用Gear法求解病态的引信球转子运动常微分方程组

Solution to Stiff Ordinary Differential Equations on the Movement of Fuze Ball Rotor with Gear Method

应用欧拉角及欧拉动力学方程、欧拉运动学方程所建立的描述引信球转子转正运动的数学模型,为强非线性的病态常微分方程组。为了准确、高效地分析球转子的运动过程,以某火炮引信球转子为例,针对不同参量和积分精度,对比地应用了Gear方法和Runge-Kutta方法,对该方程组进行了数值模拟。Gear方法比Runge-Kutta方法易于获得准确解,并且耗用机时也短。

The mathematical model of fuze ball rotor established by Euler angles system, Euler dynamics equation and Euler kinematics equation is a set of strongly nonlinear stiff ordinary differential equations. In order to exactly analyse the motion of ball rotor with high efficiency,a certain fuze ball rotor was taken as an example, the differential equations were numerically simulated by Gear method and Runge-Kutta method with different parameters and integral precision. The simulation shows that Gear method is easier than Runge-Kutta method to get exact solution,and needs less time.