约束系统的变换和推广的Killing方程

本文从约束系统的作用量和约束方程的普遍变换性质出发,得到了约束系统的推广Killing方程组,此方程组的解所生成的变换可产生经典Noether定理的守恒量。讨论了连续系统的时空变换和内禀变换,在变换保持约束方程不变时,指出此变换能导致守恒流的充要条件,给出了对不可压缩连续介质的应用,讨论了对广义力学和经典力学的应用,并给出了推广Killing方程组解的某些实例,将Poincare不变量推广到了受约束广义力学系统。 关键词：

THE TRANSFORMATION OF CONSTRAINED SYSTEM AND GENERALIZED KILLING'S EQUATIONS

Starting from the transformation properties of constrained system which is a general transformation results of action and constrained equations, we obtain generalized killing's equations of constrained system. The transformation generated by the solution of generalized killing's equations, may yield classical Noether's conservation quantities. We have considered the time-space and internal transformation of continuous constrained system which leave constrained equations invariant and give a necessary and sufficient condition that transformations may yield conservation current. The application to incompressible continuous media are presented. The application to generalized and classical mechanics are discussed and some illustrations for the solution of generalized killing's equations are also given. The Poincare's invariant is generalized to constrained generalized mechanical system.