Angle measures, general rotations, and roulettes in normed planes

V. Balestro, Á. G. Horváth and H. Martini, Angle measures, general rotations, and roulettes in normed planes, Analysis and Mathematical Physics 7(4), pp. 549-575, 2017. (arXiv link) (journal link)

Comments: Fixing a Borel measure in the unit circle (or even in any star-like Jordan curve in the plane) one can define a group of “fixed angle rotations”. With this tool in hands, it is possible to define rigid motions of the plane. Finally, roulettes are defined and analogous to the Euler-Savary equations are obtained.