基于运动方程的弹道导弹建模仿真方法

Modeling and simulation of ballistic missiles based on motion equation

针对弹道导弹在不同飞行环境下的多阶段运动特点,结合主动段的飞行过程,分三步设计了弹道导弹主动段飞行程序。根据弹道导弹在不同运动阶段的受力情况,充分考虑大气阻力、摄动力等因素,在地心惯性坐标系下分别构建了参数时变的弹道导弹主动段、自由飞行段、再入段运动模型。利用该模型对两级火箭助推的弹道导弹进行了仿真,并分析了飞行过程中弹道导弹飞行高度、速度、倾角、加速度等随时间的变化规律。仿真结果表明,该模型可有效用于弹道导弹飞行轨迹的仿真计算。

In view of the multi-stage motion characteristics of a ballistic missile in different flight environments, this paper firstly combines with the flight process in the active phase to design a three-step flight program of a ballistic missile in the active phase. Secondly, according to force conditions of the ballistic missile at different motion stages, this paper constructs the motion models of the ballistic missile in the active phase, the free flight phase and the re-entry phase with time-varying parameters in the geocentric inertial coordinate system by fully considering the factors such as atmospheric resistance and perturbation force. Finally, the model is used to simulate the two-stage rocket-propelled ballistic missile, and the variation laws of ballistic missile flight altitude, velocity, inclination and acceleration with time are analyzed. The simulation results show that the model can be effectively used to simulate the trajectory of ballistic missiles.