Hamiltonian Function for Satellite Motion in an Elliptic Orbit under The Influence of Aerodynamic Torque

This paper deals with the non-linear oscillation of a satellite in an elliptic orbit around the Earth under the influence of aerodynamic and gravitational torque. It is assumed that the orbital plane coincides with the equatorial plane of the Earth. Using Euler's dynamical equation of motion, the equation of motion and Hamiltonian function for the problem is derived. Taking aerodynamic torque of the order of eccentricity, it is observed that Hamiltonian function is dependent on aerodynamic torque. The equilibrium points and Double Asymptotic solutions related to the problem are calculated. It is concluded that in the phase space (0, 2) and (π, 2) are the equilibrium points, out of which (0, 2) is a stable and (π, 2) is an unstable equilibrium point.