广义线性非完整力学系统的Hojman守恒量

Hojman conserved quantities of generalized linear nonholonomic mechanical systems

研究广义线性非完整力学系统的Lie对称性导致的Hojman守恒量,在时间不变的特殊Lie对称变换下,给出系统的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守恒量以及广义线性非完整力学系统的弱Hojman守恒量和强Hojman守恒量,并举一算例说明结果的应用.

We study the Lie symmetries and Hojman conserved quantities of generalized linear nonholonomic mechanical systems. Under special infinitesimal transformations in which the time is invariable,the determining equations,the constrained restriction equations and the additional restriction equations of the nonholonomic mechanical systems are obtained. The Hojman conserved quantity of the corresponding holonomic systems,the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the linear nonholonomic systems are obtained. An example to illustrate the application of the result is given.