Two problems are the main contents of this paper. The first one is the problem of so-called ‘unnatural’ constraints, which are obtained by a limiting process and are nonlinear in the velocities. For these constraints the generalized d’Alembert principle is not valid anymore. The second one is the reduction problem for mechanical systems with nonholonomic constraints.
The author proposes a geometric setting for the Hamiltonian description of these systems and compares his approach where he considered only time-independent constraints to the known ones. The realization of these possibly nonconservative systems can now be found in sensors, servomechanisms and other high tech devices. The kinematic properties of the constraint are described by the Hamiltonian constraint submanifold of the phase space whereas the dynamical properties by a vector subbundle of the tangent bundle to the phase space along the Hamiltonian constraint submanifold. The author generalizes the setting by using a Poisson structure on the phase space instead of the canonical symplectic structure of a cotangent bundle. So a very straightforward reduction procedure can now be applied.