Cyclic Integral and Reduction of Generalized Birkhoff System

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.