Heteroclinic bifurcations in rigid bodies containing internally moving parts and a viscous damper

Melnikov's method is used to analytically study chaotic dynamics in an atti tude transition maneuver of a torque-free rigid body in going from minor ax is to major axis spin under the influence of viscous damping and nonautonom ous perturbations. The equations of motion are presented their phase space is discussed, and then they are transformed into a form suitable for the ap plication of Melnikov's method. Melnikov's method yields an analytical crit erion for homoclinic chaos in the form of an inequality that gives a necess ary condition for chaotic dynamics in terms of the system parameters. The c riterion is evaluated for its physical significance and for its application to the design of spacecraft. In addition, the Melnikov criterion is compar ed with numerical simulations of the system. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping are invest igated. In particular it is found that for certain ranges of viscous dampin g values, the rate of kinetic energy dissipation goes down when damping is increased. This has a profound effect on the criterion for chaos.