The athletics equation and stability of gyro-spacecraft with flexible accessories and controlled-wheels is researched in the paper. The mechanics model is established. The Lagrange equation is utilized to conclude the athletics equation based-on oscillation model analysis results. The stability of nonlinear equation zero-roots to some variables is proved; the sufficient and necessary conditions of asymptotic stability are given. The conclusion that the incomplete damp by wheel-velocity feedback can not always guarantee asymptotic stability, but can damp the centre-body and flexible accessories on certain conditions is proved.
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