The Sliding Ball - Maple program as rollball.pdf

A rolling-sliding ball given arbitrary kinetic and rotational energy is analyzed in terms of a kinetic energy Lagrangian coupled to the differential anholonomic constraint of rolling without friction by means of a Lagrange multiplier. The Action 1-form defines a symplectic manifold of dimension 6, with a density distribution whose zero set corresponds to rolling without friction. The Torsion vector indicates an irreversible decay of momentum and energy until the singular condition of rolling without friction is obtained. From then on the process is on a contact manifold of dimension 5 and proceeds in a conservative Hamiltonian manner.


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