尾翼式弹道修正弹Hopf分岔特性分析

Hopf bifurcation analysisfor a fin-stabilized projectile with course correction fuse

为分析尾翼式二维弹道修正弹锥形运动失稳原因,提高其修正精度,建立了该弹丸有控飞行阶段四维非线性角运动方程。利用Matcont软件确定系统分岔点后,运用中心流形定理对系统进行降维,并对降维后系统的Hopf分岔点类型进行判别,最后数值仿真验证了理论分析方法的正确性。在此分析方法基础上针对修正机构参数对角运动稳定性影响进行分析。结果表明,为保证弹箭飞行稳定性并使其具有良好气动布局,应将修正机构靠近质心位置安装。

In order to analyze the reason of the unstability of coning motion of a two-dimensional fin-stabilized projectile with course correction fuse and improve its correction accuracy,a four dimensional nonlinear angular motion equation of the controlled projectile was established.After using the Matcont software to determine the bifurcation point of the system,the central manifold theory was used to transfer the system dimension,and the type of bifurcation point after reducing the system dimension was judged.Finally,a numerical simulation proved the correctness of the theoretical analysis method.On this basis,the influence of correction mechanism parameters on the stability of angular motion was analyzed.The results show that for ensuring the flight stability of the projectile and making a good aerodynamic layout,it should make the position of the correction mechanism close to the center of mass.