The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

Details The Second Euler-Lagrange Equation of Variational Calculus on Time Scales The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

2010-03-30

arxiv.org/abs/1003.5826v1

Eur. J. Control 17 (2011), no. 1, 9-18

Mathematics

Optimization and Control

This work was partially presented at the Workshop in Control, Nonsmooth Analysis and Optimization, celebrating Francis Clarke'

Scientific paper

10.3166/EJC.17.9-18

The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and simpler proof to the Noether theorem on time scales recently obtained in [J. Math. Anal. Appl. 342 (2008), no. 2, 1220-1226].

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