Hamiltonization of solids of revolution through reduction (Q1685149)

The connection between the presence of conserved quantities for a nonholonomic system and its hamiltonization is analyzed. The geometric techniques developed in [the author and \textit{L. C. García-Naranjo}, Arch. Ration. Mech. Anal. 205, No. 1, 267--310 (2012; Zbl 1284.70028); the author, Arch. Ration. Mech. Anal. 214, No. 2, 453--501 (2014; Zbl 1321.70014)] are used to show that ``for certain types of symmetries admitting conserved quantities, one can distinguish particular 2-forms that can be used to modify the classical nonholonomic bracket (by means of gauge transformations); the reduction in such modified brackets to the orbit space are genuine Poisson brackets, relative to which the reduced equations of motion are hamiltonian.'' As application, the hamiltonization of solids of revolution rolling on a plane without sliding and the classical example of an inhomogeneous ball rolling on a plane are established.