On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework

The structure of the equations of motion of a time-dependent mechanical sys tem, subject to time-dependent non-holonomic constraints, Is investigated i n the Lagrangian as well as in the Hamiltonian setting. The treatment appli es to systems with general nonlinear constraints, and the ambient space in which the constraint submanifold is embedded is equipped with a cosymplecti c structure. In analogy with the autonomous case, it is sl:own that one can define an almost-Poisson structure on the constraint submanifold, which pl ays;I prominent role in the description of nonholonomic dynamics. Moreover, it is seen that the corresponding almost-Poisson bracket can also be inter preted as a Dirac-type bracket. Systems with a Lagrangian of mechanical typ e sind affine non-holonomic constraints are treated as a special case and t wo examples are discussed. AMS classification scheme numbers: 58F05, 70F25. 70Hxx.