turunan waktu</a> dari <a href="https://id-m-wikipedia-org.translate.goog/wiki/Momentum?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Momentum">momentum</a> sistem". Berdasarkan hukum kedua Newton, turunan waktu pertama dari momentum adalah gaya. Momentum massa ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah hasil kali antara massa dan kecepatannya: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {p} _{i}=m_{i}\mathbf {v} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> p </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {p} _{i}=m_{i}\mathbf {v} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28e54c5e37ede6999487907d71ee8499d0d69ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.434ex; height:2.176ex;" alt="{\displaystyle \mathbf {p} _{i}=m_{i}\mathbf {v} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 10.434ex;height: 2.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c28e54c5e37ede6999487907d71ee8499d0d69ef" data-alt="{\displaystyle \mathbf {p} _{i}=m_{i}\mathbf {v} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dan turunan waktunya adalah <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\mathbf {p} }}_{i}={\dot {m}}_{i}\mathbf {v} _{i}+m_{i}{\dot {\mathbf {v} }}_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> p </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> m </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> + </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\dot {\mathbf {p} }}_{i}={\dot {m}}_{i}\mathbf {v} _{i}+m_{i}{\dot {\mathbf {v} }}_{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c2b119a006243de5bc3b43a42eb812311c6409c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.325ex; height:2.676ex;" alt="{\displaystyle {\dot {\mathbf {p} }}_{i}={\dot {m}}_{i}\mathbf {v} _{i}+m_{i}{\dot {\mathbf {v} }}_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 18.325ex;height: 2.676ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c2b119a006243de5bc3b43a42eb812311c6409c" data-alt="{\displaystyle {\dot {\mathbf {p} }}_{i}={\dot {m}}_{i}\mathbf {v} _{i}+m_{i}{\dot {\mathbf {v} }}_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Di banyak aplikasi, massa adalah konstan dan persamaan ini dirubah menjadi <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\mathbf {p} }}_{i}=m_{i}{\dot {\mathbf {v} }}_{i}=m_{i}\mathbf {a} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> p </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\dot {\mathbf {p} }}_{i}=m_{i}{\dot {\mathbf {v} }}_{i}=m_{i}\mathbf {a} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01bb885739d53753464d53cbcf5e43ae71c199f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.472ex; height:2.676ex;" alt="{\displaystyle {\dot {\mathbf {p} }}_{i}=m_{i}{\dot {\mathbf {v} }}_{i}=m_{i}\mathbf {a} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 18.472ex;height: 2.676ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01bb885739d53753464d53cbcf5e43ae71c199f4" data-alt="{\displaystyle {\dot {\mathbf {p} }}_{i}=m_{i}{\dot {\mathbf {v} }}_{i}=m_{i}\mathbf {a} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Namun, beberapa aplikasi melibatkan perubahan massa (misalnya, rantai yang digulung atau dibuka) dan dalam kasus tersebut kedua istilah <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {m}}_{i}\mathbf {v} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> m </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\dot {m}}_{i}\mathbf {v} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88c1fc364c60fd8ce080b4be91d32c6f797d5859" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.051ex; height:2.509ex;" alt="{\displaystyle {\dot {m}}_{i}\mathbf {v} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 5.051ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88c1fc364c60fd8ce080b4be91d32c6f797d5859" data-alt="{\displaystyle {\dot {m}}_{i}\mathbf {v} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}{\dot {\mathbf {v} }}_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}{\dot {\mathbf {v} }}_{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8a22ada9b8435eecce5f9767cbf03282cab1199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.051ex; height:2.509ex;" alt="{\displaystyle m_{i}{\dot {\mathbf {v} }}_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 5.051ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8a22ada9b8435eecce5f9767cbf03282cab1199" data-alt="{\displaystyle m_{i}{\dot {\mathbf {v} }}_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  harus tetap ada, sehingga <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <mo stretchy="false"> ( </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> m </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4bfeb962994d6199ea327a14e4009868d41c1e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:32.208ex; height:5.509ex;" alt="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 32.208ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4bfeb962994d6199ea327a14e4009868d41c1e6" data-alt="{\displaystyle \sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i}-{\dot {m}}_{i}\mathbf {v} _{i})\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  <div class="mw-heading mw-heading3"> <h3 id="Kasus_khusus_dengan_massa_konstan">Kasus khusus dengan massa konstan</h3> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Kasus khusus dengan massa konstan" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> Pertimbangkan hukum Newton untuk sistem partikel dengan massa konstan, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . Gaya total pada setiap partikel adalah<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:2-5">[5]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}^{(T)}=m_{i}\mathbf {a} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> ( </mo> <mi> T </mi> <mo stretchy="false"> ) </mo> </mrow> </msubsup> <mo> = </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}^{(T)}=m_{i}\mathbf {a} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549d6aabbba8648aacb2490636358ec9d57e07d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.389ex; height:3.676ex;" alt="{\displaystyle \mathbf {F} _{i}^{(T)}=m_{i}\mathbf {a} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 12.389ex;height: 3.676ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/549d6aabbba8648aacb2490636358ec9d57e07d6" data-alt="{\displaystyle \mathbf {F} _{i}^{(T)}=m_{i}\mathbf {a} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dimana: <ul> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.482ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.482ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" data-alt="{\displaystyle \mathbf {F} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya total yang bekerja pada partikel sistem,</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}\mathbf {a} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}\mathbf {a} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb0b7015885937d38b6ab4fec236ecd571657906" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.939ex; height:2.009ex;" alt="{\displaystyle m_{i}\mathbf {a} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 4.939ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb0b7015885937d38b6ab4fec236ecd571657906" data-alt="{\displaystyle m_{i}\mathbf {a} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya inersia yang dihasilkan dari gaya total.</li> </ul> Memindahkan gaya inersia ke kiri memberikan ekspresi yang dapat dianggap mewakili keseimbangan kuasi-statis, tetapi sebenarnya hanya merupakan manipulasi aljabar kecil dari hukum Newton:<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:2-5">[5]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}^{(T)}-m_{i}\mathbf {a} _{i}=\mathbf {0} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> ( </mo> <mi> T </mi> <mo stretchy="false"> ) </mo> </mrow> </msubsup> <mo> − </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold"> 0 </mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}^{(T)}-m_{i}\mathbf {a} _{i}=\mathbf {0} } </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7f0227341c9e6e6dc8edce6130cad5a2eacd555" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.566ex; height:3.676ex;" alt="{\displaystyle \mathbf {F} _{i}^{(T)}-m_{i}\mathbf {a} _{i}=\mathbf {0} }"> </noscript><span class="lazy-image-placeholder" style="width: 16.566ex;height: 3.676ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7f0227341c9e6e6dc8edce6130cad5a2eacd555" data-alt="{\displaystyle \mathbf {F} _{i}^{(T)}-m_{i}\mathbf {a} _{i}=\mathbf {0} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Mempertimbangkan <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerja_maya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerja maya">kerja maya</a>, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> W </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta W} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973e6b089758466f338610e76ab50fd4093efbc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.484ex; height:2.343ex;" alt="{\displaystyle \delta W}"> </noscript><span class="lazy-image-placeholder" style="width: 3.484ex;height: 2.343ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973e6b089758466f338610e76ab50fd4093efbc8" data-alt="{\displaystyle \delta W}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , dilakukan oleh gaya total dan inersia secara bersamaan melalui perpindahan maya yang berubah-ubah, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta \mathbf {r} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta \mathbf {r} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.95ex; height:2.676ex;" alt="{\displaystyle \delta \mathbf {r} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.95ex;height: 2.676ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" data-alt="{\displaystyle \delta \mathbf {r} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , dari sistem mengarah ke identitas nol, karena gaya yang terlibat berjumlah nol untuk setiap partikel.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:2-5">[5]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}^{(T)}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> W </mi> <mo> = </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> ( </mo> <mi> T </mi> <mo stretchy="false"> ) </mo> </mrow> </msubsup> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}^{(T)}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b42995b6dd8da9e115f96d40a6b37dd7376c243" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:39.717ex; height:5.676ex;" alt="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}^{(T)}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 39.717ex;height: 5.676ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b42995b6dd8da9e115f96d40a6b37dd7376c243" data-alt="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}^{(T)}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Persamaan vektor asli dapat dipulihkan dengan mengenali bahwa ekspresi kerja harus berlaku untuk perpindahan yang berubah-ubah. Memisahkan gaya total menjadi gaya yang diterapkan, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.482ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.482ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" data-alt="{\displaystyle \mathbf {F} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , dan gaya pembatas, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {C} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {C} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61e9b87195beeab6d53f1debbc855c8d7b9e2d1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.509ex;" alt="{\displaystyle \mathbf {C} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.731ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61e9b87195beeab6d53f1debbc855c8d7b9e2d1f" data-alt="{\displaystyle \mathbf {C} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , menghasilkan<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:2-5">[5]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}+\sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> W </mi> <mo> = </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> + </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}+\sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89d36cf41cff9f0160ae05770c26f7dae2f27f7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:51.791ex; height:5.509ex;" alt="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}+\sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 51.791ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89d36cf41cff9f0160ae05770c26f7dae2f27f7a" data-alt="{\displaystyle \delta W=\sum _{i}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}+\sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}-\sum _{i}m_{i}\mathbf {a} _{i}\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Jika perpindahan maya sembarang diasumsikan dalam arah yang ortogonal terhadap gaya pembatas (biasanya tidak demikian sehingga turunan ini hanya berlaku untuk kasus-kasus khusus), gaya pembatas tidak bekerja. Perpindahan tersebut dikatakan konsisten dengan batasan.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-6">[6]</a> Hal ini mengarah pada perumusan asas d'Alembert, yang menyatakan bahwa perbedaan gaya yang diterapkan dan gaya inersia untuk sistem dinamis tidak melakukan kerja maya:<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:2-5">[5]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W=\sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i})\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> W </mi> <mo> = </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <mo stretchy="false"> ( </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> − </mo> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta W=\sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i})\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdae5d0aa2a3751e012935f269751c18e2a1512c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:30.899ex; height:5.509ex;" alt="{\displaystyle \delta W=\sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i})\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 30.899ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdae5d0aa2a3751e012935f269751c18e2a1512c" data-alt="{\displaystyle \delta W=\sum _{i}(\mathbf {F} _{i}-m_{i}\mathbf {a} _{i})\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Ada juga prinsip yang sesuai untuk sistem statis yang disebut <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerja_maya?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerja maya">prinsip kerja maya untuk gaya yang diterapkan</a>. </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <h2 id="Gaya_inersia_asas_d'Alembert">Gaya inersia asas d'Alembert</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Gaya inersia asas d'Alembert" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> D'Alembert menunjukkan bahwa seseorang dapat mengubah benda tegar yang berakselerasi menjadi sistem statis yang setara dengan menambahkan "<a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gaya_inersia&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Gaya inersia (halaman belum tersedia)">gaya inersia</a>" dan "torsi inersia" atau momen. Gaya inersia harus bekerja melalui pusat massa dan torsi inersia dapat bekerja di mana saja. Sistem ini kemudian dapat dianalisis persis seperti sistem statis yang mengalami "gaya dan momen inersia" ini dan gaya eksternal. Keuntungannya adalah bahwa dalam sistem statis yang setara, seseorang dapat mengambil momen di titik mana pun (bukan hanya pusat massa). Hal ini sering kali menghasilkan perhitungan yang lebih sederhana karena gaya apa pun (pada gilirannya) dapat dihilangkan dari persamaan momen dengan memilih titik yang sesuai untuk menerapkan persamaan momen (jumlah momen = nol). Bahkan dalam mata kuliah Dasar-Dasar Dinamika dan Kinematika Mesin, asas ini membantu dalam menganalisis gaya yang bekerja pada sebuah sambungan mekanisme ketika bergerak. Dalam buku teks dinamika teknik, hal ini kadang disebut sebagai asas d'Alembert. Beberapa pendidik memperingatkan bahwa upaya untuk menggunakan mekanika inersia d'Alembert mengarahkan siswa untuk sering membuat kesalahan tanda.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:3-7">[7]</a> Penyebab potensial dari kesalahan ini adalah tanda <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Gaya_inersia&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Gaya inersia (halaman belum tersedia)">gaya inersia</a>. Gaya inersia dapat digunakan untuk menggambarkan gaya semu dalam <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerangka_acuan_non-inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Kerangka acuan non-inersia">kerangka acuan non-inersia</a> yang memiliki percepatan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} } </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"> </noscript><span class="lazy-image-placeholder" style="width: 1.299ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" data-alt="{\displaystyle \mathbf {a} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  terhadap <a href="https://id-m-wikipedia-org.translate.goog/wiki/Kerangka_acuan_inersia?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kerangka acuan inersia">kerangka acuan inersia</a>. Dalam kerangka acuan non-inersia, sebuah massa yang diam dan memiliki percepatan nol dalam sistem acuan inersia, karena tidak ada gaya yang bekerja padanya, masih akan memiliki percepatan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\mathbf {a} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo> − </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle -\mathbf {a} } </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a3cf31849160dbc62a43fc0f601083f526edac1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:3.108ex; height:2.176ex;" alt="{\displaystyle -\mathbf {a} }"> </noscript><span class="lazy-image-placeholder" style="width: 3.108ex;height: 2.176ex;vertical-align: -0.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a3cf31849160dbc62a43fc0f601083f526edac1" data-alt="{\displaystyle -\mathbf {a} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dan gaya inersia semu, atau semu atau <a href="https://id-m-wikipedia-org.translate.goog/wiki/Gaya_fiktif?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Gaya fiktif">gaya fiktif</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -m\mathbf {a} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo> − </mo> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle -m\mathbf {a} } </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/040f0b07b224d2cf09bad79500239ad901b15597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.148ex; height:2.176ex;" alt="{\displaystyle -m\mathbf {a} }"> </noscript><span class="lazy-image-placeholder" style="width: 5.148ex;height: 2.176ex;vertical-align: -0.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/040f0b07b224d2cf09bad79500239ad901b15597" data-alt="{\displaystyle -m\mathbf {a} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  akan tampak bekerja padanya: dalam situasi ini gaya inersia memiliki tanda minus.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:3-7">[7]</a> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"> <h2 id="Ekuilibrium_dinamis">Ekuilibrium dinamis</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=6&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Ekuilibrium dinamis" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-4 collapsible-block" id="mf-section-4"> Bentuk prinsip kerja maya d'Alembert menyatakan bahwa sistem benda tegar berada dalam ekuilibrium dinamis ketika kerja maya dari jumlah gaya yang diterapkan dan gaya inersia adalah nol untuk setiap perpindahan maya sistem. Dengan demikian, ekuilibrium dinamis dari sistem <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> n </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle n} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"> </noscript><span class="lazy-image-placeholder" style="width: 1.395ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" data-alt="{\displaystyle n}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  benda tegar dengan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"> </noscript><span class="lazy-image-placeholder" style="width: 2.04ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" data-alt="{\displaystyle m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  koordinat umum membutuhkan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta W=\left(Q_{1}+Q_{1}^{*}\right)\delta q_{1}+\dots +\left(Q_{m}+Q_{m}^{*}\right)\delta q_{m}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> W </mi> <mo> = </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <msubsup> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗ </mo> </mrow> </msubsup> </mrow> <mo> ) </mo> </mrow> <mi> δ </mi> <msub> <mi> q </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> + </mo> <mo> ⋯ </mo> <mo> + </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> </msub> <mo> + </mo> <msubsup> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗ </mo> </mrow> </msubsup> </mrow> <mo> ) </mo> </mrow> <mi> δ </mi> <msub> <mi> q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta W=\left(Q_{1}+Q_{1}^{*}\right)\delta q_{1}+\dots +\left(Q_{m}+Q_{m}^{*}\right)\delta q_{m}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cc098044bcae5184e1ed291a850c2b496a63e78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:49.033ex; height:3.009ex;" alt="{\displaystyle \delta W=\left(Q_{1}+Q_{1}^{*}\right)\delta q_{1}+\dots +\left(Q_{m}+Q_{m}^{*}\right)\delta q_{m}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 49.033ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cc098044bcae5184e1ed291a850c2b496a63e78" data-alt="{\displaystyle \delta W=\left(Q_{1}+Q_{1}^{*}\right)\delta q_{1}+\dots +\left(Q_{m}+Q_{m}^{*}\right)\delta q_{m}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  untuk setiap set perpindahan maya <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta q_{j}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msub> <mi> q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta q_{j}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/441a20906f8cb69dffa8848cd7593c525cfc9a8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.995ex; height:3.009ex;" alt="{\displaystyle \delta q_{j}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.995ex;height: 3.009ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/441a20906f8cb69dffa8848cd7593c525cfc9a8c" data-alt="{\displaystyle \delta q_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dengan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{j}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle Q_{j}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5db0ad37e47589c5a9f270ca9c06affdacd6c66f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.748ex; height:2.843ex;" alt="{\displaystyle Q_{j}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.748ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5db0ad37e47589c5a9f270ca9c06affdacd6c66f" data-alt="{\displaystyle Q_{j}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya terapan yang digeneralisasi dan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{j}^{*}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗ </mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle Q_{j}^{*}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a551182a25fb29d5afdae30915c7f02d6271aa7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.893ex; height:3.176ex;" alt="{\displaystyle Q_{j}^{*}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.893ex;height: 3.176ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a551182a25fb29d5afdae30915c7f02d6271aa7" data-alt="{\displaystyle Q_{j}^{*}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya inersia yang digeneralisasi. Kondisi ini menghasilkan persamaan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"> </noscript><span class="lazy-image-placeholder" style="width: 2.04ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" data-alt="{\displaystyle m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> : <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{j}+Q_{j}^{*}=0,\quad j=1,\ldots ,m}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> <mo> + </mo> <msubsup> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗ </mo> </mrow> </msubsup> <mo> = </mo> <mn> 0 </mn> <mo> , </mo> <mspace width="1em"></mspace> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle Q_{j}+Q_{j}^{*}=0,\quad j=1,\ldots ,m} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95bfa99b688b7eade253db22b619c280e6af00a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:28.536ex; height:3.176ex;" alt="{\displaystyle Q_{j}+Q_{j}^{*}=0,\quad j=1,\ldots ,m}"> </noscript><span class="lazy-image-placeholder" style="width: 28.536ex;height: 3.176ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95bfa99b688b7eade253db22b619c280e6af00a0" data-alt="{\displaystyle Q_{j}+Q_{j}^{*}=0,\quad j=1,\ldots ,m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  juga dapat ditulis dengan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {q}}_{j}}}-{\frac {\partial T}{\partial q_{j}}}=Q_{j},\quad j=1,\ldots ,m}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> d </mi> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> T </mi> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> q </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo> − </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> T </mi> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo> = </mo> <msub> <mi> Q </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> j </mi> </mrow> </msub> <mo> , </mo> <mspace width="1em"></mspace> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {q}}_{j}}}-{\frac {\partial T}{\partial q_{j}}}=Q_{j},\quad j=1,\ldots ,m} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a924bb447328a81071627f9ed5defa771816f4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:35.915ex; height:6.343ex;" alt="{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {q}}_{j}}}-{\frac {\partial T}{\partial q_{j}}}=Q_{j},\quad j=1,\ldots ,m}"> </noscript><span class="lazy-image-placeholder" style="width: 35.915ex;height: 6.343ex;vertical-align: -2.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a924bb447328a81071627f9ed5defa771816f4b" data-alt="{\displaystyle {\frac {d}{dt}}{\frac {\partial T}{\partial {\dot {q}}_{j}}}-{\frac {\partial T}{\partial q_{j}}}=Q_{j},\quad j=1,\ldots ,m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Hasilnya adalah seperangkat persamaan gerak <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"> </noscript><span class="lazy-image-placeholder" style="width: 2.04ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" data-alt="{\displaystyle m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  yang mendefinisikan dinamika sistem benda tegar. </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"> <h2 id="Formulasi_menggunakan_Lagrangian">Formulasi menggunakan Lagrangian</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=7&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Formulasi menggunakan Lagrangian" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-5 collapsible-block" id="mf-section-5"> Asas d'Alembert dapat ditulis ulang dalam bentuk Lagrangian L=T-V dari sistem sebagai versi umum dari <a href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_Hamilton&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Asas Hamilton (halaman belum tersedia)">asas Hamilton</a> sebagai berikut, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msubsup> <mo> ∫ </mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </msubsup> <mi> L </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> , </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> , </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mi> d </mi> <mi> t </mi> <mo> + </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msubsup> <mo> ∫ </mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mi> d </mi> <mi> t </mi> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13e18fac392d7b7c896ec5186371c014acc19bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:41.084ex; height:6.843ex;" alt="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}"> </noscript><span class="lazy-image-placeholder" style="width: 41.084ex;height: 6.843ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13e18fac392d7b7c896ec5186371c014acc19bdb" data-alt="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dimana: <ul> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {r} =(\mathbf {r} _{1},...,\mathbf {r} _{N})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> = </mo> <mo stretchy="false"> ( </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> . </mo> <mo> . </mo> <mo> . </mo> <mo> , </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> N </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {r} =(\mathbf {r} _{1},...,\mathbf {r} _{N})} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a18dda81ea83087fcd9ee3deb6b5880512e484af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.129ex; height:2.843ex;" alt="{\displaystyle \mathbf {r} =(\mathbf {r} _{1},...,\mathbf {r} _{N})}"> </noscript><span class="lazy-image-placeholder" style="width: 16.129ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a18dda81ea83087fcd9ee3deb6b5880512e484af" data-alt="{\displaystyle \mathbf {r} =(\mathbf {r} _{1},...,\mathbf {r} _{N})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.482ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.482ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" data-alt="{\displaystyle \mathbf {F} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya yang diterapkan</li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta \mathbf {r} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta \mathbf {r} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.95ex; height:2.676ex;" alt="{\displaystyle \delta \mathbf {r} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.95ex;height: 2.676ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a56ef713418eb51bfcd06f4833292c71b063af42" data-alt="{\displaystyle \delta \mathbf {r} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah perpindahan maya dari partikel ke- <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> i </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle i} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"> </noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , konsisten dengan batasan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d106d7b6ccfe3d57c7b943cd7b5908a4f922e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.363ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 15.363ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d106d7b6ccfe3d57c7b943cd7b5908a4f922e8" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </li> <li>kurva kritis memenuhi batasan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8cba73d9a3c6951492c142d5f4a8f019a067a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.375ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 14.375ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8cba73d9a3c6951492c142d5f4a8f019a067a8" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </li> </ul> Dengan Lagrangian <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> L </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> , </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> , </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57ec898fdc7448fec62340dc8878b564d33fe091" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.46ex; height:6.343ex;" alt="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 22.46ex;height: 6.343ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57ec898fdc7448fec62340dc8878b564d33fe091" data-alt="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  pernyataan sebelumnya dari asas d'Alembert dipulihkan. </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"> <h2 id="Generalisasi_untuk_termodinamika">Generalisasi untuk termodinamika</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=8&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Generalisasi untuk termodinamika" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-6 collapsible-block" id="mf-section-6"> Ekstensi dari asas d'Alembert dapat digunakan dalam termodinamika.<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:1-4">[4]</a> Sebagai contoh, untuk <a href="https://id-m-wikipedia-org.translate.goog/wiki/Sistem_termodinamika?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sistem termodinamika">sistem termodinamika</a> yang tertutup secara adiabatik yang dijelaskan oleh Lagrangian yang bergantung pada entropi tunggal <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> S </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle S} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"> </noscript><span class="lazy-image-placeholder" style="width: 1.499ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" data-alt="{\displaystyle S}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dan dengan massa konstan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.84ex; height:2.009ex;" alt="{\displaystyle m_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.84ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" data-alt="{\displaystyle m_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , seperti <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}-V(\mathbf {r} ,S)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> L </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> , </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> , </mo> <mi> S </mi> <mo> , </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> − </mo> <mi> V </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> , </mo> <mi> S </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}-V(\mathbf {r} ,S)} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8352e79f297bb089599ceac4b4e5a4ad65dfca2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.065ex; height:6.343ex;" alt="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}-V(\mathbf {r} ,S)}"> </noscript><span class="lazy-image-placeholder" style="width: 35.065ex;height: 6.343ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8352e79f297bb089599ceac4b4e5a4ad65dfca2f" data-alt="{\displaystyle L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)=\sum _{i}{\frac {1}{2}}m_{i}{\dot {\mathbf {r} }}_{i}^{2}-V(\mathbf {r} ,S)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dituliskan sebagai berikut <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <msubsup> <mo> ∫ </mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </msubsup> <mi> L </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> , </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> , </mo> <mi> S </mi> <mo> , </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mi> d </mi> <mi> t </mi> <mo> + </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msubsup> <mo> ∫ </mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mi> d </mi> <mi> t </mi> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63f6c9a21c938a2aa48b5665bdf3e8680d383ac4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:43.617ex; height:6.843ex;" alt="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}"> </noscript><span class="lazy-image-placeholder" style="width: 43.617ex;height: 6.843ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63f6c9a21c938a2aa48b5665bdf3e8680d383ac4" data-alt="{\displaystyle \delta \int _{t_{1}}^{t_{2}}L(\mathbf {r} ,{\dot {\mathbf {r} }},S,t)dt+\sum _{i}\int _{t_{1}}^{t_{2}}\mathbf {F} _{i}\cdot \delta \mathbf {r} _{i}dt=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dimana batasan sebelumnya <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d106d7b6ccfe3d57c7b943cd7b5908a4f922e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.363ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 15.363ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d106d7b6ccfe3d57c7b943cd7b5908a4f922e8" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  dan <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8cba73d9a3c6951492c142d5f4a8f019a067a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.375ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 14.375ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8cba73d9a3c6951492c142d5f4a8f019a067a8" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  digeneralisasi untuk melibatkan entropi sebagai: <ul> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}+T\delta S=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <mi> δ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> + </mo> <mi> T </mi> <mi> δ </mi> <mi> S </mi> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}+T\delta S=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bccda4ea8b30f8ac58214f071b00ed88e5e51eae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.388ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}+T\delta S=0}"> </noscript><span class="lazy-image-placeholder" style="width: 22.388ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bccda4ea8b30f8ac58214f071b00ed88e5e51eae" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot \delta \mathbf {r} _{i}+T\delta S=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </li> <li> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}+T{\dot {S}}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> + </mo> <mi> T </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> S </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}+T{\dot {S}}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/060571f53b564d1af2b1457be2c3cdd63b6b472c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.424ex; height:5.509ex;" alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}+T{\dot {S}}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 20.424ex;height: 5.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/060571f53b564d1af2b1457be2c3cdd63b6b472c" data-alt="{\displaystyle \sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}+T{\dot {S}}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </li> </ul> Di sini <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=\partial V/\partial S}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> T </mi> <mo> = </mo> <mi mathvariant="normal"> ∂ </mi> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi mathvariant="normal"> ∂ </mi> <mi> S </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle T=\partial V/\partial S} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cc6c2cd0b54cf080bed8094a1f9c64415b1fa4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.82ex; height:2.843ex;" alt="{\displaystyle T=\partial V/\partial S}"> </noscript><span class="lazy-image-placeholder" style="width: 11.82ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cc6c2cd0b54cf080bed8094a1f9c64415b1fa4e" data-alt="{\displaystyle T=\partial V/\partial S}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah suhu sistem, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.482ex; height:2.509ex;" alt="{\displaystyle \mathbf {F} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.482ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d49039f831a156e0c33270962d8d159d553a8bc" data-alt="{\displaystyle \mathbf {F} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya eksternal, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {C} _{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {C} _{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61e9b87195beeab6d53f1debbc855c8d7b9e2d1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.731ex; height:2.509ex;" alt="{\displaystyle \mathbf {C} _{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.731ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61e9b87195beeab6d53f1debbc855c8d7b9e2d1f" data-alt="{\displaystyle \mathbf {C} _{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  adalah gaya disipatif internal. Hal ini menghasilkan persamaan keseimbangan mekanis dan termal:<a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-:1-4">[4]</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{i}\mathbf {a} _{i}=-{\frac {\partial V}{\partial \mathbf {r} _{i}}}+\mathbf {C} _{i}+\mathbf {F} _{i},\;\;i=1,...,N\qquad \qquad T{\dot {S}}=-\sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> = </mo> <mo> − </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> V </mi> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> + </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> , </mo> <mspace width="thickmathspace"></mspace> <mspace width="thickmathspace"></mspace> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> <mo> , </mo> <mo> . </mo> <mo> . </mo> <mo> . </mo> <mo> , </mo> <mi> N </mi> <mspace width="2em"></mspace> <mspace width="2em"></mspace> <mi> T </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> S </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mo> − </mo> <munder> <mo> ∑ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> C </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <mo> ⋅ </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mo> ˙ </mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}\mathbf {a} _{i}=-{\frac {\partial V}{\partial \mathbf {r} _{i}}}+\mathbf {C} _{i}+\mathbf {F} _{i},\;\;i=1,...,N\qquad \qquad T{\dot {S}}=-\sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be5049626984963b59eb982be06da84bc8925493" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:67.324ex; height:6.509ex;" alt="{\displaystyle m_{i}\mathbf {a} _{i}=-{\frac {\partial V}{\partial \mathbf {r} _{i}}}+\mathbf {C} _{i}+\mathbf {F} _{i},\;\;i=1,...,N\qquad \qquad T{\dot {S}}=-\sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 67.324ex;height: 6.509ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be5049626984963b59eb982be06da84bc8925493" data-alt="{\displaystyle m_{i}\mathbf {a} _{i}=-{\frac {\partial V}{\partial \mathbf {r} _{i}}}+\mathbf {C} _{i}+\mathbf {F} _{i},\;\;i=1,...,N\qquad \qquad T{\dot {S}}=-\sum _{i}\mathbf {C} _{i}\cdot {\dot {\mathbf {r} }}_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  Aplikasi umum dari asas ini mencakup sistem termo-mekanis, transportasi membran, dan reaksi kimia. Untuk <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta S={\dot {S}}=0}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> δ </mi> <mi> S </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> S </mi> <mo> ˙ </mo> </mover> </mrow> </mrow> <mo> = </mo> <mn> 0 </mn> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \delta S={\dot {S}}=0} </annotation> </semantics> </math> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db451cade3308f2063a6320943828144398ec027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.48ex; height:2.843ex;" alt="{\displaystyle \delta S={\dot {S}}=0}"> </noscript><span class="lazy-image-placeholder" style="width: 11.48ex;height: 2.843ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db451cade3308f2063a6320943828144398ec027" data-alt="{\displaystyle \delta S={\dot {S}}=0}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  asas dan persamaan d'Alembert klasik ditemukan kembali. </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"> <h2 id="Referensi">Referensi</h2> <a role="button" href="https://id-m-wikipedia-org.translate.goog/w/index.php?title=Asas_D'Alembert&action=edit&section=9&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Sunting bagian: Referensi" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> sunting </a> </div> <section class="mf-section-7 collapsible-block" id="mf-section-7"> <ol class="references"> <li id="cite_note-:0-1">^ <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:0_1-0">a</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:0_1-1">b</a> <cite class="citation book">Lanczos, Cornelius (1964). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://archive.org/details/variationalprinc00lanc">The variational principles of mechanics</a>. Internet Archive. Toronto, University of Toronto Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+variational+principles+of+mechanics&rft.pub=Toronto%2C+University+of+Toronto+Press&rft.date=1964&rft.aulast=Lanczos&rft.aufirst=Cornelius&rft_id=http%3A%2F%2Farchive.org%2Fdetails%2Fvariationalprinc00lanc&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> </li> <li id="cite_note-2"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-2">^</a> <cite class="citation book">Alembert, Jean Le Rond d' (1743). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.co.id/books?id%3DXrEWAAAAQAAJ%26redir_esc%3Dy">Traité de dynamique</a> (dalam bahasa Prancis). David l'aîné.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Trait%C3%A9+de+dynamique&rft.pub=David+l%27a%C3%AEn%C3%A9&rft.date=1743&rft.aulast=Alembert&rft.aufirst=Jean+Le+Rond+d%27&rft_id=https%3A%2F%2Fbooks.google.co.id%2Fbooks%3Fid%3DXrEWAAAAQAAJ%26redir_esc%3Dy&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> </li> <li id="cite_note-3"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-3">^</a> <cite class="citation journal">Udwadia, F.E.; Kalaba, R.E. (2002-09). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://linkinghub.elsevier.com/retrieve/pii/S0020746201000336">"On the foundations of analytical dynamics"</a>. International Journal of Non-Linear Mechanics (dalam bahasa Inggris). 37 (6): 1079–1090. <a href="https://id-m-wikipedia-org.translate.goog/wiki/Digital_object_identifier?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://doi.org/10.1016%252FS0020-7462%252801%252900033-6">10.1016/S0020-7462(01)00033-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Non-Linear+Mechanics&rft.atitle=On+the+foundations+of+analytical+dynamics&rft.chron=2002-09&rft.volume=37&rft.issue=6&rft.pages=1079-1090&rft_id=info%3Adoi%2F10.1016%2FS0020-7462%2801%2900033-6&rft.aulast=Udwadia&rft.aufirst=F.E.&rft.au=Kalaba%2C+R.E.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0020746201000336&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988">  Periksa nilai tanggal di: <code style="color:inherit; border:inherit; padding:inherit;">|date=</code> (<a href="https://id-m-wikipedia-org.translate.goog/wiki/Bantuan:Galat_CS1?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#bad_date" title="Bantuan:Galat CS1">bantuan</a>)</li> <li id="cite_note-:1-4">^ <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:1_4-0">a</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:1_4-1">b</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:1_4-2">c</a> <cite class="citation journal">Gay-Balmaz, François; Yoshimura, Hiroaki (2018-12-23). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://www.mdpi.com/1099-4300/21/1/8">"From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective"</a>. Entropy (dalam bahasa Inggris). 21 (1): 8. <a href="https://id-m-wikipedia-org.translate.goog/wiki/Digital_object_identifier?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://doi.org/10.3390%252Fe21010008">10.3390/e21010008</a>. <a href="https://id-m-wikipedia-org.translate.goog/wiki/International_Standard_Serial_Number?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.worldcat.org/issn/1099-4300">1099-4300</a>. <a href="https://id-m-wikipedia-org.translate.goog/wiki/PubMed_Central?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514189">7514189</a>  <noscript> <img alt="alt=Dapat diakses gratis" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" data-file-width="512" data-file-height="813"> </noscript><span class="lazy-image-placeholder" style="width: 9px;height: 14px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" data-alt="alt=Dapat diakses gratis" data-width="9" data-height="14" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-class="mw-file-element"> . <a href="https://id-m-wikipedia-org.translate.goog/wiki/PubMed_Identifier?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="PubMed Identifier">PMID</a> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.ncbi.nlm.nih.gov/pubmed/33266724">33266724</a> Periksa nilai <code style="color:inherit; border:inherit; padding:inherit;">|pmid=</code> (<a href="https://id-m-wikipedia-org.translate.goog/wiki/Bantuan:Galat_CS1?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#bad_pmid" title="Bantuan:Galat CS1">bantuan</a>).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=From+Lagrangian+Mechanics+to+Nonequilibrium+Thermodynamics%3A+A+Variational+Perspective&rft.volume=21&rft.issue=1&rft.pages=8&rft.date=2018-12-23&rft_id=%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMCPMC7514189&rft.issn=1099-4300&rft_id=info%3Apmid%2F33266724&rft_id=info%3Adoi%2F10.3390%2Fe21010008&rft.aulast=Gay-Balmaz&rft.aufirst=Fran%C3%A7ois&rft.au=Yoshimura%2C+Hiroaki&rft_id=http%3A%2F%2Fwww.mdpi.com%2F1099-4300%2F21%2F1%2F8&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> Pemeliharaan CS1: Format PMC (<a href="https://id-m-wikipedia-org.translate.goog/wiki/Kategori:Pemeliharaan_CS1:_Format_PMC?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kategori:Pemeliharaan CS1: Format PMC">link</a>) </li> <li id="cite_note-:2-5">^ <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:2_5-0">a</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:2_5-1">b</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:2_5-2">c</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:2_5-3">d</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:2_5-4">e</a> <cite class="citation book">Torby, Bruce J. (1984). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://archive.org/details/advanceddynamics0000torb">Advanced Dynamics for engineers</a>. HRW series in mechanical engineering. New York: Holt, Rinehart and Winston. <a href="https://id-m-wikipedia-org.translate.goog/wiki/International_Standard_Book_Number?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Istimewa:Sumber_buku/978-0-03-063366-9?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Istimewa:Sumber buku/978-0-03-063366-9">978-0-03-063366-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Dynamics+for+engineers&rft.place=New+York&rft.series=HRW+series+in+mechanical+engineering&rft.pub=Holt%2C+Rinehart+and+Winston&rft.date=1984&rft.isbn=978-0-03-063366-9&rft.aulast=Torby&rft.aufirst=Bruce+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fadvanceddynamics0000torb&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> </li> <li id="cite_note-6"><a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-6">^</a> <cite class="citation journal">Jong, Ing-Chang (2005). "Improving Mechanics of Materials". Teaching Students Work and Virtual Work Method in Statics: A Guiding Strategy with Illustrative Examples.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Teaching+Students+Work+and+Virtual+Work+Method+in+Statics%3A++A+Guiding+Strategy+with+Illustrative+Examples&rft.atitle=Improving+Mechanics+of+Materials&rft.date=2005&rft.aulast=Jong&rft.aufirst=Ing-Chang&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> </li> <li id="cite_note-:3-7">^ <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:3_7-0">a</a> <a href="https://id-m-wikipedia-org.translate.goog/wiki/Asas_D'Alembert?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-:3_7-1">b</a> <cite class="citation web"><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://ruina.tam.cornell.edu/Book/">"Ruina/Pratap Dynamics Text"</a>. ruina.tam.cornell.edu. Diakses tanggal 2024-02-25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ruina.tam.cornell.edu&rft.atitle=Ruina%2FPratap+Dynamics+Text&rft_id=http%3A%2F%2Fruina.tam.cornell.edu%2FBook%2F&rfr_id=info%3Asid%2Fid.wikipedia.org%3AAsas+D%27Alembert" class="Z3988"> </li> </ol>   </section> </div> <noscript> <img src="https://login.m.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&mobile=1" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Diperoleh dari "<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://id.wikipedia.org/w/index.php?title%3DAsas_D%2527Alembert%26oldid%3D25414180">https://id.wikipedia.org/w/index.php?title=Asas_D%27Alembert&oldid=25414180</a>" </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" 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hreflang="hy" data-title="Դ'Ալամբերի սկզբունք" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target">Հայերեն</a></li> <li class="interlanguage-link interwiki-it mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/wiki/Principio_di_D%2527Alembert" title="Principio di D'Alembert – Italia" lang="it" hreflang="it" data-title="Principio di D'Alembert" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target">Italiano</a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ja.wikipedia.org/wiki/%25E3%2583%2580%25E3%2583%25A9%25E3%2583%25B3%25E3%2583%2599%25E3%2583%25BC%25E3%2583%25AB%25E3%2581%25AE%25E5%258E%259F%25E7%2590%2586" title="ダランベールの原理 – Jepang" lang="ja" hreflang="ja" data-title="ダランベールの原理" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target">日本語</a></li> <li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://kk.wikipedia.org/wiki/%25D0%2594%25E2%2580%2599%25D0%2590%25D0%25BB%25D0%25B0%25D0%25BC%25D0%25B1%25D0%25B5%25D1%2580_%25D0%25BF%25D1%2580%25D0%25B8%25D0%25BD%25D1%2586%25D0%25B8%25D0%25BF%25D1%2596" title="Д’Аламбер принципі – Kazakh" lang="kk" hreflang="kk" data-title="Д’Аламбер принципі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li> <li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ko.wikipedia.org/wiki/%25EB%258B%25AC%25EB%259E%2591%25EB%25B2%25A0%25EB%25A5%25B4%25EC%259D%2598_%25EC%259B%2590%25EB%25A6%25AC" title="달랑베르의 원리 – Korea" lang="ko" hreflang="ko" data-title="달랑베르의 원리" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target">한국어</a></li> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nn.wikipedia.org/wiki/D%2527Alemberts_prinsipp" title="D'Alemberts prinsipp – Nynorsk Norwegia" lang="nn" hreflang="nn" data-title="D'Alemberts prinsipp" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norwegia" class="interlanguage-link-target">Norsk nynorsk</a></li> <li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pl.wikipedia.org/wiki/Zasada_d%25E2%2580%2599Alemberta" title="Zasada d’Alemberta – Polski" lang="pl" hreflang="pl" data-title="Zasada d’Alemberta" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target">Polski</a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pt.wikipedia.org/wiki/Princ%25C3%25ADpio_de_d%2527Alembert" title="Princípio de d'Alembert – Portugis" lang="pt" hreflang="pt" data-title="Princípio de d'Alembert" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target">Português</a></li> <li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ru.wikipedia.org/wiki/%25D0%259F%25D1%2580%25D0%25B8%25D0%25BD%25D1%2586%25D0%25B8%25D0%25BF_%25D0%25B4%25E2%2580%2599%25D0%2590%25D0%25BB%25D0%25B0%25D0%25BC%25D0%25B1%25D0%25B5%25D1%2580%25D0%25B0" title="Принцип д’Аламбера – Rusia" lang="ru" hreflang="ru" data-title="Принцип д’Аламбера" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target">Русский</a></li> <li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sl.wikipedia.org/wiki/D%2527Alembertovo_na%25C4%258Delo" title="D'Alembertovo načelo – Sloven" lang="sl" hreflang="sl" data-title="D'Alembertovo načelo" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target">Slovenščina</a></li> <li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sq.wikipedia.org/wiki/Parimi_i_D%2527Alembertit" title="Parimi i D'Alembertit – Albania" lang="sq" hreflang="sq" data-title="Parimi i D'Alembertit" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target">Shqip</a></li> <li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sr.wikipedia.org/wiki/%25D0%259B%25D0%25B0%25D0%25B3%25D1%2580%25D0%25B0%25D0%25BD%25D0%25B6-%25D0%2594%25D0%25B0%25D0%25BB%25D0%25B0%25D0%25BC%25D0%25B1%25D0%25B5%25D1%2580%25D0%25BE%25D0%25B2_%25D0%25BF%25D1%2580%25D0%25B8%25D0%25BD%25D1%2586%25D0%25B8%25D0%25BF" title="Лагранж-Даламберов принцип – Serbia" lang="sr" hreflang="sr" data-title="Лагранж-Даламберов принцип" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target">Српски / srpski</a></li> <li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sv.wikipedia.org/wiki/D%2527Alemberts_princip" title="D'Alemberts princip – Swedia" lang="sv" hreflang="sv" data-title="D'Alemberts princip" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target">Svenska</a></li> <li class="interlanguage-link interwiki-te mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://te.wikipedia.org/wiki/%25E0%25B0%25A1%25E0%25B1%2580%25E0%25B0%2585%25E0%25B0%25B2%25E0%25B0%2582%25E0%25B0%25AC%25E0%25B0%25B0%25E0%25B1%258D%25E0%25B0%259F%25E0%25B1%258D_%25E0%25B0%25B8%25E0%25B1%2582%25E0%25B0%25A4%25E0%25B1%258D%25E0%25B0%25B0%25E0%25B0%25AE%25E0%25B1%2581" title="డీఅలంబర్ట్ సూత్రము – Telugu" lang="te" hreflang="te" data-title="డీఅలంబర్ట్ సూత్రము" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li> <li class="interlanguage-link interwiki-th mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://th.wikipedia.org/wiki/%25E0%25B8%25AB%25E0%25B8%25A5%25E0%25B8%25B1%25E0%25B8%2581%25E0%25B8%2581%25E0%25B8%25B2%25E0%25B8%25A3%25E0%25B8%2594%25E0%25B8%25B2%25E0%25B8%25A5%25E0%25B9%2587%25E0%25B8%25AD%25E0%25B8%2587%25E0%25B9%2581%25E0%25B8%259A%25E0%25B8%25A3%25E0%25B9%258C" title="หลักการดาล็องแบร์ – Thai" lang="th" hreflang="th" data-title="หลักการดาล็องแบร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li> <li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uk.wikipedia.org/wiki/%25D0%259F%25D1%2580%25D0%25B8%25D0%25BD%25D1%2586%25D0%25B8%25D0%25BF_%25D0%25B4%2527%25D0%2590%25D0%25BB%25D0%25B0%25D0%25BC%25D0%25B1%25D0%25B5%25D1%2580%25D0%25B0_%25E2%2580%2594_%25D0%259B%25D0%25B0%25D0%25B3%25D1%2580%25D0%25B0%25D0%25BD%25D0%25B6%25D0%25B0" title="Принцип д'Аламбера — Лагранжа – Ukraina" lang="uk" hreflang="uk" data-title="Принцип д'Аламбера — Лагранжа" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target">Українська</a></li> <li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uz.wikipedia.org/wiki/D%2527Alembert_prinsipi" title="D'Alembert prinsipi – Uzbek" lang="uz" hreflang="uz" data-title="D'Alembert prinsipi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li> <li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh.wikipedia.org/wiki/%25E9%2581%2594%25E6%259C%2597%25E8%25B2%259D%25E7%2588%25BE%25E5%258E%259F%25E7%2590%2586" title="達朗貝爾原理 – Tionghoa" lang="zh" hreflang="zh" data-title="達朗貝爾原理" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target">中文</a></li> <li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh-yue.wikipedia.org/wiki/%25E9%2581%2594%25E6%259E%2597%25E4%25BC%25AF%25E7%2589%25B9%25E5%258E%259F%25E5%2589%2587" title="達林伯特原則 – Kanton" lang="yue" hreflang="yue" data-title="達林伯特原則" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target">粵語</a></li> </ul> </section> </div> <div class="minerva-footer-logo"> <img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"> </div> <ul id="footer-info" class="footer-info hlist hlist-separated"> <li id="footer-info-lastmod">Halaman ini terakhir diubah pada 9 Maret 2024, pukul 23.16.</li> <li id="footer-info-copyright">Konten tersedia di bawah <a class="external" rel="nofollow" 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Asas D'Alembert - Wikipedia bahasa Indonesia, ensiklopedia bebas