On the discrete-continuous dynamical systems

Abstract

The main idea of our study is a direct treatise of the dynamical systems of discrete-continuous type our aim is to: formulate a discrete-continuous variational principle and deduce the discrete-continuous Euler-Lagrange equations (solution for the direct problem); establish the selfadjointing conditions of Helmholtz type for difference equation systems (solution for the inverse problem); study the question of the conservation laws for discrete Lagrangians and formulate a discrete version of the Noether’s theorem; obtain the discrete Euler-Lagrange-Hamilton equations based on a result established in the section 2.