Chaplygin's ball rolling problem is Hamiltonian
From MaRDI portal
Publication:1810010
DOI10.1023/A:1012995330780zbMath1030.70002OpenAlexW10942839MaRDI QIDQ1810010
Alexey V. Borisov, Ivan. S. Mamaev
Publication date: 15 June 2003
Published in: Mathematical Notes (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1023/a:1012995330780
Hamilton's equations (70H05) Nonholonomic systems related to the dynamics of a system of particles (70F25) Motion of a rigid body in contact with a solid surface (70E18)
Related Items
First integrals and symmetries of nonholonomic systems ⋮ Adiabatic invariants, diffusion and acceleration in rigid body dynamics ⋮ Chaplygin's ball with a rotor: non-degeneracy of singular points ⋮ On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals ⋮ Generalisation of Chaplygin’s reducing multiplier theorem with an application to multi-dimensional nonholonomic dynamics ⋮ Conserved quantities and Hamiltonization of nonholonomic systems ⋮ Rolling balls over spheres in $ \newcommand{\m}{\mathfrak m} {\mathbb{R}^n}$ ⋮ Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics ⋮ Hamiltonization and integrability of the Chaplygin sphere in \(\mathbb R^{n}\) ⋮ One family of conformally Hamiltonian systems ⋮ Hamiltonization of solids of revolution through reduction ⋮ Gyroscopic Chaplygin systems and integrable magnetic flows on spheres ⋮ Momentum map reduction for nonholonomic systems ⋮ Two nonholonomic chaotic systems. II: On the rolling of a nonholonomic bundle of two bodies ⋮ Symmetries and reduction in nonholonomic mechanics ⋮ Integrable discretization and deformation of the nonholonomic Chaplygin ball ⋮ Comparison of the system ``Chaplygin ball with a rotor and the Zhukovskii system from the rough Liouville equivalence point of view ⋮ On the Chaplygin problem of the rolling of a ball ⋮ Dynamics of the Chaplygin ball on a rotating plane ⋮ Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems ⋮ Chaplygin ball over a fixed sphere: an explicit integration ⋮ Hamiltonization of the generalized Veselova LR system ⋮ The problem of drift and recurrence for the rolling Chaplygin ball ⋮ Rubber rolling over a sphere ⋮ Reduction of almost Poisson brackets for nonholonomic systems on Lie groups ⋮ Gauge momenta as Casimir functions of nonholonomic systems ⋮ Stochastic Chaplygin systems ⋮ Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups ⋮ Gauge transformations, twisted Poisson brackets and Hamiltonization of nonholonomic systems ⋮ Topological types of isoenergy surfaces in the system of the Chaplygin ball with a rotor ⋮ On the Lie integrability theorem for the Chaplygin ball ⋮ Poisson structures for two nonholonomic systems with partially reduced symmetries ⋮ The geometry of nonholonomic Chaplygin systems revisited ⋮ Integrability of the \(n\)-dimensional axially symmetric Chaplygin sphere ⋮ Different models of rolling for a robot ball on a plane as a generalization of the Chaplygin ball problem ⋮ Cartan meets Chaplygin ⋮ Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere ⋮ Demchenko’s nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis ⋮ ON GENERALIZED NONHOLONOMIC CHAPLYGIN SPHERE PROBLEM ⋮ Hamiltonization and separation of variables for a Chaplygin ball on a rotating plane ⋮ Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds ⋮ Dynamics of the Chaplygin sphere with additional constraint ⋮ A geometric characterization of certain first integrals for nonholonomic systems with symmetries
This page was built for publication: Chaplygin's ball rolling problem is Hamiltonian
