Nonlinearity · 1995 · 71 citations · 6 references
Natural SciencesMathematicsDynamical SystemsGeometryInvariant ManifoldsToric GeometryConstraint ManifoldGeometric MechanicsInvariant ToriPeriodic MotionQuasi-periodic DynamicsQuasi-periodic MotionQuasi-periodic OrbitsQuasi-periodic Oscillations
We consider the equations of motion of a dynamically symmetric sphere, rolling on a convex surface of revolution. We prove that the eight dimensional constraint manifold is filled up with tori of dimension at most three, on which we have quasi-periodic motion. The vector field on these tori depends on three coordinates only.
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<i>Classical Mechanics (2nd ed.)</i>
H. C. Corben, P. Stehle, Nicholas Chako · Physics Today · 1961 · 1.3K citations
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Non-holonomic Chaplygin systems
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