Linearization of nonlinear connections on vector and affine bundles, and some applications

TL;DR

This paper introduces an intrinsic linearization method for nonlinear connections on vector and affine bundles, enabling applications in Classical Mechanics by transforming complex connections into linear ones.

Contribution

It presents a new intrinsic linearization procedure for nonlinear connections on vector and affine bundles, with applications demonstrated in Classical Mechanics.

Findings

A linearization procedure for nonlinear connections is developed.

The method is intrinsic and applicable to affine bundles after homogenization.

Applications in Classical Mechanics are successfully demonstrated.

Abstract

A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization and restriction. Several applications in Classical Mechanics are provided.