Study on the Chaotic Dynamics in Attitude Maneuver of Liquid-Filled Flexible Spacecraft

摘要

In this paper, the chaotic dynamics in an attitude transition maneuver of a coupled slosh-spacecraft with a flexible appendage in going from minor axis to major axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to undergo only torsional vibration is investigated. The coupled slosh-spacecraft with a flexible appendage in attitude maneuver carrying a sloshing liquid is considered a multibody system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is on the way in which the dynamics of the liquid and the flexible appendage vibration are coupled. The equations of motion are derived and then transformed into a form suitable for the application of the Melnikov method. The Melnikov integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of the system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction, and torsional vibration frequency of the flexible appendage are investigated. In addition, extensive numerical simulations are carried out to check the range of validity of the Melnikov result.