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Stability of Vertical Rotations of an Axisymmetric Ellipsoid on a Vibrating Plane

Author

Listed:
  • Alexander A. Kilin

    (Ural Mathematical Center, Udmurt State University, Izhevsk 426034, Russia)

  • Elena N. Pivovarova

    (Ural Mathematical Center, Udmurt State University, Izhevsk 426034, Russia)

Abstract

In this paper, we address the problem of an ellipsoid with axisymmetric mass distribution rolling on a horizontal absolutely rough plane under the assumption that the supporting plane performs periodic vertical oscillations. In the general case, the problem reduces to a system with one and a half degrees of freedom. In this paper, instead of considering exact equations, we use a vibrational potential that describes approximately the dynamics of a rigid body on a vibrating plane. Since the vibrational potential is invariant under rotation about the vertical, the resulting problem with the additional potential is integrable. For this problem, we analyze the influence of vibrations on the linear stability of vertical rotations of the ellipsoid.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3948-:d:1241667
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. Evgeny V. Vetchanin & Ivan S. Mamaev, 2024. "Numerical Analysis of a Drop-Shaped Aquatic Robot," Mathematics, MDPI, vol. 12(2), pages 1-17, January.

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