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

Alexander A. Kilin and Elena N. Pivovarova ()
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Alexander A. Kilin: Ural Mathematical Center, Udmurt State University, Izhevsk 426034, Russia
Elena N. Pivovarova: Ural Mathematical Center, Udmurt State University, Izhevsk 426034, Russia

Mathematics, 2023, vol. 11, issue 18, 1-17

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.

Keywords: axisymmetric ellipsoid; vibrating plane; nonholonomic constraint; permanent rotations; vertical rotations; stability; vibrational potential; integrability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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