Differential, integral, and variational delta-embeddings of Lagrangian   systems
  We introduce the differential, integral, and variational delta-embeddings. We prove that the integral delta-embedding of the Euler-Lagrange equations and the variational delta-embedding coincide on an arbitrary time scale. In particular, a new coherent embedding for the discrete calculus of variations that is compatible with the least action principle is obtained. 
Jacky Cresson, Agnieszka B. Malinowska, Delfim F. M. Torres
math.OC