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