Linear connections and shape maps for second order ODEs with and without constraints

TL;DR

This paper introduces a novel method for constructing linear connections related to second order ODEs, including constrained cases, providing explicit formulas for the Massa-Pagani connection and its extension.

Contribution

It presents a new approach to glue submodule covariant derivatives, enabling explicit construction of connections for second order ODEs with and without constraints.

Findings

Explicit formulas for Massa-Pagani connection

Extension of connections to constrained ODEs

A novel method for gluing covariant derivatives

Abstract

We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method allowing glueing of submodule covariant derivatives to produce new, closed form expressions for the Massa-Pagani connection and our extension of it to the constrained case.