Integrable Euler top and nonholonomic Chaplygin ball

Abstract

We discuss the Poisson structures, Lax matrices, $r$-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.

25 pages, LaTeX with AMS fonts, final version

References in corpus (9)

• Chaplygin ball over a fixed sphere: explicit integration
• Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
• On the Integration Theory of Equations of Nonholonomic Mechanics
• Poisson Yang-Baxter maps with binomial Lax matrices
• New variables of separation for particular case of the Kowalevski top
• On the generalized integrable Chaplygin system
• On natural Poisson bivectors on the sphere
• On bi-hamiltonian geometry of the Lagrange top
• Chaplygin systems associated to Cartan decompositions of semi-simple Lie algebras

Cited by in corpus (15)

• Rattleback: a model of how geometric singularity induces dynamic chirality
• One invariant measure and different Poisson brackets for two nonholonomic systems
• Integrable discretization and deformation of the nonholonomic Chaplygin ball
• On the Routh sphere problem
• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations
• Remarks on N=1 supersymmetric extension of the Euler top
• On the Lie integrability theorem for the Chaplygin ball
• Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere
• Simple non-Hamiltonian systems with an invariant measure
• Integrability of Nonholonomic Heisenberg Type Systems
• On Integrable Perturbations of Some Nonholonomic Systems
• On generalized nonholonomic Chaplygin sphere problem
• On the nonholonomic Stubler model
• Poisson structures for two nonholonomic systems with partially reduced symmetries