弹箭非线性角运动稳定性Hopf分岔分析

为了分析弹箭的角运动稳定性，推导了弹箭的非线性角运动方程组，给出弹箭的非线性角运动Hopf分岔分析方法。以某型火箭弹高原试验为例，选取空气密度作为分岔参数，采用霍尔维茨判据判断了系统的稳定性，并确定了分岔点。由中心流形定理对系统进行降维，计算了Hopf分岔的3阶规范形，并作出了系统的分岔图，分析了分岔参数对极限环摆幅的影响。进行了仿真验证，结果表明，采用分岔分析方法能准确判断系统的稳定性及分析系统的极限环运动。

Hopf Bifurcation Analysis of Nonlinear Angular Motion Stability of Projectile

In order to analyze the angular motion stability of projectile, the equations of the nonlinear angular motion are derived, and the Hopf bifurcation analysis method of the nonlinear angular motion of projectile is given. Taking a rocket plateau test as an example, the air density is selected as the bifurcation parameter, and the Hurwitz criterion is used to judge the stability of the system. The bifurcation point is determined. Center manifold theory is proposed to reduce the system dimension, and then a three-order normal form of Hopf bifurcation is calculated by plotting the bifurcation diagram. In addition, the effect of the bifurcation parameter on the swing of the limit cycle is analyzed. The numerical simulations show that the bifurcation analysis method can be used to judge the stability of the system correctly and analyze the motion of limit cycle in the system accurately.