摘要
研究推坐标下非完整系统的Lie对称性．首先，对准坐标下非完整力学系统定义无限小变换生成元，由微分方程在无限小变换下的不变性，建立Lie对称性的确定方程，得到结构方程并求出守恒量；其次，研究上述问题的逆问题：根据已知积分求相应的Lie对称性．举例说明结果的应用．
This paper involves Lie symmetries and conservation laws of nonholnomlc systems in terms of quasi-coordinates. We studied two kinds of problems on Lie symmetries and conserved quantities. One is the direct problem of Lie symmetries:finding out the corresponding conserved quantity according to a given Lie symmetry. We gives the definition of the infiniteshmal generator for the nonholonomic systems in terms of quasi-coordinates.Using the invariance of the ordinary differential equations under the infinitesimal transformations, establishes the determining equations of the Lic symmetries. Obtains the structure equation and conserved quantities. The another kinds of problem is called the inverse problem of Lie symmetries:find out the corresponding Lie symmetry according to a known conserved quantity. Gives an example to illustrate the application of the result.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2000年第1期63-69,共7页
Acta Mathematica Scientia
基金
国家自然科学基金
高校博士学科点专项科研基金
关键词
分析力学
准坐标
非完整系统
LIE对称性
守恒量
Analytical mechanics, Quasi-coordinate, Lie symmetry, Conserved quantity,Nonholonomic mechanical system
