广义经典完整非保守力学系统Lie对称性及其守恒量

广义经典完整非保守力学系统Lie对称性及其守恒量

董文山

山东潍坊学院物理与电子科学系，山东潍坊 261061

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-10-24 发布日期:2006-10-24
通讯作者: 董文山

Lie symmetries and conserved quantities of holonomic non-conservative dynamical systems in generalizad classical machanics

DONG Wen-shan

Department of Physics, Weifang University, Weifang 261061, Shandong, China

Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
Contact: DONG Wen-shan

摘要/Abstract

摘要： 研究了广义完整非保守力学系统的Lie对称性及其守恒量. 建立了系统的运动微分方程，给出其确定方程、结构方程和守恒量，得到了系统的Lie对称性定理和逆定理，最后举例说明结果的应用.

关键词: 广义力学系统, Lie对称性, 守恒量

Abstract: Lie symmetries and conserved quantities of holonomic non-conservative dynamical systems in generalized classical mechanics were studied. First, the determining equations of Lie symmetries are established by using Lie's invariance method of infinitesimal transformations of differential equations. Second, the structure equations and the conserved quantities were obtained. Third, the inverse Lie symmetries system problems were discussed. Finally, an example to illustrate the application of the results was given.

Key words: conserved quantities , Lie symmetries, generalized mechanics system

中图分类号:

O320

董文山 . 广义经典完整非保守力学系统Lie对称性及其守恒量[J]. J4, 2007, 42(9): 30-35 .

DONG Wen-shan . Lie symmetries and conserved quantities of holonomic non-conservative dynamical systems in generalizad classical machanics[J]. J4, 2007, 42(9): 30-35 .

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