Conserved quantities and Hamiltonization of nonholonomic systems

Abstract This paper studies hamiltonization of nonholonomic systems using geometric tools, building on [1] , [5] . The main novelty in this is the use symmetries and suitable first integrals system to explicitly define a new bracket reduced space that codifies dynamics carries, additionally, an almost symplectic foliation (determined by common level sets integrals); particular cases interest, Poisson structure hamiltonizes system. Our construction based gauge transformation global 2-form we describe. We study various features brackets apply our formulas obtain proof homogeneous ball rolling without sliding interior side convex surface revolution.