Ricci-based chaos analysis for roto-translatory motion of a Kelvin-type gyrostat satellite

Abstract

The chaotic dynamics of roto-translatory motion of a triaxial Kelvin-type gyrostat satellite under gravity gradient perturbations is considered. The Hamiltonian approach is used for modelling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation using the Serret-Andoyer variables. Therefore, this reduction leads to the derivation of the perturbation form of the Hamiltonian that can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos phenomenon. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate the presence of a strange attraction and chaotic responses in the perturbed system. The simulation results based on numerical methods such as Poincaré section, trajectories of phase portrait and time series responses quantitatively confirm the heteroclinic bifurcation and chaotic behaviour in the rotational–translational dynamics of the gyrostat satellite system.

Keywords

Riemannian manifold Ricci curvature Lyapunov exponent chaos Earth satellite system

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