单面完整约束系统的速度依赖对称性与Lutzky守恒量

研究单面完整约束系统的对称性与守恒量.给出单面完整约束系统Lie对称性的定义，得到了由依赖于速度的一般Lie对称性直接导致的Lutzky守恒量，并给出了它的若干特例：有多余坐标的完整约束系统、非保守力学系统、Lagrange系统的Lutzky守恒量.并举例说明结果的应用. 关键词： 分析力学 单面约束 Lie对称性 Lutzky守恒量

Lutzky conserved quantities and velocity-dependent symmetries for systems with unilateral holonomic constraints

This paper studies the symmetries and the conserved quantities for systems with unilateral holonomic constraints. The definitions of Lie symmetries for the systems are given, and the Lutzky conserved quantities are directly deduced from the general velocity-dependent Lie symmetries of the systems. The Lutzky conserved quantities of some special cases, for example, the holonomic systems with remainder coordinetes, the non-conservative mechanical systems, and the Lagrangian systems, are given. At the end of the paper, two examples are given to illustrate the application of the results.