Lagrangian formalism and Noether-type theorems for second-order delay ODEs

TL;DR

This paper develops a Lagrangian formalism and Noether-type theorems for second-order delay differential equations, providing a framework for deriving conserved quantities from symmetries in such systems.

Contribution

It introduces a novel Lagrangian formalism and Noether-type theorems specifically for second-order delay ODEs, expanding the theoretical tools available for these equations.

Findings

Derived Noether-type operator identities for second-order delay ODEs

Presented algebraic methods to construct integrals based on symmetries

Demonstrated the approach with illustrative examples

Abstract

The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction of integrals for DODEs based on symmetries are demonstrated by examples.