摘要
给出高维增广相空间中广义力学系统的Lie对称定理及其逆定理 .首先 ,根据运动微分方程在无限小变换下的不变性建立完整非保守广义力学系统Lie对称的确定方程 .得到Lie对称的结构方程和守恒方程 .其次 ,讨论了Lie对称的逆问题 .
In this paper,the Lie's symmetrical theorem and its inverse of generalized mechanical systems in dimensional extended phase space are given.Firstly,according to the invariance of differential equations of motion under the infinitesimal transformations,the determining equations of the Lie symmetry of the holonomic non conservative generalized mechanical systems are established.The Lie's symmetrical structural equation and conservative equations are obtained.Secondly,the inverse problem of the Lie symmetry is discussed.Finally,an example to illustrate the application of the result is given.
出处
《商丘师范学院学报》
CAS
2000年第4期1-5,共5页
Journal of Shangqiu Normal University
基金
黑龙江省自然科学基金资助项目! (1 9950 7)
关键词
高维增广相空间
Lie对称定理
广义力学系统
dimensional extended phase space
generalized mechanics
Lie's symmetrical theorem
conservative quantity
