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Research on the dynamic stability of an orbital reentry vehicle in pitching

Zhang Han-xin, Yuan Xian-xu, Ye You-da, Xie Yu-fei (National Laboratory of CFD, Beijing 100083,China; China Aerodynamics Research and development center, Mianyan 621000,China)  
In this paper, the single-DOF (degree of freedom) pitching angular motion of an orbital reentry vehicle around static trim angle of attack is investigated by a nalytic and numerical methods. Criteria of the dynamic stability of the pitching motion are given by nonlinear dynamic theory. Supposing θ(t) is the pitching angle from static trim angle of attack, C m is the aerodynamic pitching mo ment coefficient, C μ(θ,[AKθ· )· AKθ· is the frictional damping m oment. It can be proved analytically that λ=λ(M ∞)=[JB(][JB([][JB((][SX(] C m[][AKθ·][SX)][JB))] 0+C μ(0,0)[JB)]][JB)/ JB([]1-[JB((][SX(] C m[][AKθ¨][SX)][JB))] 0[JB)]  is an important parameter to determin e the angular motion behavior, If λ(M ∞) changes from negative to positiv e with decrease in Mach numbers, then the pitching motion will become a stable L imit Cycle oscillation from damping oscillation with a point attractor. The Mach number corresponding to λ(M ∞)=0 is the critical Mach number M cr , at which the Hopf bifurcation is occuring.The Hopf bifurcation process of a single-DOF pitching motion of an orbital reentry vehicle around static trim ang le of attack is simulated by solving the coupled pitching motion equation and Na vier-Stokes equations, the agreement between the analysis and numerical simulat ion is quite satisfactory.
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