Approximate Solutions of Nonsmooth Systems via Generalized Euler-Lagrange and Hamiltonian Equations
S. Soradi Zeid *
Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran and Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
M. Yousefi
National Iranian Oil Products Distribution Company (NIOPDC), Zahedan Region, Zahedan, Iran
A. Vahidian Kamyad
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
*Author to whom correspondence should be addressed.
Abstract
Recently the traditional calculus of variations has been extended to be applicable for systems
containing nonsmooth function. In this paper, we have investigated the generalized derivative
of nonsmooth functions. The obtained results were applied to investigate the generalized Euler-
Lagrange and Hamilton equations for constrained system. The approach was applied within an
illustrative.
Keywords: Generalized Derivative, calculus of variations, Euler-Lagrange equation, Hamilton equation