Effects of Curvature on Dynamics

TL;DR

This paper explores how curvature influences the dynamics of physical systems moving adiabatically in curved spaces, providing geometric insights and models for phenomena like the Foucault Pendulum and planetary perihelion shift.

Contribution

It offers a geometric framework to understand curvature effects on dynamics and presents models for phenomena such as perihelion shift without relying on higher-dimensional references.

Findings

Curvature affects the dynamics of systems in curved space.

Geometric models can explain phenomena like perihelion shift.

Intrinsic measurement of curvature is possible through dynamical effects.

Abstract

In this article we discuss the effect of curvature on dynamics when a physical system moves adiabatically in a curved space. These effects give a way to measure the curvature of the space intrinsically without referring to higher dimensional space. Two interesting examples, the Foucault Pendulum and the perihelion shift of planetary orbits, are presented in a simple geometric way. A paper model is presented to see the perihelion shift.