Chaotic dynamics of an asymmetrical gyrostat

The chaotic motions of an asymmetrical gyrostat, composed of an asymmetrica l carrier and three wheels installed along its principal axes and rotating about the mass center of the entire system under the action of both damping torques and periodic disturbance torques, are investigated in detail in th is paper. By introducing the Deprit's variables, one can derive the attitud e dynamical equations that are well suited for the utilization of the Metni kov's integral developed by Wiggins and Shaw. By using the elliptic functio n theory, the homoclinic solutions of the attitude motion of a torque-free asymmetrical gyrostat are obtained analytically, based upon the Wangerin's method developed by Wittenburg. Transversal intersections of the stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) are detected by the techniques of Melnikov's functions. The bifurca tion curve between the compound parameters is depicted and discussed. By us ing a fourth-order Runge-Kutta integration algorithm as a tool of the numer ical simulation, the long-term dynamical behavior of the system shows that the technique of the Melnikov's function could successfully be employed to predict the compound physical parameters that correspond to the chaotic dyn amical motions of an asymmetrical gyrostat. (C) 2001 Elsevier Science Ltd. All rights reserved.