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MathGroup Archive 2007

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Re: pursuit curve (differential equations)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72863] Re: [mg72843] pursuit curve (differential equations)
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 23 Jan 2007 04:43:12 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200701220847.DAA17062@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

What's poc0?

Why use a dot?  Don't you mean a simple multiplication (denoted by * or 
just juxtaposition with no symbol)?  After all, p, q, x, and y 
presumably are already scalar-valued, not vector-valued.

Trijezni Pijanac wrote:
> hi i am doing pursuit curve in mathematica.. for instance, fox is chasing a
> rabbit - rabbit has a certain defined path (for example - a circle
> {cos(t),sin(t)}. fox always heads directly toward the rabbit. 
> 
> k - relative speed fox/rabbit
> p,q - rabbit's path (for instance a circle {cos(t),sin(t)}
> x,y - fox's path
> t - time :)
> 
> soln = NDSolve[
>       {
>         x'[t] == k.Sqrt[p'[t]^2 + q'[t]^2].(p - x[t])
> 		/Sqrt[(p - x[t])^2 + (q - y[t])^2],
>         y'[t] == k.Sqrt[p'[t]^2 + q'[t]^2].(y - q[t])
> 		/Sqrt[(p - x[t])^2 + (q - y[t])^2],
>         x[0] == poc0[[1]],
>         y[0] == poc0[[2]]
>         },
>       {x[t], y[t]}, {t, t0, t1}];
> 
> but this wont work, any suggestions?
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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