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MathGroup Archive 2007

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pursuit curve (differential equations)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72843] pursuit curve (differential equations)
  • From: Trijezni Pijanac <trijezni.pijanac at gmail.com>
  • Date: Mon, 22 Jan 2007 03:47:07 -0500 (EST)
  • Reply-to: trijezni.pijanac at gmail.com

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?


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