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Non-Linear Resonances and Chaotic Dynamics of a Rotating Gyroscope Under a Fractional Order Derivative Damping

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Abstract

This paper deals with the action of the fractional order derivative on nonlinear resonances and its analysis on the chaotic dynamics of an excited rotating gyroscope has been investigated. After the mathematical modeling of the system, we determined the possible resonances of the system using the method of multiple scales. The stability conditions for each resonance were obtained using the Routh-Hurwitz criterion. The different system parameters have been studied and it is concluded that the different resonance states can be controlled by each of the system parameters. Moreover, using bifurcation diagrams, Lyapunov exponents, phase portraits and time series, it was shown that for certain values of the parameters the considered gyroscope exhibits several rich dynamics. The chaos has been reduced, even eliminated with the progressive increase of the other parameters, in particular of the order \( \mu \) of the fractional derivative up to a certain value.

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Authors and Affiliations

  1. Laboratoire de la Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Bénin

    S. O. Hounnan, C. H. Miwadinou & V. A. Monwanou

  2. Research Unit of Industrial Systems Engineering and Environment (URISEE, Fotso Victor University Institute of Technology, University of Dschang, Dschang, Cameroon

    P. R. Nwagoum Tuwa

  3. Département de Physique, ENS-Natitingou, Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM), Abomey, Bénin

    C. H. Miwadinou

  4. Laboratoire de Physique et Applications (LPA) du Centre Universitaire de Natitingou, Université Nationale des Sciences, Technologiques, Ingénierie et Mathématiques (UNSTIM), Abomey, Bénin

    C. H. Miwadinou

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  1. S. O. Hounnan
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  2. P. R. Nwagoum Tuwa
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  3. C. H. Miwadinou
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  4. V. A. Monwanou
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Correspondence to C. H. Miwadinou.

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Hounnan, S.O., Tuwa, P.R.N., Miwadinou, C.H. et al. Non-Linear Resonances and Chaotic Dynamics of a Rotating Gyroscope Under a Fractional Order Derivative Damping. Int J Theor Phys 63, 89 (2024). https://doi.org/10.1007/s10773-024-05620-z

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