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Analytical Research of the Hopf Bifurcation in the Problem of Motion of the Rattleback

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Abstract

The motion problem for a heavy rigid body on a perfectly rough horizontal plane, which is a classical problem of the nonholonomic system dynamics, is considered. The effect from the loss of stability of a body’s permanent rotation at a certain critical value of its angular velocity is discussed. It is proven that this effect is accompanied by the occurrence of periodic motions of the body with a frequency close to the critical value; that is, the Hopf bifurcation takes place. It is proven by means of the direct calculation of the first Lyapunov coefficient that the corresponding periodic motions are unstable.

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Funding

The work was supported by the Russian Foundation for Basic Research, project no. 20-01-00637.

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Correspondence to A. S. Kuleshov or E. N. Pikunova.

Additional information

In memory of Professor A. V. Karapetyan (1950–2021)

Translated by A. Muravnik

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Kuleshov, A.S., Pikunova, E.N. Analytical Research of the Hopf Bifurcation in the Problem of Motion of the Rattleback. Vestnik St.Petersb. Univ.Math. 55, 203–211 (2022). https://doi.org/10.1134/S1063454122020078

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  • DOI: https://doi.org/10.1134/S1063454122020078

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