Dynamics of the \(n\)-dimensional Suslov problem

DOI10.1016/S0393-0440(99)00058-3zbMath0989.70010MaRDI QIDQ1576289

Dmitry V. Zenkov, Anthony M. Bloch

Publication date: 14 July 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

invarianceLie groupnonholonomic systemssymmetry groupreconstructionsystems with symmetryEuler topeffective reducibilityquasi-periodic flow\(n\)-dimensional Suslov problemnonholonomic momentumreconstruction equationreduced Lagrange-d'Alembert-Poincaré equationsrelative quasi-periodic orbits

Mathematics Subject Classification ID

Dynamical systems in classical and celestial mechanics (37N05) Nonholonomic systems related to the dynamics of a system of particles (70F25) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

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Quasi-periodicity in relative quasi-periodic tori ⋮ The phenomenon of reversal in the Euler-Poincaré-Suslov nonholonomic systems ⋮ Dynamics of an unbalanced disk with a single nonholonomic constraint ⋮ Interconnection of Lagrange–Dirac systems through nonstandard interaction structures ⋮ Hamiltonicity and integrability of the Suslov problem ⋮ Hirota-Kimura type discretization of the classical nonholonomic Suslov problem ⋮ Reduction of Dirac structures and the Hamilton-Pontryagin principle ⋮ Quasi-Chaplygin systems and nonholonomic rigid body dynamics ⋮ Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization ⋮ Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere ⋮ Nonintegrability of the Suslov problem ⋮ Asymptotic Hamiltonian dynamics: The Toda lattice, the three-wave interaction and the non-holonomic Chaplygin sleigh ⋮ Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method ⋮ Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors ⋮ Non-holonomic Euler-Poincare´ equations and stability in Chaplygin's sphere

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