Saturn–Hyperion System Dynamics under the Influence of Aerodynamic Torque

This paper discussed the nonlinear oscillation of a natural satellite Hyperion in an elliptic orbit around the Saturn under the influence of aerodynamic and gravitational torque. Consider that the orbital plane of Hyperion coincides with the equatorial plane of the Saturn. In this paper, the equation of motion, Hamiltonian function and Melnikov's integral for the problem has been derived by using Euler's dynamical equation of motion. The unperturbed double asymptotic solution exists. It is observed that Hamiltonian function is dependent on aerodynamic torque by taking aerodynamic torque of the order of eccentricity. It is observed that equations of motion are non-integrable by using Melnikov's integral. Numerical simulation is done for Saturn–Hyperion system and which shows that aerodynamic torque has a great impact on changing the regular motion to chaotic.