广义经典力学系统的Hojman守恒定理

A conservation theorem of Hojman for systems of generalized classical mechanics

研究广义经典力学系统的对称性与守恒定理 .利用常微分方程在无限小变换下的不变性 ,建立了系统在高维增广相空间中仅依赖于正则变量的Lie对称变换 ,并直接由系统的Lie对称性得到了系统的一类守恒律 .实际上 ,这是Hojman的守恒定理对广义经典力学系统的推广 .举例说明结果的应用 .

The conservation theorem and the symmetries for systems of generalized classical mechanics are studied. In terms of the invariance of the ordinary differential equations under the infinitesimal transformations, this paper established the Lie symmetrical transformations of the systems in the high-dimensional extended phase space, which only depend on the canonical variables, and a new type of conservation laws are directly obtained from the Lie symmetries of the systems. Actually. the conservation laws are the generalization of a conservation theorem of Hojman to generalized classical mechanics. Finally, an example is given to illustrate the application of the results.