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廣義力 Connected to: {{::readMoreArticle.title}} 廣義力是拉格朗日力學裏面的一個基本概念。在一個物理系統裏,因為力 F {\displaystyle \mathbf {F} \,\!} ,一個粒子經過虛位移 δ r {\displaystyle \delta \mathbf {r} \,\!} ,所作的虛功 δ W {\displaystyle \delta W\,\!} 是 δ W = F ⋅ δ r {\displaystyle \delta W=\mathbf {F} \cdot \delta \mathbf {r} \,\!} 。轉換至廣義坐標 q 1 , q 2 , q 3 , … q N {\displaystyle q_{1},\ q_{2},\ q_{3},\ \dots \ q_{N}\,\!} , δ W = ∑ j = 1 N F ⋅ ∂ r ∂ q j δ q j {\displaystyle \delta W=\sum _{j=1}^{N}\ \mathbf {F} \cdot {\frac {\partial \mathbf {r} }{\partial q_{j))}\delta q_{j}\,\!} 。在上面这个方程的右端,位于虚位移前面的这两项的整体即为廣義力,用 F {\displaystyle {\boldsymbol {\mathcal {F))}\,\!} 表示为: F j = F ⋅ ∂ r ∂ q j {\displaystyle {\mathcal {F))_{j}=\mathbf {F} \cdot {\frac {\partial \mathbf {r} }{\partial q_{j))}\,\!} 。虛功與廣義力的關係是 δ W = ∑ j = 1 N F j δ q j {\displaystyle \delta W=\sum _{j=1}^{N}\ {\mathcal {F))_{j}\delta q_{j}\,\!} 。稱 F j {\displaystyle {\mathcal {F))_{j}\,\!} 為關於廣義坐標 q j {\displaystyle q_{j}\,\!} 的廣義力。因為 F j q j {\displaystyle {\mathcal {F))_{j}q_{j}\,\!} 的量綱是功,如果 q j {\displaystyle q_{j}\,\!} 是距離,則 F j {\displaystyle {\mathcal {F))_{j}\,\!} 與力的量綱相同;如果 q j {\displaystyle q_{j}\,\!} 是角,則它與力矩的量綱相同。 參閱[编辑]拉格朗日力學 哈密頓力學 自由度 虛功 分类 分类:力學经典力学拉格朗日力學哈密顿力学 {{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).