Chaotic Dynamics of Spin-Orbit Motion in a Gyrostat Satellite Using Ricci Method

Chaotic dynamics of spin-orbit motion of a triaxial gyrostat satellite under the gravity gradient perturbations is considered. The Hamiltonian approach is used for modeling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation. This reduction yields to the derivation of the perturbation form of the Hamiltonian which can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate the presence of a strange attractor and chaos phenomenon in the perturbed system. The simulation results based on the numerical methods such as Poincare'' section، trajectories of phase portrait، and time series responses confirm the heteroclinic bifurcation and chaos in the system.