相空间中单面完整约束力学系统的对称性与守恒量

在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程；给出了系统的Norther对称性，Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量，研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用.关键词：分析力学单面约束对称性守恒量相空间

Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space

The symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in extended phase space is studied. The differential equations of motion of the systems are established. The criterions of Noether symmetry, Lie symmetry and Mei symmetry are given, and the relations between the symmetries are researched. The Noether conserved quantity and two types of new conserved quantities, called the Hojman quantity and Mei quantity, for the systems are obtained, and intrinsic relations between the three symmetries and three types of conserved quantities are researched. An example is given to illustrate the application of the results.