辛Runge-Kutta方法在求解Lagrange-Maxwell方程中的应用研究

摘要

In this paper, we show the numerical integration method of solving Lagrange-Maxwell equation by using the symplectic Runge-Kutta (R-K) method, and numerically study the motion of the plate in an RLC circuit spring coupled system and the current changes. Its result is consistent with that obtained by the traditional R-K method, which demonstrates symplectic integration algorithm is reasonable and effective in studying the electro-mechanical systems. And on this basis, the form invariance of Noether sense is studied by using the symplectic Runge-Kutta method.%　　给出了采用辛Runge-Kutta (R-K)方法求解Lagrange-Maxwell方程的数值积分方法，并数值研究了RLC电路弹簧耦联系统中极板的运动及电流的变化情况，其计算结果和传统的R-K方法相一致，说明利用辛积分算法研究机电动力系统是合理和有效的，并在此基础上采用辛R-K方法研究了Noether意义下的形式不变性。