Relativistic and Non-relativistic Equations of Motion

TL;DR

This paper demonstrates that non-relativistic second order equations of motion can be interpreted as geodesic equations with respect to a non-linear connection, establishing a link between relativistic and non-relativistic dynamics.

Contribution

It introduces a geometric framework connecting non-relativistic equations of motion to relativistic geodesic equations via non-linear connections.

Findings

Non-relativistic equations can be viewed as geodesics in a suitable geometric setting.

A relationship between relativistic and non-relativistic equations of motion is established.

The approach provides a unified geometric perspective on dynamics.

Abstract

It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.