Chaotic Pitch Motion of a Magnetic Spacecraft with Viscous Drag in an Elliptical Polar Orbit

Resumen

We study the pitch attitude dynamics of an asymmetric magnetic spacecraft in an almost circular orbit under the influence of a gravity gradient torque. The spacecraft is also subject to the influence of three perturbations: the small eccentricity of the elliptical orbit, a small magnetic torque due to the interaction with the Earth's magnetic field, and a small aerodynamic viscous drag generated by the action of the Earth's atmosphere. Under these perturbations, we show that the pitch motion exhibits heteroclinic chaotic behavior by means of the Melnikov method. This method gives us an analytical criterion for the existence of heteroclinic chaos in terms of the system parameters. This analytical criterion is confirmed numerically with good agreement. In spite of the chaos generated by the perturbations, we also find, by means of Poincaré surfaces of section that some periodic pitch motions persist in the perturbed system with the same period as the orbital motion of the spacecraft. Finally, we carry out a bifurcation analysis of these periodic motions by numerical continuation of them in terms of the perturbation parameters. © 2011 World Scientific Publishing Company.