Angle measures, general rotations, and roulettes in normed planes

TL;DR

This paper introduces the concept of general rotations in normed planes, expanding the understanding of plane motions and roulettes, and proves an analogue of the Euler-Savary equations in this context.

Contribution

It defines the group of general rotations in normed planes, extending the isometry group, and develops Minkowskian roulettes and motions with a new approach.

Findings

Established the group of general rotations as a superset of isometries.

Proved an analogue of the Euler-Savary equations for Minkowskian roulettes.

Linked general rotations to flexible motions in normed planes.

Abstract

In this paper a special group of bijective maps of a normed plane, called the group of general rotations, is introduced; it contains the isometry group as a subgroup. The concept of general rotations leads to the notion of flexible motions of the plane, and to the concept of Minkowskian roulettes. As a nice consequence of this new approach to motions the validity of a strong analogue to the Euler-Savary equations for Minkowskian roulettes is proved.