Gibbs-Appel Formulation of Non-Holonomic Motion of a Ball on a Spherical Surface

Abstract eng:
A new type of a passive vibration absorber is proposed and investigated as a non-linear non-holonomic system. It consists of Wherical horizontal cavity in which a ball of a smaller diameter is rolling. The system of six degrees of freedom with three non- holonomic constraints is investigated. Instead of conventional way via Hamiltonian functional and Lagrangian procedure, the respective differential system is derived using the Gibbs-Appel function and related steps. Comparison of both approaches has been done. The system has an auto-parametric character and hence the semi-trivial solution and dynamic stability is investigated. Some principal post-critical regimes are outlined and qualitatively evaluated in the resonance neighborhood. Numerical experiments are performed and physically interpreted.

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