广义Birkhoff方程的积分方法

Integral methods for the generalized Birkhoff equations

场方法和最终乘子法是求解运动微分方程的基本方法.本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分;根据Jacobi最终乘子定理求出了广义Birkhoff方程的解.并举例说明结果的应用.

The field method and the last multiplier method are general integral methods for solving the differential equations of motion. The two methods are applied to the generalized Birkhoff system,and the complete integrals of the basic partial differential equation are given. Furthermore,the solutions of the generalized Birkhoff equations are obtained by Jacobi last multiplier theorem. An example is given to illustrate the application of the results.