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Bifurcation Diagram of the Model of a Lagrange Top with a Vibrating Suspension Point

Author

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  • Pavel E. Ryabov

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 125993 Moscow, Russia
    Mechanical Engineering Research Institute of the Russian Academy of Sciences, 101990 Moscow, Russia
    These authors contributed equally to this work.)

  • Sergei V. Sokolov

    (Mechanical Engineering Research Institute of the Russian Academy of Sciences, 101990 Moscow, Russia
    Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia
    These authors contributed equally to this work.)

Abstract

The article considers a model system that describes a dynamically symmetric rigid body in the Lagrange case with a suspension point that performs high-frequency oscillations. This system, reduced to axes rigidly connected to the body, after the averaging procedure, has the form of the Hamilton equations with two degrees of freedom and has the Liouville integrability property of a Hamiltonian system with two degrees of freedom, which describes the dynamics of a Lagrange top with an oscillating suspension point. The paper presents a bifurcation diagram of the moment mapping. Using the bifurcation diagram, we presented in geometric form the results of the study of the problem of stability of singular points, in particular, singular points of rank zero and rank one.

Suggested Citation

  • Pavel E. Ryabov & Sergei V. Sokolov, 2023. "Bifurcation Diagram of the Model of a Lagrange Top with a Vibrating Suspension Point," Mathematics, MDPI, vol. 11(3), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:533-:d:1040590
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    Cited by:

    1. Alexander A. Kilin & Elena N. Pivovarova, 2023. "Stability of Vertical Rotations of an Axisymmetric Ellipsoid on a Vibrating Plane," Mathematics, MDPI, vol. 11(18), pages 1-17, September.

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