Torsten
Posts:
1,136
Registered:
11/8/10
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Re: Spiral with constant velocity (same distance betwee coordinate)
Posted:
Feb 27, 2013 2:26 AM
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On 26 Feb., 20:56, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> "Torsten" wrote in message <kghobs$5q...@newscl01ah.mathworks.com>...
> > Given a point on the spiral
> > (t0*cos(t0)*Width,t0*sin(t0)*Width),
> > the distance squared to another point on the spiral is given by
> > d^2=(t*cos(t)*Width-t0*cos(t0)*Width)^2 + (t*sin(t)*Width-t0*sin(t0)*Width)^2.
> > This is a quadratic equation in t you can solve analytically.
>
> I don't think it's quadratic in t.
>
> It is plausible to imagine a circle centered about a fixed point that might intersect the spiral in as much as many considered turns (take a very large circle, where the arc looks like almost a radial line). An equation that has more than 2 solutions cannot be a quadratic polynomial equation.
>
> Bruno
You are right ; I only saw the quadratic term and didn't notice that
the linear term still
contains trigonometric expressions in t.
So I think there is no other way than to solve the above nonlinear
equation using MATLAB's "fzero" for t.
Best wishes
Torsten.
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