Kinematik in der Laguerre-Ebene II: 97-0197-0197-01-Bewegungen mit Polkurven

This second part of kinematics in the Laguerre-plane contains differential geometric properties of -motions. In this paper we consider only such -motions which are instantaneous products of a rotation and a homothetic transformation with common center. The centers, called poles of a -motion, generate a curve on a ruled surface consisting of fixed lines. First we investigate the dependence of a -motion on the pair of strips along the pole curves which contact each other. Furthermore the points with isotropic tangents of their paths lie on a cone at each time of a -motion. On this cone there exist curves of some interest like the curves of the cycles of inflection and of the vertical cycles and the Bresse-curves. The isotropic tangents of the paths in the cycles of inflection define a socalled hypercycle of Blaschke.