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Heteroclinic Bifurcation and Chaotic Analysis in Rotational-Translational Motion of a Kelvin-Type Gyrostat Satellite

Author Affiliations

  • 1 Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, IRAN

Res. J. Recent Sci., Volume 2, Issue (9), Pages 77-85, September,2 (2013)

Abstract

The different methodologies for the study of nonlinear asymmetric Kelvin-type gyrostat satellite consisting of the heteroclinic bifurcation and chaos are investigated in this work. The dynamical model of the gyrostat satellite involves the attitude orientation along with the translational motion in the circular orbit. The mathematical model of the Kelvin-type gyrostat satellite is first derived using the Hamiltonian approach in the Roto-Translatory motion under the gravity gradient perturbations. Since the model of the system is too complex, the coupled equations of motion are reduced using the modified Deprit canonical transformation by the Serret-Andoyer variables in the spin-orbit dynamics. The simulation results demonstrate the heteroclinic bifurcation route to chaos in the Roto-Translatory motion of the gyrostat satellite due to the effects of the orbital motion and the gravity gradient perturbation on the attitude dynamics. According to the numerical solutions, the intersection of the stable and unstable manifolds in the heteroclinic orbits around the saddle point lead to the occurrence of the heteroclinic bifurcation and chaotic responses in the perturbed system. Chaos behaviour in the system is also analyzed using the phase portrait trajectories, Poincare' section, and the time history responses. Moreover, the Lyapunov exponent criterion verifies numerically the existence of chaos in the Roto-Translatory motion of the system.

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