The geometry of the Routh problem

DOI10.1007/BF01209025zbMath0864.70004MaRDI QIDQ2564216

Dmitry V. Zenkov

Publication date: 26 January 1997

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

invariant torisurface of revolutionsufficient condition for stabilityquasiperiodic motionshomogeneous ballmotion without slidingnecessary condition for stabilitynondegenerate invariant manifoldsstationary periodic motions

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Free motion of a rigid body (70E15)

Related Items (12)

Conservation of `moving' energy in nonholonomic systems with affine constraints and integrability of spheres on rotating surfaces ⋮ First integrals and symmetries of nonholonomic systems ⋮ Nonholonomic mechanical systems with symmetry ⋮ Quasivelocities and symmetries in non-holonomic systems ⋮ On the dynamics of a heavy symmetric ball that rolls without sliding on a uniformly rotating surface of revolution ⋮ The geometry and integrability of the Suslov problem ⋮ Conserved quantities and Hamiltonization of nonholonomic systems ⋮ On some aspects of the dynamics of a ball in a rotating surface of revolution and of the kasamawashi art ⋮ Momentum map reduction for nonholonomic systems ⋮ Poisson structures for two nonholonomic systems with partially reduced symmetries ⋮ Various approaches to conservative and nonconservative nonholonomic systems ⋮ The energy-momentum method for the stability of non-holonomic systems

Cites Work

• On a Routh problem
• Nonholonomic reduction
• Nonholonomic mechanical systems with symmetry
• Lectures on Mechanics
• A symmetric sphere rolling on a surface
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