Time scale differential, integral, and variational embeddings of Lagrangian systems

Jacky Cresson (1) , A.B. Malinowska (2) , D.F.M. Torres (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Faculty of Computer Science - University of Białystok

We introduce 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. © 2012 Elsevier Ltd. All rights reserved.

Domaines: Equations aux dérivées partielles [math.AP]

Jacky Cresson, A.B. Malinowska, D.F.M. Torres. Time scale differential, integral, and variational embeddings of Lagrangian systems. Computers & Mathematics with Applications, 2012, 64 (7), pp.2294-2301. ⟨10.1016/j.camwa.2012.03.003⟩. ⟨hal-00865003⟩