Chaotic motion in a class of asymmetrical Kelvin type gyrostat satellite

Abstract

This work is an investigation on the roots of chaotic attitudinal motion in a class of asymmetrical gyrostat satellites. The result shows that for a class of Kelvin type gyrostat satellite, there is an equivalent rigid spinning satellite with the same attitude dynamics. Finding some constants of motion and eliminating the cyclic coordinates, the rotational kinetic energy is changed to a quadratic form and using Jordan canonical form of the associated inertia tensor and transforming the coordinate system, the Hamiltonian has been changed to those of a rigid satellite. The Hamiltonian has been split into integrable and non-integrable parts. Using Deprit canonical transformation and Andoyer variables the integrable part has been reduced to a one-dimensional form. The reduced Hamiltonian shows that the regular dynamics of the satellite can be chaotic, under the influence of gravitational effects. To demonstrate various attitudinal dynamics of the satellite, a second-order Poincaré map is employed. This research shows firstly, that the attitudinal dynamics of Kelvin type gyrostat satellites and rigid satellites follow the same dynamical patterns, secondly, for non-linear analysis of dynamics of gyrostat satellite based on the perturbation methods, there is a preferable form for Hamiltonian of the system in the near-integrable fashion and thirdly the chaotic motion is originated from the gravitational field effects that can be suppressed by increasing the attitudinal energy of the satellite in comparison with the translational energy.