相空间中单面完整约束系统的Lie对称性研究  

Lie Symmetries of Holonomic Systems with Unilateral Constraints in Phase Space

作　　者：张毅[1] 梅凤翔[1] 

机构地区：[1]北京理工大学应用力学系,北京100081

出　　处：《北京理工大学学报》1999年第5期531-537,共7页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金!资助项目 (19572 0 18) ;高等学校博士学科点专项科研基金

摘　　要：目的　研究具有单面约束的完整系统在相空间中的Lie对称性与守恒量方法利用常微分方程在无限小变换下的不变性,建立系统Lie对称性的确定方程和限制方程结果与结论　得到结构方程与守恒量形式,给出了Lie对称逆问题的解。Aim To study the Lie symmetries and the conserved quantities of holonomic systems with unilateral constraints in phase space. Methods The invariance of ordinary differential equations under the infinitesimal transformations was used to establish the determining equations and the restriction equations of the Lie symmetries of systems. Results and Conclusion The structure equations and the form of conserved quantities were obtained, and the solution of the inverse problem was presented. Two examples were given to illustrate the application of the results.

关 键 词：分析力学 单面约束 相空间 完整系统 李对称性 

分 类 号：O316[理学—一般力学与力学基础]