物理学报2012，Vol.61Issue(21)：299-304,6.
相对论性力学系统的Birkhoff对称性与守恒量
Symmetry of Birkhoffians and conserved quantity for a relativistic mechanical system
摘要
Abstract
A new symmetry of a relativistic mechanical system is put forward, and the corresponding conserved quantity is given. The new symmetry is defined in such a way that if each solution to the differential equations of motion of a relativistic mechanical system corresponding to a set of Birkhoff's dynamical functions satisfies the differential equations of motion obtained by other set of Birkhoff's dynamical functions and vice versa, then the corresponding invariance is called a symmetry of Birkhoffians. We prove that the coefficient matrix which relates to the relativistic Birkhoff's equations obtained from two sets of Birkhoff's dynamical functions, is such that the trace of all its integer powers is a conserved quantity of the system, and therefore a theorem known for nonsingular equivalent Lagrangians presented by Currie and Saletan is extended to a relativistic Birkhoffian system. Two examples are given to illustrate the application of the results.关键词
相对论性力学系统/Birkhoff对称性/守恒量Key words
relativistic mechanical system/symmetry of Birkhoffians/conserved quantity分类
数理科学引用本文复制引用
张毅..相对论性力学系统的Birkhoff对称性与守恒量[J].物理学报,2012,61(21):299-304,6.基金项目
国家自然科学基金,(批准号：10972151,11272227)资助的课题. （批准号：10972151,11272227）
