可控约束Hamilton系统的Lie对称性与守恒量研究  

Lie symmetries and conserved quantities of controllable constrained Hamilton system

作　　者：郑明亮[1] ZHENG Mingliang(School of Mechanical and Control Engineering,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学机械与控制学院,浙江杭州310018

出　　处：《苏州科技大学学报（自然科学版）》2018年第1期6-11,共6页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11472247)

摘　　要：在相空间中研究带有约束控制参数的奇异系统的Lie对称性及其守恒量问题,可为奇异系统先进控制策略的设计奠定基础。将可控约束处理成外在通常的非完整约束,在考虑此约束与系统固有内在约束相容的基础上,给出了可控约束Hamilton系统的正则方程;基于沿系统运动轨线任意力学量对时间的全导数计算法则,进一步利用微分方程和代数方程在无限小变换下的不变性,给出可控约束Hamilton系统Lie对称性判定的确定方程、限制方程和附加限制方程;构造规范函数满足的条件结构方程,得到相空间中可控奇异系统Lie对称性导致守恒量的形式。最后举例说明文中内容和方法的应用。This paper investigated the Lie symmetries and conserved quantities of singular systems with controllable constrained parameters in phase space,which can lay the foundation for the design of advanced control strategies for singular systems.The controllable constraints were treated as external and usually nonholonomic constraints.Considering the consistency between the constraint and the inherent constraints of the system,the author presented the canonical equations of the controllable constrained Hamilton system.Based on the total derivative calculation of arbitrary mechanical quantities along the trajectory system,the author provided the determination equations,the limiting equations and the additional limiting equations for the determination of the Lie symmetry of the Hamilton system with controllable constraints by using the invariance of differential equations and algebraic equations under infinitesimal transformations.By constructing the conditional structure equation satisfied by norm functions,the author obtained the form of conserved quantities by Lie symmetry of controllable singular systems in phase space.Finally,an example for the application was given.

关 键 词：可控参数 约束HAMILTON系统 LIE对称 守恒量 

分 类 号：O316[理学—一般力学与力学基础] O322[理学—力学]