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href="javascript:void()">Thing</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine a system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation.</p> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:abstract" lang="en" >In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine a system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >( 이 문서는 해밀턴 역학에서 좌표 변환에 쓰이는 함수에 관한 것입니다. 조합론에서 쓰이는 생성함수(generating function)에 대해서는 생성함수 (수학) 문서를 참고하십시오.) 해밀턴 역학에서 모함수(母函數, generating function)는 두 개의 일반화 좌표간의 정준변환을 연결해주는 함수이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="zh" >在哈密頓力學裏，當計算正則變換時，生成函數扮演的角色，好似在兩組正則坐標，之間的一座橋。為了要保證正則變換的正確性，採取一種間接的方法，稱為生成函數方法。這兩組變數必須符合方程式；(1) 其中，是舊廣義坐標，是舊廣義動量，是新廣義坐標，是新廣義動量，分別為舊哈密頓量與新哈密頓量，是生成函數，是時間。生成函數的參數，除了時間以外，一半是舊的正則坐標；另一半是新的正則坐標。視選擇出來不同的變數而定，一共有四種基本的生成函數。每一種基本生成函數設定一種不同的變換，從舊的一組正則坐標變換為新的一組正則坐標。這變換保證是正則變換。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID"><small>dbo:</small>wikiPageID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageID" datatype="xsd:integer" >7952767</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength"><small>dbo:</small>wikiPageLength</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageLength" datatype="xsd:nonNegativeInteger" >3608</span><small> (xsd:nonNegativeInteger)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageRevisionID"><small>dbo:</small>wikiPageRevisionID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageRevisionID" datatype="xsd:integer" >1088908012</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr 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property="rdfs:comment" lang="en" >In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine a system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >( 이 문서는 해밀턴 역학에서 좌표 변환에 쓰이는 함수에 관한 것입니다. 조합론에서 쓰이는 생성함수(generating function)에 대해서는 생성함수 (수학) 문서를 참고하십시오.) 해밀턴 역학에서 모함수(母函數, generating function)는 두 개의 일반화 좌표간의 정준변환을 연결해주는 함수이다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="zh" >在哈密頓力學裏，當計算正則變換時，生成函數扮演的角色，好似在兩組正則坐標，之間的一座橋。為了要保證正則變換的正確性，採取一種間接的方法，稱為生成函數方法。這兩組變數必須符合方程式；(1) 其中，是舊廣義坐標，是舊廣義動量，是新廣義坐標，是新廣義動量，分別為舊哈密頓量與新哈密頓量，是生成函數，是時間。生成函數的參數，除了時間以外，一半是舊的正則坐標；另一半是新的正則坐標。視選擇出來不同的變數而定，一共有四種基本的生成函數。每一種基本生成函數設定一種不同的變換，從舊的一組正則坐標變換為新的一組正則坐標。這變換保證是正則變換。</span><small> (zh)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="rdfs:label" lang="en" >Generating function (physics)</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >모함수 (물리학)</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="zh" >正則變換生成函數</span><small> (zh)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.026l8cn" href="http://rdf.freebase.com/ns/m.026l8cn"><small>freebase</small>:Generating function (physics)</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" 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