Generalized Chaplygins transformation and explicit integration of a system with a spherical support

MaRDI QIDQ6654193

I. S. Mamaev, Alexander A. Kilin, A. V. Borisov

Publication date: 18 December 2024

Published in: Nelineĭnaya Dinamika (Search for Journal in Brave)

zbMATH Keywords

isomorphismbifurcation analysisspherical supportnonholonomic mechanicsChaplygin ballexplicit integration

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Constrained dynamics, Dirac's theory of constraints (70H45) Nonholonomic systems related to the dynamics of a system of particles (70F25) Motion of a rigid body in contact with a solid surface (70E18) Nonholonomic dynamical systems (37J60)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Rubber rolling over a sphere
• Rolling of a non-homogeneous ball over a sphere without slipping and twisting
• The dynamics of Chaplygin ball: the qualitative and computer analysis
• Nonholonomic manipulators.
• Control of single wheel robots.
• Separable systems of Stäckel.
• LR and L+R systems
• Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's top

Related Items (10)

On the motion of a mechanical system inside a rolling ball ⋮ The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere ⋮ The problem of optimal control of a Chaplygin ball by internal rotors ⋮ Two non-holonomic integrable systems of coupled rigid bodies ⋮ On deformations of the canonical Poisson bracket for the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems on zero-level of the area integral. I ⋮ On the bi-Hamiltonian structure of the Chaplygin and Borisov-Mamaev-Fedorov systems at a zero constant of areas. II ⋮ On the Poisson structures for the Chaplygin ball and its generalizations ⋮ On the nonholonomic Veselova and Chaplygin systems ⋮ Topological analysis of one integrable system related to the rolling of a ball over a sphere ⋮ The dynamics of the Chaplygin ball with a fluid-filled cavity

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