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Question: Draw the osculating circle of a curve

Question:Draw the osculating circle of a curve

pyr0rrzzz 145 Maple
October 26 2009
0

Hi, I need to plot the curve specified by t->(t,t^3) as well as its osculating circle at several points. I know how to compute the radius of the circle but I have no idea how to get the whole thing.

I tried the following:

> g := PositionVector([s, s^3]);
> V := VectorCalculus[`+`](VectorCalculus[`+`](g, VectorCalculus[`*`](PrincipalNormal(g, s, normalized), RadiusOfCurvature(g))), PositionVector([VectorCalculus[`*`](RadiusOfCurvature(g), cos(s)), VectorCalculus[`*`](RadiusOfCurvature(g), sin(s))]));

But I don't know how to plot V as it isn't a position vector anymore.


Thanks in advance.
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