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偏转弹头控制是一种新型的导弹控制方式,精确动力学模型的建立对于导弹性能、稳定性和控制的分析是必不可少的。本文采用多体动力学建模方法中的凯恩(Kane)方法对偏转弹头导弹建立了动力学模型。首先建立合适的坐标系,选取8个变量的速率为广义速率,之后推导了弹身弹头的运动学方程,接着得到广义主动力和广义惯性力,其中将控制弹头偏转的作动力矩视为主动力矩而非理想约束考虑进广义主动力的计算中,最终得到导弹的8个标量动力学方程。推导过程显示凯恩方法比牛顿-欧拉方法推导过程更为简化。利用得到的精确动力学模型进行动态仿真,通过比较研究了采用弹头质心位于弹头偏转铰链中心假设下的简化模型对导弹动态响应的影响,结果显示,在弹头偏转较慢时简化模型会带来较大的动态响应误差。
Deflection warhead control is a new type of missile control mode. The establishment of accurate dynamic model is essential for missile performance, stability and control analysis. In this paper, Kane method in multi-body dynamics modeling is used to establish the dynamic model of deflection warhead missile. Firstly, a suitable coordinate system is established, the rate of eight variables is chosen as generalized rate, and then the kinematic equation of the projectile’s warhead is deduced. Then the generalized generalized and generalized inertial forces are obtained. The moment which controls the warhead deflection is regarded as active Torque instead of the ideal constraint Consider into the calculation of the generalized projectile force, and finally get the eight scalar kinetic equations of the missile. The derivation process shows that the Kane method is more simplified than the Newton-Euler method derivation. The dynamic model is used to simulate the dynamics of the missile. The simplified model under the assumption that the center of mass of the projectile is located at the center of the warhead deflection hinge is used to simulate the dynamic response of the missile. The results show that simplifying the model when the projectile deflection is relatively slow Large dynamic response error.