Chaos and Bifurcation in Roto-Translatory Motion of Gyrostat Satellite

Subject Areas : Analytical and Numerical Methods in Mechanical Design

Seyed Mahdi Abtahi ¹ , Seyed Hosein Sadati ²

1 - Department of Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Department of Mechanical Engineering, Sharif University of Technology, Iran

Received: 2023-04-09 Accepted : 2023-04-09 Published : 2022-12-01

Keywords: Roto-Translatory motion, Gyrostat satellite, chaotic dynamics, heteroclinic bifurcation, Melnikov method,

Abstract :

The chaotic dynamics of Roto-Translatory motion for a triaxial Gyrostat satellite is considered in this study based on the Hamiltonian approach. Higher complexity in the coupled spin-orbit equations motivates the reduction of the Hamiltonian in the study of this nonlinear system. This reduction is done by the use of the Deprit canonical transformation developed here by the new Serret-Andoyer variables used as rotational and translational variables. The results obtained from the Hamiltonian reduction can be written as a perturbed equation near Integrable-Hamiltonian form, where the perturbed part of the equations consists the orbital and gravity gradient effects. Increasing the perturbation parameter causes the trajectories of the system to pass throughout heteroclinic bifurcation zone introducing chaos in the system. Also heteroclinic bifurcation and transversally stable and unstable manifolds are mathematically proven using Melnikov method. Through the Melnikov integral, the bounded variations in the design parameters are determined so as to prevent the system from a chaotic behavior. The simulation results based on the numerical methods such as the time series responses, trajectories of phase portrait, Poincare section, and Lyapunov exponent criterion quantitatively verify chaos in the system in the presence of perturbation influences..