Dynamics and chaos control of gyrostat satellite

We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.

► Free dual-spin gyrostat with a small rotor asymmetry is considered.
► Equations in Andoyer-Deprit canonical dimensionless variables are obtained.
► Phase space heteroclinic and homoclinic trajectories are written in closed form.
► Modified Melnikov function is used to construct the control that eliminates chaos.