Reduction of Dirac structures and the Hamilton-Pontryagin principle (Q925787)

The paper establishes a geometric reduction theory for Dirac structures. Dirac structures have been introduced in order to synthesize Poisson structures and pre-symplectic structures. In this work, the authors consider the case when the configuration manifold is a Lie group. Then, they investigate a reduction of Dirac structures which includes in a unified way the reduction of implicit Lagrangian systems and reduction of implicit Hamiltonian systems. The link with the Hamilton-Pontryagin principle is then discussed. Finally, they construct the associated Euler-Poincaré-Suslov and Lie-Poisson Suslov reductions, together with the Suslov problem in nonholonomic mechanics.