变质量完整动力学系统的共形不变性与守恒量

Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass

研究变质量完整力学系统在无限小变换下微分方程的共形不变性.提出了该系统共形不变性的概念,推导出变质量完整力学系统运动微分方程具有共形不变性,同时又是Lie对称性的充分必要条件.得到由共形不变性导致的Noether守恒量.

In this paper, the conformal invariance of holonomic mechanical systems with variable mass is studied. The necessary and the sufficient conditions of eouformal invariance of the system are obtained and shown to be also those of Lie symmetry simultaneously. Finally the Noether conserved quantities of conformal invariance are presented.