Hamiltonian Formalism in the Presence of Higher Derivatives

TL;DR

This paper reviews Hamiltonian formalism in classical mechanics for systems with Lagrangians involving multiple derivatives, including non-local models with infinitely many derivatives, highlighting the extension of traditional methods.

Contribution

It provides a concise overview of Hamiltonian formalism adaptations for higher-derivative and non-local models in classical mechanics.

Findings

Summarizes Hamiltonian formulas for higher-derivative Lagrangians.

Extends formalism to non-local models with infinite derivatives.

Clarifies the structure of Hamiltonian dynamics in complex systems.

Abstract

A short review of basic formulas from Hamiltonian formalism in classical mechanics in the case when Lagrangian contains N time-derivatives of n coordinate variables. For non-local models N=infinity.