积分事件空间中Birkhoff参数方程的场方法

A FIELD METHOD FOR INTEGRATING BIRKHOFF'S PARAMETRIC EQUATIONS IN EVENT SPACE

研究事件空间中Birkhoff系统的积分方法.给出了事件空间中Birkhoff系统的参数方程.选取事件空间中某一个Birkhoff变量作为其余变量的函数,建立了拟线性的基本偏微分方程组,并将场方法推广应用于积分事件空间中Birkhoff参数方程.由于具体问题中可以选取事件空间中任意一个Birkhoff变量作为余下变量的函数,因此本文方法具有灵活性.该方法的主要困难在于求基本偏微分方程组的完全解.一旦求出完全解,就可以不用进一步积分而求得系统的运动.文末,举例说明结果的应用.

The integration method of Birkhoffian systems in event space was studied,and the parametric equations of the Birkhoffian systems in the event space were given.By choosing a Birkhoff＇s variable in the event space as the function of the rest of the variables,the basic system of quasi-linear partial differential equation was set up,and the idea of field method was generalized to the integration of Birkhoff＇s parametric equations in the event space.Since any Birkhoff＇s variable can be chosen as the function of the remaining variables in a specific problem,so the method has flexibility.The major difficulty of this method lies in how to find the complete solution of the basic partial differential equation.Once the complete solution was found,the motion of the systems can be obtained without doing further integration.At the end of the paper,an example was given to illustrate the application of the results.