Friday, December 29, 2017

calculus - determine unit outward normal vector on a curve

It is necessary for me to find unit outward normal vector for the curve:



$$\gamma=(x(t),y(t))$$



where
$$x(t)=(0.6)\cos(t)-(0.3)\cos(3t)$$
and
$$y(t)=(0.7)\sin(t)+(0.07)\sin(7t)+(0.1)\sin(3t)$$
I know how to find unit outward normal vector for this: using




$$T=\frac{\gamma'(t)}{||\gamma(t)||},\;\text{ so }\,N=\frac{T'(t)}{||T(t)||}$$



but my problem is that I do not have $t$. Just I have $x(t)$ and $y(t)$.
How could I find $t$ or $N$ without need to $t$.



Is there any command in MATLAB or MAPLE to this?

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