Chaos Analysis for Roto-Translatory Motion of a Gyrostat Satellite Using Melnikov Method

Interactions of the translational motion of a gyrostat satellite on its attitude dynamics is considered in this paper. The mathematical model is first derived using the Hamiltonian method for the rotation-Translation motion of the gyrostat satellite followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method along with the numerical Lyapunov exponent criterion, Poincare' section, trajectories of phase portrait, and the time history responses are used to study the heteroclinic bifurcation and chaos phenomena on the reduced model. On the basis of the results obtained from Melnikov integral, the parameters of the gyrostat satellite can be designed to prevent chaos in the system in the absence of a control system.