Nonholonomic Constraints in Time-Dependent Mechanics
  The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle $Q\to R$ is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle $VQ$ of $Q\to R$, the Hamiltonian of a nonholonomic constrained system is constructed. 
G.Giachetta, L.Mangiarotti and G.Sardanashvily