Hamiltonian dynamics and constrained variational calculus: continuous   and discrete settings
  The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained. 
Manuel de Leon, Fernando Jimenez and David Martin de Diego
math-ph math.DG math.MP math.NA