In this work we propose a new and more general approach to the calculus of
variations on time scales that allows to obtain, as particular cases, both
delta and nabla results. More precisely, we pose the problem of minimizing or
maximizing the composition of delta and nabla integrals with Lagrangians that
involve directional derivatives. Unified Euler-Lagrange necessary optimality
conditions, as well as sufficient conditions under appropriate convexity
assumptions, are proved. We illustrate presented results with simple examples.Comment: 7 pages, presented at the 2010 Chinese Control and Decision
Conference, Xuzhou, China, May 26-28, 201
