关于飞船的动态稳定问题

On the Dynamic Stability of an Orbital Reentry Vehicle

本文研究了以平衡攻角为中心作俯仰振荡的飞船，其动态稳定形态随来流马赫数Ｍ∞的变化。设θ（ｔ）是由平衡攻角起算的俯仰振荡角，ｃｍ（θ，θ）是作用于飞船上的气动力矩系数，ｃμ（θ，θ）θ是阻尼力矩（天上飞行时为零），可以证明λ＝（ｃｍθ）θ＝θ＝０＋ｃμ（０，０）＝λ（Ｍ∞）是决定动稳定形态的重要参数。如果随Ｍ∞变化，λ由小于零经λ＝０变化到λ＞０，则飞船将由稳定的点吸引子状态（即稳定在平衡攻角状态）发展为时间周期吸引子状态（即作周期振荡），对应于λ（Ｍ∞）＝０的那个马赫数Ｍｃｒ是出现该Ｈｏｐｆ分岔的临界马赫数。本文利用耦合求解俯仰振荡方程和ＮＳ方程的数值模拟方法，模拟了这种运动形态。

In this paper,the angular motion of an orbital reentry vehicle around static trim angle of attack is investigated using a single degree of freedom method.The angular motion behavior with decrease in Mach number is discussed.Supposing θ(t) is the pitching motion angle from static trim angle of attack, c m(θ,) is the damping in pitch derivatives and c μ(θ,) is the frictional damping moment coefficint which is negative in proportion to θ, we have proved analytically that θ=c m θ==0 +c μ(0,0)=λ(M ∞) is an important parameter to determine the angular motion behavior.If λ changes from negative to positive with decrease in Mach number,then the angular motion will become a limiting cycle oscillation from damping oscillation with a point attractor.The Mach number M ∞ corresponding to λ(M ∞)=0 is the critical one appearing the Hopf bifurcation.In addition,the solution coupling of an angular motion of a vehicle with numerical simulation of NS equations is presented.The agreement between the analysis and numerical simulation is very satisfactory.