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单词 Generalized force
释义

Generalized force

中文百科

广义力 Generalized forces

(重定向自Generalized force)

广义力是拉格朗日力学里面的一个基本概念。在一个物理系统里,因为力\mathbf{F}\,\!,一个粒子经过虚位移\delta \mathbf{r}\,\!,所作的虚功\delta W\,\!

\delta W = \mathbf{F} \cdot \delta \mathbf{r}\,\!

转换至广义坐标q_1,\ q_2,\ q_3,\ \dots\ q_N\,\!

\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广义力,用\boldsymbol{\mathcal{F}}\,\!表示为:

\mathcal{F}_j=  \mathbf{F} \cdot  \frac {\partial \mathbf{r}}{\partial q_j}\,\!

虚功与广义力的关系是

\delta W = \sum_{j=1}^N\ \mathcal{F}_j\delta q_j\,\!

 \mathcal{F}_j\,\!为关于广义坐标q_j\,\!的广义力。因为\mathcal{F}_j q_j\,\!的量纲是功,如果q_j\,\!是距离,则\mathcal{F}_j\,\!与力的量纲相同;如果q_j\,\!是角,则它与力矩的量纲相同。

英语百科

Generalized forces 广义力

(重定向自Generalized force)

Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates. They are obtained from the applied forces, Fi, i=1,..., n, acting on a system that has its configuration defined in terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate.

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更新时间:2025/6/21 21:23:00