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廣義位勢 Connected to: {{::readMoreArticle.title}} 拉格朗日力學時常涉及廣義位勢,因為拉格朗日量 L {\displaystyle {\mathcal {L))\,\!} 的廣義式定義包含了廣義位勢: L = T − V {\displaystyle {\mathcal {L))=T-{\mathcal {V))\,\!} ;其中, V {\displaystyle {\mathcal {V))\,\!} 是廣義位勢, T {\displaystyle T\,\!} 是動能。 定義廣義位勢為一個函數, V = V ( q 1 , q 2 , … , q N , q ˙ 1 , q ˙ 2 , … , q ˙ N , t ) {\displaystyle {\mathcal {V))={\mathcal {V))(q_{1},\ q_{2},\ \dots ,\ q_{N},\ {\dot {q))_{1},\ {\dot {q))_{2},\ \dots ,\ {\dot {q))_{N},\ t)\,\!} ,滿足下述與廣義力 F {\displaystyle {\mathcal {F))\,\!} 的關係: F i = − ∂ V ∂ q i + d d t ( ∂ V ∂ q i ˙ ) {\displaystyle {\mathcal {F))_{i}=-{\frac {\partial {\mathcal {V))}{\partial q_{i))}+{\frac {d}{dt))\left({\frac {\partial {\mathcal {V))}{\partial {\dot {q_{i))))}\right)\,\!} ;其中, q i {\displaystyle q_{i}\,\!} 是廣義坐標, q i ˙ {\displaystyle {\dot {q_{i))}\,\!} 是廣義速度, t {\displaystyle t\,\!} 是時間。 假若一個物理系統滿足上述關係,此系統是單演系統。 假若一個單演系統的廣義位勢只跟廣義坐標有關, V = V ( q 1 , q 2 , … , q N ) {\displaystyle {\mathcal {V))={\mathcal {V))(q_{1},\ q_{2},\ \dots ,\ q_{N})\,\!} ,則此系統是保守系統。廣義力與廣義位勢的關係是 F i = − ∂ V ∂ q i {\displaystyle {\mathcal {F))_{i}=-{\frac {\partial {\mathcal {V))}{\partial q_{i))}\,\!} 。參閱[编辑]拉格朗日力學 哈密頓力學 分类 分类:力學经典力学拉格朗日力學勢 {{bottomLinkPreText}} {{bottomLinkText}} This page is based on a Wikipedia article written by contributors (read/edit). Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses. Cover photo is available under {{::mainImage.info.license.name || 'Unknown'}} license. Cover photo is available under {{::mainImage.info.license.name || 'Unknown'}} license. Credit: (see original file).