Gyrostat Model Regular And Chaotic Behavior

Abstract

AbstractDuring recent years, the interest in the phenomena of chaos in gyroscopic systems has been increasing. It is well-known, that depending on the speed of rotation, a gyroscopic system may lose or gain stability. Despite the overwhelming number of studies reporting the occurrence of various chaotic structures, little is known yet about the construction details and the generality of the underlying bifurcation scenarios that give rise to such chaotic (complex) behaviour.In this paper, we report a detailed investigation of the abundance of regular and chaotic behaviour for rigid body (gyrostat) motion. The model contains 6 parameters that may be tuned to produce rich dynamical scenarios. The results confirm that homoclinic and heteroclinic structures with two fixed points from saddle-focus type occur and the emergence of Shilnikov chaos takes place. Finally, we find new results concerning the system’s evolution and bifurcation scenarios for its routes to chaos.