Conserved quantities from Lie symmetries for nonholonomic systems

非完整系统的Lie对称性守恒量(英文)

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

提出了由非完整系统的Lie对称性求守恒量的一种新方法 ,该方法不依赖于系统的La grangian函数或Hamiltonian结构 .建立了系统的运动微分方程 ,给出了系统仅依赖于广义坐标的无限小群变换的Lie对称变换的定义 ,并直接由系统的Lie对称性构造守恒量 ,得到了Lie对称性导致守恒量的条件及守恒量的形式 .最后举例说明结果的应用 .