On the Motion of a Curve or Surface Rolling Over Another Curve or Surface in Multiplicative Calculus

This study revisits the notion of “On the motion of a curve or surface rolling over another curve or surface in multiplicative calculus and develops a broader formulation of it within the framework of homothetic motionsin Multiplicative Euclidean spaces of arbitrary dimension n. The findings ofthe paper may be outlined as follows:The behavior of the motion remains the same regardless of whether n is an even or an odd integer;for any dimension n, homothetic motions represent a class of regular motions, where the associated polar trajectories exhibit a mutual sliding and rolling interaction; at each instant t, a single instantaneous pole point can be uniquely determined. The results obtained here are discussed in relation to previously published investigations in the same area. As a finalremark, it is shown that the a¢ ne situation appears as a special case in which the homothetic scaling factor is constantly equal to e1 = e.