广义完整非保守力学系统的Noether对称性及其守恒量

Noether Synnetries and Conserved Quantities for Holonomic Nonconservative Dynamical Systems in Generalized Classical Mechanics

研究广义完整非保守力学系统的Noether对称性与守恒量.建立系统逆变代数形式的运动微分方程,基于Hamilton作用量在无限小变换群作用下的不变性,给出系统的Noether广义准对称变换和广义Killing方程,得到系统的广义Noether定理及逆定理;最后举例说明结果的应用.

In this paper,Noether synnetries and conserved quantities for holonomic nonconservative dynamical systems in generalized classical mechanics are studied. Based on the invariance of hamiltonian action under infinitesimal transformation, the differential equations of motion forcontravariant algebra form of the systems are established. The Noether generalized quasi-symmetic transformations and generalized Killing equations are given. The generalized Noether＇s theorem and the inverse theorem of the systems are obtained; and an example is given to illustrate the application of the result.