Effects of unsymmetrical stability derivative characteristics on re-entry vehicle transient angular motion

A quasi-steady analytical theory is developed to investigate the effects that unsymmetrical stability derivative characteristics can have on the transient angular motion behavior of slender rolling re-entry vehicles. The theoretical results indicate that the presence of unsymmetrical stability derivatives can alter the motion patterns, frequency, and damping sufficiently to invalidate the use of previous analytical models developed for vehicles with symmetrical stability derivative characteristics. Between the resonances small asymmetries in the static moment slope coefficients are shown to cause a static instability which results in an exponential growth of the transient angle of attack. The analytically derived expressions and the analytically predicted trends are verified by numerical analyses.