Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

DOI10.1134/S1560354713040047zbMath1338.37033arXiv1306.4237MaRDI QIDQ381023

Juan Carlos Marrero, Luis C. García-Naranjo

Publication date: 15 November 2013

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4237

zbMATH Keywords

reductionsymmetriesnonholonomic mechanical systemsinvariant volume forms

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Nonholonomic dynamical systems (37J60)

Related Items (8)

Permanent rotations in nonholonomic mechanics. Omnirotational ellipsoid ⋮ Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints ⋮ An invariant measure and the probability of a fall in the problem of an inhomogeneous disk rolling on a plane ⋮ Unimodularity and preservation of volumes in nonholonomic mechanics ⋮ Dynamics and control of an omniwheel vehicle ⋮ Invariant measure in the problem of a disk rolling on a plane ⋮ Cartan meets Chaplygin ⋮ Hamiltonization of elementary nonholonomic systems

Cites Work

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• The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
• Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals
• Unimodularity and preservation of volumes in nonholonomic mechanics
• Nonholonomic mechanical systems with symmetry
• The nonexistence of an invariant measure for an inhomogeneous ellipsoid rolling on a plane
• On the geometry of generalized Chaplygin systems
• Invariant measures of nonholonomic flows with internal degrees of freedom
• Non-holonomic geodesic flows on Lie groups and the integrable Suslov problem onSO(4)

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