       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)

```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 == poc0[],
y == poc0[]
},
{x[t], y[t]}, {t, t0, t1}];

but this wont work, any suggestions?

```

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