Hamiltonian and chaotic attitude dynamics of an orbiting gyrostat satellite under gravity-gradient torques

The chaotic instability of the spinning motion of a gyrostat satellite is investigated in this paper. The circularly orbiting satellite under the action of gravity-gradient torques consists of a platform and axisymmetric wheels rotating with fixed relative speeds. The Hamiltonian equations in terms of Deprit’s canonical variables are derived for the attitude motion. An explicit criterion is established to predict the occurrence of attitude chaos in the sense of Smale’s horseshoe. The Poincaré–Arnold–Melnikov (PAM) integral developed by Holmes and Marsden [Indiana Univ. Math. J. 32 (1983) 273] is adopted. A fixed speed of the wheel of a torque-free bias momentum satellite is identified to ensure the existence of homoclinic orbits. The criterion is applied to predict the attitude chaos for both the bias momentum satellites and the orbiting symmetric gyrostat satellites under gravity-gradient torques. The Poincaré map is used to crosscheck the analytical results.