Evolution of Ehresmann's jet theory

TL;DR

This paper discusses modifications to Ehresmann's jet theory to reduce its reliance on local coordinates and explores its applications in calculus of variations and mechanics.

Contribution

It introduces coordinate-independent modifications to jet theory and extends its applications to variational calculus and mechanics.

Findings

Reduced coordinate dependence in jet theory.

Extended jet theory applications to mechanics.

Proposed new formulations for variational calculus.

Abstract

Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions of the theory with applications to the calculus of variations and mechanics are also proposed.