关键词: 分析力学, 单面约束, 非完整约束, Lie对称性, 守恒量, 逆问题.

Abstract:

This paper studies the Lie symmetries of nonholonomic mechanical systems with unilateral constraints. It gives the conditions and the form of conserved quantities due to the Lie symmetries of the systems, and presents the inverse problem of the above problem, i.e., finding the corresponding Lie symmetry transformation according to a given integral of the systems. Finally, it gives an example to illustrate the application of the results.

Key words:  Analytical mechanics ')"> Analytical mechanics , Unilateral constraint, Nonholonomic constraint, Lie symmetry, Conserved quantity, inverse problem