A Monge normal form for the rolling distribution

TL;DR

This paper introduces a Monge normal form for the rolling distribution of two hyperboloid surfaces, utilizing a specific parametrization of sl_2 related to fractional linear transformations.

Contribution

It presents a novel Monge normal form for the rolling distribution of hyperboloids based on a specialized sl_2 parametrization from Clarkson and Olver's work.

Findings

Derived a Monge normal form for hyperboloid rolling

Connected group action parametrization to geometric rolling

Provided a new framework for analyzing hyperboloid interactions

Abstract

Using a parametrisation of $sl_2$ given by the second prolongation of the group action of unimodular fractional linear transformations as presented in an article of Clarkson and Olver, we find a Monge normal form describing the rolling of two hyperboloid surfaces over each other.