Variational integrators in discrete vakonomic mechanics (Q1935054)

The authors consider variational integrators in discrete vakonomic mechanics. They introduce new concepts: ``admissible section'', ``admissible infinitesimal variation'' and ``constrained variational integrator'', they show that critical sections are extremals of a variational problem without constraints canonically associated to the initial system (Lagrange multiplier rule), and show, under certain regularity conditions, that the integrators can be locally constructed from a generating function of the second kind in the sense of symplectic geometry. Examples on an isoperimetric problem and an optimal control problem illustrate the theoretical results.