An Action of a Regular Curve on R3 and Matlab Applications

Abstract

We define an action set of a regular curve not passing origin using a normed projection. If alpha(t) is a regular curve not passing origin, then the curve beta( t) = alpha( t)/parallel to alpha(t)parallel to is on unit sphere. beta(t) is called normed projection of alpha(t) [ 3]. Every point b(t) subset of beta(t) defines an orthogonal matrix using Cayley's Formula. So we define an action set R-alpha(t) subset of SO(3) of alpha(t). We study in this article some important relations alpha(t) and R-alpha(P), orbit of point P is an element of R-3. At the end we give some applications in Matlab.