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class="vector-pinnable-header-label">Nội dung</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ẩn</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Đầu</div> </a> </li> <li id="toc-Định_nghĩa" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Định_nghĩa"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Định nghĩa</span> </div> </a> <button aria-controls="toc-Định_nghĩa-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Hiện/ẩn mục Định nghĩa</span> </button> <ul id="toc-Định_nghĩa-sublist" class="vector-toc-list"> <li id="toc-Tham_khảo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tham_khảo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Tham khảo</span> </div> </a> <ul id="toc-Tham_khảo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liên_kết_ngoài" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liên_kết_ngoài"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Liên kết ngoài</span> </div> </a> <ul id="toc-Liên_kết_ngoài-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Nội dung" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Đóng mở mục lục" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Đóng mở mục lục</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Góc Euler</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Xem bài viết trong ngôn ngữ khác. Bài có sẵn trong 29 ngôn ngữ" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-29" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">29 ngôn ngữ</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B2%D9%88%D8%A7%D9%8A%D8%A7_%D8%A3%D9%88%D9%8A%D9%84%D8%B1" title="زوايا أويلر – Tiếng Ả Rập" lang="ar" hreflang="ar" data-title="زوايا أويلر" data-language-autonym="العربية" data-language-local-name="Tiếng Ả Rập" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sudut_Euler" title="Sudut Euler – Tiếng Indonesia" lang="id" hreflang="id" data-title="Sudut Euler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Tiếng Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Angles_d%27Euler" title="Angles d'Euler – Tiếng Catalan" lang="ca" hreflang="ca" data-title="Angles d'Euler" data-language-autonym="Català" data-language-local-name="Tiếng Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Eulersche_Winkel" title="Eulersche Winkel – Tiếng Đức" lang="de" hreflang="de" data-title="Eulersche Winkel" data-language-autonym="Deutsch" data-language-local-name="Tiếng Đức" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CF%89%CE%BD%CE%AF%CE%B5%CF%82_%CE%8C%CE%B9%CE%BB%CE%B5%CF%81" title="Γωνίες Όιλερ – Tiếng Hy Lạp" lang="el" hreflang="el" data-title="Γωνίες Όιλερ" data-language-autonym="Ελληνικά" data-language-local-name="Tiếng Hy Lạp" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Euler_angles" title="Euler angles – Tiếng Anh" lang="en" hreflang="en" data-title="Euler angles" data-language-autonym="English" data-language-local-name="Tiếng Anh" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81ngulos_de_Euler" title="Ángulos de Euler – Tiếng Tây Ban Nha" lang="es" hreflang="es" data-title="Ángulos de Euler" data-language-autonym="Español" data-language-local-name="Tiếng Tây Ban Nha" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eulerren_angeluak" title="Eulerren angeluak – Tiếng Basque" lang="eu" hreflang="eu" data-title="Eulerren angeluak" data-language-autonym="Euskara" data-language-local-name="Tiếng Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%DB%8C%D9%87%E2%80%8C%D9%87%D8%A7%DB%8C_%D8%A7%D9%88%DB%8C%D9%84%D8%B1" title="زاویه‌های اویلر – Tiếng Ba Tư" lang="fa" hreflang="fa" data-title="زاویه‌های اویلر" data-language-autonym="فارسی" data-language-local-name="Tiếng Ba Tư" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Angles_d%27Euler" title="Angles d'Euler – Tiếng Pháp" lang="fr" hreflang="fr" data-title="Angles d'Euler" data-language-autonym="Français" data-language-local-name="Tiếng Pháp" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Na_huillinneacha_Euler" title="Na huillinneacha Euler – Tiếng Ireland" lang="ga" hreflang="ga" data-title="Na huillinneacha Euler" data-language-autonym="Gaeilge" data-language-local-name="Tiếng Ireland" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%A4%EC%9D%BC%EB%9F%AC_%EA%B0%81" title="오일러 각 – Tiếng Hàn" lang="ko" hreflang="ko" data-title="오일러 각" data-language-autonym="한국어" data-language-local-name="Tiếng Hàn" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Angoli_di_Eulero" title="Angoli di Eulero – Tiếng Italy" lang="it" hreflang="it" data-title="Angoli di Eulero" data-language-autonym="Italiano" data-language-local-name="Tiếng Italy" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%96%D7%95%D7%95%D7%99%D7%95%D7%AA_%D7%90%D7%95%D7%99%D7%9C%D7%A8" title="זוויות אוילר – Tiếng Do Thái" lang="he" hreflang="he" data-title="זוויות אוילר" data-language-autonym="עברית" data-language-local-name="Tiếng Do Thái" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%B9%D0%BB%D0%B5%D1%80_%D0%B1%D2%B1%D1%80%D1%8B%D1%88%D1%82%D0%B0%D1%80%D1%8B" title="Эйлер бұрыштары – Tiếng Kazakh" lang="kk" hreflang="kk" data-title="Эйлер бұрыштары" data-language-autonym="Қазақша" data-language-local-name="Tiếng Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Euler-sz%C3%B6gek" title="Euler-szögek – Tiếng Hungary" lang="hu" hreflang="hu" data-title="Euler-szögek" data-language-autonym="Magyar" data-language-local-name="Tiếng Hungary" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hoeken_van_Euler" title="Hoeken van Euler – Tiếng Hà Lan" lang="nl" hreflang="nl" data-title="Hoeken van Euler" data-language-autonym="Nederlands" data-language-local-name="Tiếng Hà Lan" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E8%A7%92" title="オイラー角 – Tiếng Nhật" lang="ja" hreflang="ja" data-title="オイラー角" data-language-autonym="日本語" data-language-local-name="Tiếng Nhật" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Eulervinkler" title="Eulervinkler – Tiếng Na Uy (Bokmål)" lang="nb" hreflang="nb" data-title="Eulervinkler" data-language-autonym="Norsk bokmål" data-language-local-name="Tiếng Na Uy (Bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/K%C4%85ty_Eulera" title="Kąty Eulera – Tiếng Ba Lan" lang="pl" hreflang="pl" data-title="Kąty Eulera" data-language-autonym="Polski" data-language-local-name="Tiếng Ba Lan" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%82ngulos_de_Euler" title="Ângulos de Euler – Tiếng Bồ Đào Nha" lang="pt" hreflang="pt" data-title="Ângulos de Euler" data-language-autonym="Português" data-language-local-name="Tiếng Bồ Đào Nha" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Unghiurile_lui_Euler" title="Unghiurile lui Euler – Tiếng Romania" lang="ro" hreflang="ro" data-title="Unghiurile lui Euler" data-language-autonym="Română" data-language-local-name="Tiếng Romania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%B3%D0%BB%D1%8B_%D0%AD%D0%B9%D0%BB%D0%B5%D1%80%D0%B0" title="Углы Эйлера – Tiếng Nga" lang="ru" hreflang="ru" data-title="Углы Эйлера" data-language-autonym="Русский" data-language-local-name="Tiếng Nga" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Eulerjevi_koti" title="Eulerjevi koti – Tiếng Slovenia" lang="sl" hreflang="sl" data-title="Eulerjevi koti" data-language-autonym="Slovenščina" data-language-local-name="Tiếng Slovenia" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D1%98%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D0%B8_%D0%B8_%D0%A2%D0%B5%D1%98%D1%82-%D0%91%D1%80%D0%B0%D1%98%D0%B0%D0%BD%D0%BE%D0%B2%D0%B8_%D1%83%D0%B3%D0%BB%D0%BE%D0%B2%D0%B8" title="Ојлерови и Тејт-Брајанови углови – Tiếng Serbia" lang="sr" hreflang="sr" data-title="Ојлерови и Тејт-Брајанови углови" data-language-autonym="Српски / srpski" data-language-local-name="Tiếng Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Eulervinklar" title="Eulervinklar – Tiếng Thụy Điển" lang="sv" hreflang="sv" data-title="Eulervinklar" data-language-autonym="Svenska" data-language-local-name="Tiếng Thụy Điển" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%B9%D0%BB%D0%B5%D1%80%D0%BE%D0%B2%D1%96_%D0%BA%D1%83%D1%82%D0%B8" title="Ейлерові кути – Tiếng Ukraina" lang="uk" hreflang="uk" data-title="Ейлерові кути" data-language-autonym="Українська" data-language-local-name="Tiếng Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%90%E6%8B%89%E8%A7%92" title="歐拉角 – Tiếng Quảng Đông" lang="yue" hreflang="yue" data-title="歐拉角" data-language-autonym="粵語" data-language-local-name="Tiếng Quảng Đông" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AC%A7%E6%8B%89%E8%A7%92" title="欧拉角 – Tiếng Trung" lang="zh" hreflang="zh" data-title="欧拉角" data-language-autonym="中文" data-language-local-name="Tiếng Trung" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q751290#sitelinks-wikipedia" title="Sửa liên kết giữa ngôn ngữ" class="wbc-editpage">Sửa liên kết</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Không gian tên"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/G%C3%B3c_Euler" title="Xem bài viết [c]" accesskey="c"><span>Bài viết</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="vi" dir="ltr"><p><b>Góc Euler</b> là ba góc được giới thiệu bởi <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> để miêu tả định hướng của một vật thể rắn. Để miêu tả như một định hướng trong không gian ba chiều Euclide theo ba tham số được yêu cầu. Chúng có thể được đưa ra bằng nhiều cách và Góc Euler là một trong số chúng.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading1"><h1 id="Định_nghĩa"><span id=".C4.90.E1.BB.8Bnh_ngh.C4.A9a"></span>Định nghĩa</h1><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=G%C3%B3c_Euler&veaction=edit&section=1" title="Sửa đổi phần “Định nghĩa”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=G%C3%B3c_Euler&action=edit&section=1" title="Sửa mã nguồn tại đề mục: Định nghĩa"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trước hết, sử dụng hai hệ quy chiếu: hệ cố định <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ox_{0}y_{0}z_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox_{0}y_{0}z_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26d63ad5e3c1e05df5b65c0146f4416388a907e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.486ex; height:2.509ex;" alt="{\displaystyle Ox_{0}y_{0}z_{0}}"></span> và hệ động Oxyz gắn chặt với vật chung gốc O. Gọi giao tuyến của mặt phẳng <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ox_{0}y_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox_{0}y_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42480646aa77a4361e4bc8f5aaaa51236292ab0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.351ex; height:2.509ex;" alt="{\displaystyle Ox_{0}y_{0}}"></span> và Oxy là ON. ON gọi là đường nút của vật. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File"><a href="/wiki/T%E1%BA%ADp_tin:Aa1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/vi/e/e5/Aa1.jpg" decoding="async" width="310" height="270" class="mw-file-element" data-file-width="310" data-file-height="270" /></a><figcaption></figcaption></figure> <p>Đưa vào các ký hiệu và tên gọi: Góc giữa đường nút ON và trục <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ox_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ox_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca731968a27b8992772f22586a2bdd3be96793c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.157ex; height:2.509ex;" alt="{\displaystyle Ox_{0}}"></span> ký hiệu là <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> và gọi là góc tiến động của vật. Góc giữa đường nút ON và trục Ox ký hiệu là <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> và gọi là góc quay riêng của vật. Góc giữa các trục <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Oz_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Oz_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c7b79a98fef45324a8bb30766adeeb321a11686" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.909ex; height:2.509ex;" alt="{\displaystyle Oz_{0}}"></span> và Oz ký hiệu là <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> gọi là góc chương động hay góc túi sai của vật. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File"><a href="/wiki/T%E1%BA%ADp_tin:Aaa1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/vi/6/6c/Aaa1.jpg" decoding="async" width="392" height="351" class="mw-file-element" data-file-width="392" data-file-height="351" /></a><figcaption></figcaption></figure> <p>Các góc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> gọi là các góc Euler.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Tham_khảo"><span id="Tham_kh.E1.BA.A3o"></span>Tham khảo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=G%C3%B3c_Euler&veaction=edit&section=2" title="Sửa đổi phần “Tham khảo”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=G%C3%B3c_Euler&action=edit&section=2" title="Sửa mã nguồn tại đề mục: Tham khảo"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r71728118">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><a class="external autonumber" href="https://en.wikipedia.org/wiki/Euler_angles#cite_note-0">[1]</a> Euler Anges From Wiki</span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/EulerAngles.html">Mathworld</a> does a good job describing this issue</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Liên_kết_ngoài"><span id="Li.C3.AAn_k.E1.BA.BFt_ngo.C3.A0i"></span>Liên kết ngoài</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=G%C3%B3c_Euler&veaction=edit&section=3" title="Sửa đổi phần “Liên kết ngoài”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=G%C3%B3c_Euler&action=edit&section=3" title="Sửa mã nguồn tại đề mục: Liên kết ngoài"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="citation mathworld" id="Reference-Mathworld-Euler_Angles"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a>, "<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/EulerAngles.html">Euler Angles</a>" từ <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</span></li> <li>Java applet for the simulation of Euler angles available at <a rel="nofollow" class="external free" href="http://www.parallemic.org/Java/EulerAngles.html">http://www.parallemic.org/Java/EulerAngles.html</a>.</li> <li><a rel="nofollow" class="external text" href="https://itunes.apple.com/us/app/eulerangles/id584911325">EulerAngles</a> - An iOS app for visualizing in 3D the three rotations associated with Euler angles.</li> <li><a rel="nofollow" class="external free" href="http://sourceforge.net/projects/orilib">http://sourceforge.net/projects/orilib</a> – A collection of routines for rotation / orientation manipulation, including special tools for crystal orientations.</li> <li>Online tool to compose rotation matrices available at <a rel="nofollow" class="external free" href="http://www.vectoralgebra.info/eulermatrix.html">http://www.vectoralgebra.info/eulermatrix.html</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131208033145/http://vectoralgebra.info/eulermatrix.html">Lưu trữ</a> 2013-12-08 tại <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div class="boilerplate metadata plainlinks" id="stub"><table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai toán học"><img alt="Hình tượng sơ khai" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/45px-E-to-the-i-pi.svg.png" decoding="async" width="45" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/90px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td> <td><i>Bài viết liên quan đến <a href="/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học">toán học</a> này vẫn còn <a href="/wiki/Wikipedia:B%C3%A0i_s%C6%A1_khai" title="Wikipedia:Bài sơ khai">sơ khai</a>. Bạn có thể giúp Wikipedia <a class="external text" href="https://vi.wikipedia.org/w/index.php?title=G%C3%B3c_Euler&veaction=edit">mở rộng nội dung</a> để bài được hoàn chỉnh hơn.</i><div class="plainlinks hlist navbar mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Bản mẫu:Sơ khai toán học"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc&action=edit&redlink=1" class="new" title="Thảo luận Bản mẫu:Sơ khai toán học (trang không tồn tại)"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div></td> </tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Lấy từ “<a dir="ltr" href="https://vi.wikipedia.org/w/index.php?title=Góc_Euler&oldid=65411611">https://vi.wikipedia.org/w/index.php?title=Góc_Euler&oldid=65411611</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BB%83_lo%E1%BA%A1i" title="Đặc biệt:Thể loại">Thể loại</a>: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai toán học">Sơ khai toán học</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:G%C3%B3c" title="Thể loại:Góc">Góc</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:H%C3%ACnh_h%E1%BB%8Dc_gi%E1%BA%A3i_t%C3%ADch" title="Thể loại:Hình học giải tích">Hình học giải tích</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:Kh%C3%A1i_ni%E1%BB%87m_to%C3%A1n_h%E1%BB%8Dc_mang_t%C3%AAn_Euler" title="Thể loại:Khái niệm toán học mang tên Euler">Khái niệm toán học mang tên Euler</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Thể loại ẩn: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:B%E1%BA%A3n_m%E1%BA%ABu_webarchive_d%C3%B9ng_li%C3%AAn_k%E1%BA%BFt_wayback" title="Thể loại:Bản mẫu webarchive dùng liên kết wayback">Bản mẫu webarchive dùng liên kết wayback</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:T%E1%BA%A5t_c%E1%BA%A3_b%C3%A0i_vi%E1%BA%BFt_s%C6%A1_khai" title="Thể loại:Tất cả bài viết sơ khai">Tất cả bài viết sơ khai</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Trang này được sửa đổi lần cuối vào ngày 11 tháng 8 năm 2021, 11:05.</li> <li id="footer-info-copyright">Văn bản được phát hành theo <a href="/wiki/Wikipedia:Nguy%C3%AAn_v%C4%83n_Gi%E1%BA%A5y_ph%C3%A9p_Creative_Commons_Ghi_c%C3%B4ng%E2%80%93Chia_s%E1%BA%BB_t%C6%B0%C6%A1ng_t%E1%BB%B1_phi%C3%AAn_b%E1%BA%A3n_4.0_Qu%E1%BB%91c_t%E1%BA%BF" title="Wikipedia:Nguyên văn Giấy phép Creative Commons Ghi công–Chia sẻ tương tự phiên bản 4.0 Quốc tế">Giấy phép Creative Commons Ghi công–Chia sẻ tương tự</a>; có thể áp dụng điều khoản bổ sung. 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