Control problems on principal bundles and nonholonomic mechanics

The authors investigate some problems of open-loop control defined on principal bundles with connections. The explicit solvability of related optimal control problems from a Hamiltonian point of view is addressed. The motivations for these problems arise in the study of certain nonholonomic mechanical systems with symmetry. The authors focus on a model problem admitting SO(3) as the group of symmetries. The physical setting of this model problem corresponds to a rigid body with two oscillators. Under suitable hypotheses and approximations, symplectic and Poisson reduction is applied