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

  • Authors:

  • Jacky Cresson;Agnieszka B. Malinowska;Delfim F. M. Torres

  • Affiliations:

  • Laboratoire de Mathématiques Appliquées de Pau, Université de Pau, Pau, France and Institut de Mécanique Céleste et de Calcul des íphémérides, Observatoire ...;Faculty of Computer Science, Białystok University of Technology, 15-351 Białystok, Poland and R&D Unit CIDMA, University of Aveiro, 3810-193 Aveiro, Portugal;R&D Unit CIDMA, University of Aveiro, 3810-193 Aveiro, Portugal and Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2012

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Abstract

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.