转动相对论Birkhoff约束系统积分不变量的构造

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给出一个例子说明结果的应用 关键词： 转动相对论 Birkhoff系统 约束 第一积分 积分不变量

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

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.