Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy

Abstract

Incorporating both viscous friction torque and external torque, a mathematical model of a gyrostat system consisting of three rotors and a fixed outer frame is configured. This model is transformed into a Kolmogorov-type system for force analysis. The force field in the gyrostat system includes four different torques—inertial, internal, dissipative, and external. Correspondingly, four different energies are identified and the interconversion of energies is analyzed. The Casimir power being equivalent to the error power between the supplied power and the dissipative power is found and used to analyze the mechanism underlying the different dynamical behaviors. A four-wing chaotic attractor is found when the gyrostat is subject to a combination of inertial, internal, and dissipative torques as well as the addition of an external torque. The bifurcation of the Casimir power and leaps in Casimir energy level are used as indicators of the different definitive dynamics, which is demonstrated to be identical to that appearing in the state bifurcation and the Lyapunov exponent spectrum.

Existence of Solution and Self‐Exciting Attractor in the Fractional‐Order Gyrostat Dynamical System

“…Gyrostat is a device consisting of rotors, used as an attachment in larger objects for bringing stability in their dynamics with the passage of time. e system of threedimensional ordinary differential equations for the gyrostat model is designed by Qi et al [35]:…”

“…Analytical results (29)(30)(31)(32)(33)(34)(35) are explained in Figure 4, which illustrate trajectories of system (4) around their equilibrium points. Five different colors are used for each equilibrium point, which are also highlighted as a legend in Figure 4.…”

“…It has been observed from the above-cited work and our knowledge from the literature that dynamical systems related to spacecrafts or its attached devices such as beam and gyrostat have never been considered for the existence of solution and self-exciting attractors in a fractional-order form. erefore, we have restructured the gyrostat chaotic system [35] into a fractional order along with the addition of a rotatory liquid-filled tank to discuss its unique solution, bounds, and stability using the fixed point theory. Moreover, for bringing novelty into our work, a variation iteration scheme has been used in our proposed fractional-order system to observe chaos into it.…”

Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

“…In 2001, Kuang et al [9] used Deprit's variable for the first time to investigate chaos in the attitude motion of a gyrostat satellite. A mathematical model for the orbital motion of the attitude dynamics of a gyrostat attached to a satellite was derived by Abtahi [10], whereas Qi et al [11] modeled a chaotic gyrostat system with the aid of energies and external forces. In 2018, Chegini et al [12] assumed two rigid panels were attached with springs in a gyrostat to prove its chaotic nature, whereas they also investigated the existence of chaos in a satellite system [13] moving in an orbital path.…”

Dynamics analysis of a gyrostat system with intermittent forcing

“…15 The Melnikov method is used to study chaos on the complex spin-orbit dynamics of gyrostat system, and the heteroclinic bifurcation and chaotic vibrations are proved by numerical methods. 16 Qi and Yang 17 investigate the dynamical behaviors of the gyrostat system by different torques, and a four-wing chaotic attractor is found based on the bifurcation diagram and Lyapunov exponent spectrum.…”