基于双欧拉法的鱼雷空中弹道仿真

Simulation of Torpedo Air Trajectory Based on Dual-Euler Method

传统鱼雷弹道六自由度仿真多基于欧拉角方法求解运动微分方程,可以直观地得到鱼雷的位置和姿态角。但随着鱼雷空投弹道的出现,在倾角±90°的情况下会产生奇异点,致使欧拉方程无法求解,得不到正确结果。为克服上述不足,文中采用双欧拉法建立鱼雷运动数学模型,并对鱼雷空中弹道进行数值计算。仿真结果表明,基于双欧拉法的弹道模型能够正确地反映鱼雷空中弹道运动规律,在计算过程中不会因出现奇异点而发散。

Due to its advantages of obtaining torpedo’s attitude angle and position intuitively,Euler angle representation has been extensively applied to solve the differential equation of torpedo’s six-DOF motion.However,for the torpedo air trajectory,this representation will produce singular points at the pitching angles of ± 90°,leading to the fact that the Euler equation cannot be solved.Therefore,this paper employs the dual-Euler method to avoid such singularity.Based on the dual-Euler method,a mathematical model of torpedo motion is established,and the torpedo air trajectory is numerically simulated.There is no divergence induced by the singularity during the calculation process.Simulations result shows that the torpedo air trajectory model based on the dual-Euler method can reflect the motion characteristics of torpedo air trajectory,and can achieve satisfactory performance at arbitrary angles.This work may provide a theoretical reference for the study of torpedo air trajectory.