An Action of A Regular Curve on $\mathbb{R}^{3}$ and Matlab Applications

Bulent Karakas, Senay Baydas

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 $\beta(t)=\frac{\alpha(t)}{\|\alpha(t)\|}$ is on unit sphere. $\beta(t) $ is called normed projection of $\alpha(t)$ \cite{3}. Every point $b(t)\in\beta(t)$ defines an orthogonal matrix using Cayley's Formula. So we define an action set $R_{\alpha }(t)\subset SO(3)$ of $\alpha(t)$. We study in this article some important relations $\alpha(t)$ and $R_{\alpha }(P)$, orbit of point $P\in R^{3}$. At the end we give some applications in Matlab.

Keywords


Action set; Normed projection; Regular curve

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v5i3.220

eISSN 0975-5748; pISSN 0974-875X