单面非Chetaev型非完整约束系统的非Noether守恒量

研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程；给出了系统的Lie对称性和Mei对称性的定义和判据；对于单面非Chetaev型非完整系统，证明了在一定条件下，由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量，由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量；研究了对称性和新守恒量之间的相互关系.文末，举例说明结果的应用. 关键词： 分析力学 单面约束 非完整系统 对称性 Hojman守恒量 Mei守恒量

Non-Noether conserved quantities for systems with unilateral non-Chetaev nonholonomic constraints

This paper studies the symmetries and non-Noether conserved quantities of mechanical systems with unilateral non-Chetaev nonholonomic constraints. The differential equations of motion of the systems are established, and the definitions and criterions of Lie symmetry and Mei symmetry are given. For the unilateral non-Chetaev nonholonomic constraint system, it is proved that under some conditions a new conserved quantity called Hojman conserved quantity can be directly deduced from Lie symmetry, and a new conserved quantity called Mei conserved quantity can be directly deduced from Mei symmetry. The relations between the symmetries and the new conserved quantities are researched. At the end of the paper, an example is given to illustrate the application of the results.