准坐标下广义力学系统运动微分方程的形式不变性

On the form invariance of differential equations of motion for generalized mechanical system in terms of quasi-coordinates

对称性方法是寻求守恒量的近代方法 .形式不变性是一种新的对称性 .研究准坐标下广义力学系统运动微分方程在群的无限小变换下的形式不变性 .本文给出了形式不变性的定义和判据 ,建立形式不变性导致守恒量的条件 。

Symmetry method is modern method in seeking conserved quantity. The form invariance is a new symmetry. The form invariance of differential equations of motion for generalized mechanical system in terms of quasi-coordinates is studied, under the infinitesimal transformations of groups. First, the definition and criterion of the form invariance are given. Next, the condition under which the invariance can lead to a conserved quantity is established. Finally, we give an example to illustrate the application of the result.