引信球转子运动的四元数数学模型数值仿真

Numerical Simulation on Movement of Fuze Ball Rotor with Mathematical Model of Quaternion

为寻求准确高效地描述引信球转子运动规律的数值仿真算法,分别采用Runge-Kutta方法和Gear方法,利用四元数数学模型对两种引信球转子运动进行了数值仿真。结果表明:与强非线性的欧拉角数学模型相比,线性的引信球转子四元数模型能避免章动角趋近于0°或180°时的奇异性问题;采用Runge-Kutta方法耗用机时为Gear方法的1/3左右。

To obtain the accurate and efficient numerical simulation algorithm for describing the rotation law of a fuze ball rotor,two kinds of fuze ball rotors are numerically simulated with the mathematical model of quaternion using the Runge-Kutta method and Gear method respectively.The simulation results show that compared with the strongly nonlinear mathematical model of Euler angles,the linear quaternion model of the fuze ball rotor can avoid the singularity when the nutation angle approaches 0° or 180°.The time-consumed for the Runge-Kutta method is about one third of the Gear method.