New developments in geometric mechanics

TL;DR

This paper reviews graded bundles, a generalization of vector bundles, and explores their applications in geometric mechanics, including higher order Lagrangian systems and the Plateau problem.

Contribution

It introduces the concept of graded bundles and demonstrates their applications in advanced geometric mechanics problems.

Findings

Graded bundles generalize vector bundles and their linearizations.

Applications include higher order Lagrangian systems.

Insights into the Plateau problem using geometric structures.

Abstract

We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with higher order Lagrangian and the Plateau problem.