Lie symmetries theorem and its inverse of generalized mechanical systems in terms of quasi-coordinates

被引：47

作者：

Qiao, YF ^{[1
]}

Zhao, SH ^{[1
]}

机构：

[1] NE Agr Univ, Coll Engn, Harbin 150030, Peoples R China

来源：

ACTA PHYSICA SINICA | 2001年 / 50卷 / 01期

关键词：

generalized mechanics; quasi-coordinates; Lie symmetries; determining equation; structure equation; conserved quantity;

D O I：

10.7498/aps.50.1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, Lie symmetries and conserved quantities of generalized mechanical systems in terms of quasi-coordinates were studied. First, the definition of an infinitesimal generator for the generalized mechanical systems in terms of quasi-coordinates were given, then the determining equations of the Lie symmetries were established by using Lie's method of invariance of ordinary differential equations under infinitesimal transformations. Next, the structure equation and the form of conserved quantities were obtained. Finally, the inverse problem of Lie symmetries systems were discussed and an example to illustrate the application of the result was given.

引用

页码：1 / 7

页数：7