An extended Lagrangian formalism

TL;DR

This paper introduces an extended Lagrangian formalism that generalizes the classical Lagrangian binomial to functions with higher-order derivatives, enabling broader applications in classical mechanics.

Contribution

It presents a simple formal procedure to extend the Lagrangian binomial to functions of any order derivatives, broadening the scope of classical Lagrangian mechanics.

Findings

Generalized equations of motion recover classical formulations

Provides Lagrangian components for a wide class of forces

Extends the properties of the Lagrangian binomial to higher derivatives

Abstract

A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the lagrangian components, in the classical sense of the Newton's law, for a quite general class of forces. At the same time, the generalized equations of motions recover some of the classical alternative formulations of the Lagrangian equations.