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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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