广义Birkhoff系统的循环积分及降阶法

Cyclic Integral and Reduction of Generalized Birkhoff System

将Birkhoff系统循环积分降阶法推广到广义Birkhoff系统,研究了广义Birkhoff系统循环积分的存在条件和形式.利用循环积分降阶法,将广义Birkhoff方程降两阶,且能保持方程的形式.所得结果对积分广义Birkhoff系统提供了一条途径,并举例说明了结果的应用.

The method of reduction of Birkhoff system by using of cyclic integral is applied to the generalized Birkhoff system.An existent condition and a form of the cyclic integral of the generalized Birkhoff system are studied.Through each cyclic integral,the order of the equations of the system can reduce two degrees and the form of the equations can be held.The result provides a way to the integral of generalized Birkhoff system.An example is given to illustrate the application of the result.