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词汇 Principle of virtual work
分类 英语词汇 英语翻译词典
释义

Principle of virtual work

中文百科

虚功 Virtual work

(重定向自虚功原理)
This is an engraving from Mechanics Magazine published in London in 1824.
Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train
Problème mécanique type.

在分析力学里,施加于某物体的作用力,由于给定的虚位移,所做的机械功,称为虚功英语:virtual work)。以方程序表达,虚功\delta W

其中,\mathbf{F}是作用力,\delta \mathbf{r}是虚位移。

在这篇文章里,位移指的是平移运动所造成的位移或旋转运动所造成的角位移;作用力指的是力量或力矩。虚位移不是实际的位移,而是一种虚构的、理论上的位移,是一种只涉及位置,不涉及时间的变化。每一个虚位移既是自变量(independent variable),又是任意设置的。任意性是一个很重要的特性,在数学关系式里,能够推导出许多重要的结果。例如,思考下述矩阵方程序:

英语百科

Virtual work 虚功

(重定向自Principle of virtual work)
This is an engraving from Mechanics Magazine published in London in 1824.
Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train
Problème mécanique type.

Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action, and, therefore, is the one followed by the particle by the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work.

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