转动相对论Birkhoff约束系统积分不变量的构造  

The construction of a class of integral invariants for rotational relativistic Birkhoffian system with constraints

作　　者：罗绍凯[1] 卢一兵[1] 周强 王应德[1] 欧阳实[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9期1913-1917,共5页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号:19972 0 10 );河南省自然科学基金(批准号 :9840 5 3 10 0和 9980 40 0 80 )资助的课题~~

摘　　要：研究转动相对论Birkhoff约束系统积分不变量的构造 首先 ,建立转动相对论系统的约束Birkhoff方程 ;其次 ,利用等时变分与非等时变分之间的关系建立系统的非等时变分方程 ;然后 ,研究转动相对论Birkhoff约束系统的第一积分与积分不变量之间的关系 ,证明由系统的一个第一积分可以构造一个积分不变量 ,并给出自由Birkhoff系统的相应结果 ;最后 ,讨论转动相对论Hamilton系统、相对论Birkhoff系统和Hamilton系统、经典转动系统和等时变分情形下的积分不变量的构造 ,结果表明相关的结论均为该定理的特款The construction of a class of integral invariants for rotational relativistic Birkhoffian system with constraints are studied.Firstly,the Birkhoff's equations with constraints of rotational relativistic system are given.Secodly,the equations of nonsimultaneous variation of the rolational relativistic Birkhoffian system with constraints are established by using the relation between the simultaneous variation and the nonsimultaneous variation.Thirdly,the relation between the first integral and the integral invariants of the system is studied,and it is proved that, using a first integral, we can construct an integral invariant of the system.And the relevant conclusions corresponding to the rotational relativistic free Birkhoffian system are given.Finally,the construction of integral invariants for the rotational relativistic Hamiltonian system,the relativistic Birkhoffian system and the relativistic Haniltonian system,the classical rotation system and the cases of simultaneous variation are discussed.The results show that the relevant conslusions are the deductions of the theorems of this paper.An example is given to illustrate the application of the results.

关 键 词：约束系统 转动相动论 BIRKHOFF系统 第一积分 积分不变量 分析力学 

分 类 号：O316[理学—一般力学与力学基础]