Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space

在这篇论文，在事件空格的概括 Birkhoff 系统的能量守恒定律被使用集成因素的方法学习。第一，概括 Pfaff Birkhoff 原则和概括 Birkhoff 方程被建立，并且为系统的集成的因素的定义被给。基于集成因素的概念，第二，为结果空间的概括 Birkhoff 系统的保存定理和他们的逆详细被介绍，并且在能量守恒定律和系统的集成的因素之间的关系被获得，为集成的因素的决心的概括杀死的方程被给。最后，一个例子被给说明结果的申请。

In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.