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In this paper we study the relation between conserved quantities ofnonholonomic systems and the hamiltonization problem employing the geometricmethods of [1,3]. We illustrate the theory with classical examples describingthe dynamics of solids of revolution rolling without sliding on a plane. Inthese cases, using the existence of two conserved quantities we obtain, bymeans of 'gauge transformations' and symmetry reduction, genuine Poissonbrackets describing the reduced dynamics.

Hamiltonization of solids of revolution through reduction