Energy mechanism analysis for chaotic dynamics of gyrostat system and simulation of displacement orbit using COMSOL

Abstract

Most of the existing research on gyrostat systems uses the Melnikov method to analyze chaotic dynamic characteristics. The mechanism of chaotic motion from the energy perspective of gyrostat systems has rarely been analyzed. The gyrostat system with positive damping disturbance is modeled in this paper. Casimir energy and power are given. The mechanism of the orbital expansion and contraction of the gyrostat is revealed through the sign change of Casimir power and the ellipsoid of Casimir energy. The bifurcations of the Casimir power corresponding to the state bifurcation and Lyapunov exponent spectrum reflect the evolution and transition of gyrostat's dynamics. The energy-level leap expressed by the variance of Casimir energy is found to determine the bifurcation of dynamics for the first time. The coexistence of the gyrostat is explained using Casimir power and local stability of equilibrium point. The COMSOL finite element simulation platform is built to study the state changes of the displacement orbit of the frame gyrostat model. A comparison is performed for the displacement results conducted by the COMSOL and the numerical simulation for the gyrostat system kinematic model. The different displacement states of the gyrostat system under free motion and in the presence of damping disturbance and external torques are obtained.