Canonical variational completion of differential equations

TL;DR

This paper introduces a method to convert non-variational differential equations into variational ones using the Vainberg-Tonti Lagrangian, with applications in physics.

Contribution

It proposes a novel approach to derive correction terms for non-variational systems based on the Vainberg-Tonti Lagrangian.

Findings

Effective correction terms derived for differential equations.

Applications demonstrated in general relativity and classical mechanics.

Provides a systematic way to variationally complete differential equations.

Abstract

Given a non-variational system of differential equations, the simplest way of turning it into a variational one is by adding a correction term. In the paper, we propose a way of obtaining such a correction term, based on the so-called Vainberg-Tonti Lagrangian, and present several applications in general relativity and classical mechanics.