广义经典力学与非完整力学的统一理论  

A unified theory of generalized classical mechanics and nonholonomic mechanics

作　　者：罗绍凯[1] 

机构地区：[1]长沙大学数学力学与数学物理研究所,长沙410003

出　　处：《物理学报》2002年第7期1416-1423,共8页Acta Physica Sinica

基　　金：河南省自然科学基金(批准号:934060800);河南省教育委员会科研基金 (批准号 :93 0 0 2 )资助的课题

摘　　要：建立广义经典力学与非完整力学的统一理论———广义非完整力学理论 ,构造其基本框架 .提出广义非完整力学的Чeтаeв(Chetaev)定义 ,建立广义非完整力学系统的Routh方程和正则方程 .给出广义非完整力学系统的非等时变分方程 ,证明由广义非完整力学系统的第一积分可以构造积分不变量 .研究广义非完整力学系统作用量的非等时变分 ,给出系统的Poincar啨 Cartan积分变量关系和积分不变量 ,进而给出等时变分下系统的Poincar啨积分变量关系和通用积分不变量 .给出一些推论 ,表明广义经典力学和一阶至高阶非完整力学的相关结论均为广义非完整力学理论的特款 .A unified theory of generalized classical mechanics and nonholonomic mechanics,or the theory of generalized nonholonomic mechanics,and its basic theoretical frame are constructed.Firstly,the generalized Четаев(Chetaev) condition,Routh equations and canonical equations of the generalized nonholonomic mechanical system are given.Secondly,the equations of nonsimultaneous variation of the generalized nonholonomic mechanical system are established by using the relation between the simultaneous variation and the nonsimultaneous variation.And it is proved that using a first integral we can costruct an integral invariant of the system. Thirdly,the nonsimultaneous variation of Hamilton action of the generalized nonholonomic mechanical system is studied,and the integral variants and integral invariants with Poincaré Cartan type and Poincaré type are obtained.Finally,some deductions are given.The results show that the relevant conslusions of the generalized classical mechanics and the first order or higher order nonholonomic mechanics are the deductions of the theory of generalized nonholonomic mechanics.

关 键 词：广义经典力学 非完整力学 统一理论 广义非完整力学 广义четаев定义 运动方程 积分不变量 

分 类 号：O316[理学—一般力学与力学基础]