An analytical approach to the external force-free motion of pendulums on surfaces of constant curvature

TL;DR

This paper develops an analytical framework for understanding the force-free motion of pendulums on curved surfaces, with potential applications to elastic and quantum pendulums, by deriving the system's Lagrangian.

Contribution

It introduces a novel analytical approach to model pendulum dynamics on surfaces of constant curvature, extending classical mechanics to curved geometries.

Findings

Derived the Lagrangian for pendulums on curved surfaces.

Provided a basis for studying elastic and quantum pendulums in curved spaces.

Enhanced understanding of force-free motion in non-Euclidean geometries.

Abstract

The dynamics of force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagragian of the system. As a application it is possible the study of elastic and quantum pendulums.