An Action of A Regular Curve on $\mathbb{R}^{3}$ and Matlab Applications - Karakas, Bulent; Baydas, Senay (Journal of Informatics and Mathematical Sciences, 2013)
We define an action set of a regular curve not passing origin using a normed projection. If $α(t)$ is a regular curve not passing origin, then the curve $β(t)=\frac{α(t)}{\|α(t)\|}$ is on unit sphere. $β(t) $ is called normed projection of $α(t)$ \cite{3}. Every point $b(t)\inβ(t)$ defines an orthogonal matrix using Cayley's Formula. So we define an action set $R_{α }(t)\subset SO(3)$ of $α(t)$. We study in this article some important relations $α(t)$ and $R_{α }(P)$, orbit of point $P\in R^{3}$. At the end we give some applications in Matlab.