Complex Lagrangian dynamics

TL;DR

This paper introduces a formalism of classical mechanics using complex Lagrangian functions, extending traditional concepts to accommodate non-stationary motion and providing a geometric formulation and relation to complex Hamiltonian formalism.

Contribution

It presents the first comprehensive framework for complex Lagrangian mechanics, including complex Euler-Lagrange equations and a geometric approach, expanding classical mechanics into the complex domain.

Findings

Complex Lagrangian functions are formally introduced.

A geometric formulation of complex Lagrangian mechanics is developed.

The relation to complex Hamiltonian formalism is established.

Abstract

In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a geometric formulation, and the relation to a previous complex Hamiltonian formalism. The framework is particularly suitable for non-stationary motion, and various pathways can be followed in future investigation.