高阶Maggi方程的Birkhoff化及其辛算法

Birkhoffization of Higher-Order Maggi Equation and Its Symplectic Algorithm

针对非完整系统的高阶Maggi方程,在满足一定的条件时,可以对其进行Birkhoff化.通过构造生成函数,利用Birkhoff广义辛算法对其进行数值仿真.仿真结果和传统的Runge-Kutta算法结果相比较,Birkhoff广义辛算法在长期跟踪后更加准确.

For the high-order Maggi equation of nonholonomic systems,when it meets certain conditions,the Maggi equation can be transformed into a Birkhoffian system.By constructing the generating function,the system is investigated numerically using the symplectic geometric algorithm of the Birkhoffian system.Compared with the above-mentioned algorithm with the classical Runge-Kutta method,Birkhoffian symplectic scheme is very accurate in a long-term tracing.