Variational Principles for multisymplectic second-order classical field theories

TL;DR

This paper presents a unified geometric framework for variational principles in second-order classical field theories, encompassing both Lagrangian and Hamiltonian formulations and deriving the associated field equations.

Contribution

It introduces a comprehensive geometric approach that unifies variational principles for second-order field theories, bridging Lagrangian and Hamiltonian methods.

Findings

Unified geometric variational principles for second-order theories

Recovery of standard Lagrangian and Hamiltonian field equations

Framework facilitates analysis of classical field theories

Abstract

We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.