| Abstract: |
| We analyse the dynamics of the n-dimensional generalisation of the classical nonholonomic Veselova system introduced by Fedorov and Kozlov and treated before by Fedorov and Jovanovic. Our main contribution is to show that under certain symmetric assumptions on the mass distribution of the body, the dynamics is integrable. We proceed by performing a detailed symmetry analysis that allows us to reduce the system to a singular semi-algebraic space where the dynamics is periodic. Our approach allows us to recover all the known cases of integrability that correspond to physical inertia tensors (that turn out to be axi-symmetric bodies) and to determine new ones (that we term cylindrical bodies). Moreover, in both cases we conclude quasi-periodicity of the flow in the natural time variable and without the need of a time reparametrisation. The result is particularly interesting for the cylindrical case considering that the system does not seem to allow a Chaplygin Hamiltonization. |
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