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

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  • Guoyuan Qi
  • Xiaogang Yang

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.

Suggested Citation

  • Guoyuan Qi & Xiaogang Yang, 2019. "Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    • Handle: RePEc:hin:complx:5439596
    DOI: 10.1155/2019/5439596
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    References listed on IDEAS

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    1. Qi, Guoyuan & Zhang, Jiangfeng, 2017. "Energy cycle and bound of Qi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 7-15.
    2. Pelino, Vinicio & Maimone, Filippo & Pasini, Antonello, 2014. "Energy cycle for the Lorenz attractor," Chaos, Solitons & Fractals, Elsevier, vol. 64(C), pages 67-77.
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    Cited by:

    1. Muhammad Marwan & Vagner Dos Santos & Muhammad Zainul Abidin & Anda Xiong, 2022. "Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems," Mathematics, MDPI, vol. 10(11), pages 1-15, June.

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