Almost poisson spaces and nonholonomic singular reduction

Dynamics of Hamiltonian systems with linear nonholonomic constraints is described by distributional Hamiltonian systems. We show that the space of orbits of a proper action of a symmetry group of a distributional Hamiltonian system is a differential space partitioned by smooth manifolds preserved by the evolution. The reduced dynamics is given by distributional Hamiltonian systems on the projections of the manifolds of the partition. It is described in terms of the almost Poisson algebra of smooth functions on the orbit space.