| Abstract: |
| In Hamiltonian mechanics there is a strong relationship between the presence of symmetries and the existence of first integrals. In nonholonomic mechanics the situation is different: the variational and hence the Hamiltonian character of the dynamics is broken by the presence of nonholonomic constraints and Noether`s Theorem does not hold anymore. Nevertheless, in the last forty years there have been various approaches to extend Noether`s Theorem to the nonholonomic framework. Many interesting structures and results as nonholonomic momentum map, nonholonomic reduction, Hamiltonisation and gauge momenta have been introduced and obtained. In this talk I will give a characterization of the number of horizontal gauge momenta that certain nonholonomic systems with symmetry may admit and I will link this to the broad integrability of these systems themselves. |
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