Heteroclinic Bifurcations in Rigid Bodies Containing Internally Moving Parts and a Viscous Damper

• Published in: Journal of applied mechanics 1999-09, Vol.66 (3), p.720-728
• Main Authors: Gray, G. L, Kammer, D. C, Dobson, I, Miller, A. J
• Format: Article
• Language: English
• Subjects: Bifurcation (mathematics); Chaos theory; Damping; Energy dissipation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Kinetic energy; Maneuverability; Perturbation techniques; Physics; Rigidity; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Torque
• ISSN: 0021-8936; 1528-9036
• DOI: 10.1115/1.2791660

Melnikov’s method is used to analytically study chaotic dynamics in an attitude transition maneuver of a torque-free rigid body in going from minor axis to major axis spin under the influence of viscous damping and nonautonomous perturbations. The equations of motion are presented, their phase space is discussed, and then they are transformed into a form suitable for the application of Melnikov’s method. Melnikov’s method yields an analytical criterion for homoclinic chaos in the form of an inequality that gives a necessary condition for chaotic dynamics in terms of the system parameters. The criterion is evaluated for its physical significance and for its application to the design of spacecraft. In addition, the Melnikov criterion is compared with numerical simulations of the system. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping are investigated. In particular, it is found that for certain ranges of viscous damping values, the rate of kinetic energy dissipation goes down when damping is increased. This has a profound effect on the criterion for chaos.