再入飞行器极限环运动分析

Analytical study of limit cycle phenomenon for reentry vehicle

应用控制再入飞行器纵向运动二阶微分方程,根据外形对称特征,建立气动力系数模型,对方程进行定性分析。由构造的相平面,揭示出运动的全局特性———螺旋点、鞍点、Hopf分岔、极限环以及导致振荡运动和发散的初始条件域。应用多尺度法获得运动方程的极限环振幅和频率的渐近表达式,讨论了Hopf分岔类型。对静态俯仰力矩系数变化产生的影响也进行了分析。

The second order differential equation to govern longitudinal motion of reentry vehicle and aerodynamic coefficient models resulting from symmetry considerations in the body axis system are described. The result is used to construct phase planes, which reveal the general global nature of motion-spiral points, saddle points, Hopf bifurcation, limit cycles and domains of initial conditions leading to oscillatory motion and divergence. An asymptotic approximation to the solution of the governing equation is obtained by using MMS (method of multiple scales);This result provides expressions for the amplitudes and frequencies of limit cycles. In the meantime, the type of Hopf bifurcation is also discussed. Finally, the effects on the changes of statical pitch moment have also been analyzed.