93-132
Chaos In Controlled, Gravity Gradient Satellite Pitch Dynamics Via The Method Of Melnikov-Part I - Center Stabilization*
Gary L Gray** and Mark c. Stabb***
Abstract
A generalization of Melnikov's method is used to detect chaos in the pitch dynamics of a controlled gravity gradient satellite. Small perturbations to the pitch dynamics are introduced through a nonzero orbital eccentricity and active control. The control is used to stabilize the system about a center equilibrium point in the phase space corresponding to a specific orientation of the satellite. The equations of motion are presented and their geometric structure is discussed. .Melelnikov's mcthod for high dimensional systems (> 2) is applied to these equations and analytical criteria for chaotic motion are derived in terms of the system parameters. These criteria are studied and evaluated for their significance to the design of satellites.
*Copyright 1993 by Gary L. Gray and Mark C. Stabb. Published by AAS with permission.
**Doctoral Candidate, Department o~ Engineering Mechanics and Astronautics, University of Wisconsin-Madison, 1415 Johnson Drive, Madison. Wisconsin 53706. Student Member AAS and AIAA
***Engineer, Structural Dynamics Research Corporation, 11995 El Camino Real, Suite 200, San Diego, California 92130