非完整力学系统的非Noether守恒量——Hojman守恒量

研究非完整力学系统的非Noether守恒量——Hojman守恒量. 在时间不变的特殊Lie对称变换下，给出非完整力学系统的Lie对称性确定方程、约束限制方程和附加限制方程，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本文结果的应用. 关键词： 分析力学 非完整系统 Lie对称性 非Noether守恒量

A non-Noether conserved quantity, i.e. Hojman conserved quantity, for nonholonomic mechanical systems

A non-Noether conserved quantity, i.e. Hojman conserved quantity, of the nonholonomic mechanical systems is presented. Using the special Lie symmetry under infinitesimal transformations in which the time is not variable, the determining equations, the constrained restriction equations and the additional restriction equations of the nonholonomic mechanical systems are given. The Hojman conserved quantity of the corresponding holonomic systems, the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the nonholonomic systems are obtained. An example is given to illustrate the application of the result.