First Integrals and Integral Invariants of Relativistic Birkhoffian Systems

作     者：LUOShao-Kai 

作者机构：InstituteofMathematicalMechanicsandMathematicalPhysicsChangshaUniversityChangsha410003China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2003年第40卷第2X期

页      面：133-136页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：湖南省教育厅项目 国家自然科学基金 河南省自然科学基金 

主　　题：相对论 Birkhoffian系统 Hamiltonian系统 初积分 积分不变式 哈密顿系统 

摘      要：For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t^rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.