Rotational Oscillation of Satellite in Elliptic Orbit under Magnetic Torque

Abstract

Magnetic disturbance torque results from interaction between spacecraft's residual magnetic field and geomagnetic field. The primary sources of magnetic disturbance torques are spacecraft magnetic moments, eddy currents and hysteresis. The instantaneous magnetic disturbance torque due to spacecraft effective magnetic moment is the product of geocentric magnetic flux density and sum of individual magnetic moments caused by permanent and induced magnetism and spacecraft generated current loops. Let us consider a rigid satellite S moving around the central body C and orbital plane of satellite coincides with equatorial plane of C. This paper deals with rotational oscillation of satellite under influence of magnetic torque in elliptic orbit. Non-linear planar equation of motion of model has been derived. Using BKM method, it is observed that resonances exist. The analysis regarding stability of stationary planar oscillation of satellite near resonance frequency shows that discontinuity occurs in amplitude of oscillation at frequency of e xternal periodic force which is less than frequency of the natural oscillation. The half width of chaotic separatrix has been estimated by Chirikov's criterion. Through surface of section method, it has been observed that magnetic torque parameter, eccentricity and mass ratio play an important role in changing regular motion into chaotic one.