二阶非完整力学系统的Lie对称性与守恒量

Lie Symmetries and Conserved Quantities of Second-Order Nonholonomic Mechanical System

Department of Applied Physics, University of Petroleum. Dongying, Shandong 257061, P. R. China

摘要: 研究二阶非完整力学系统的Lie对称与守恒量.首先利用系统运动微分方程在无限小变换下的不变性建立Lie对称的确定方程和限制方程,得到Lie对称的结构方程和守恒量;其次研究上述问题的逆问题;最后举例说明结果的应用.
- 二阶非完整系统 /
- Lie对称 /
- 守恒量
Abstract: The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly, the inverse problems of the Lie symmetries are studied. Finally, an example is given to illustrate the application of the result.
- second-order nonholonomic system /
- Lie symmetry /
- conserved quantity

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