Permanent Rotations in Nonholonomic Mechanics. Omnirotational Ellipsoid

    2022, Volume 27, Number 6, pp.  587-612

    Author(s): Bizyaev I. A., Mamaev I. S.

    This paper is concerned with the study of permanent rotations of a rigid body rolling without slipping on a horizontal plane (i. e., the velocity of the point of contact of the ellipsoid with the plane is zero). By permanent rotations we will mean motions of a rigid body on a horizontal plane such that the angular velocity of the body remains constant and the point of contact does not change its position. A more detailed analysis is made of permanent rotations of an omnirotational ellipsoid whose characteristic feature is the possibility of permanent rotations about any point of its surface.
    Keywords: nonholonomic mechanics, poincare map, stability, permanent rotations
    Citation: Bizyaev I. A., Mamaev I. S., Permanent Rotations in Nonholonomic Mechanics. Omnirotational Ellipsoid, Regular and Chaotic Dynamics, 2022, Volume 27, Number 6, pp. 587-612

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