Angle measures, general rotations, and roulettes in normed planes

In this paper a special group of bijective maps of a normed plane (or, more generally, even of a plane with a suitable Jordan curve as unit circle) is introduced which we call the group of general rotations of that plane. 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 strong analogues to the Euler-Savary equations for Minkowskian roulettes is proved.