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?

**Follow-Ups**:**Re: pursuit curve (differential equations)***From:*"Chris Chiasson" <chris@chiasson.name>

**Re: pursuit curve (differential equations)***From:*Murray Eisenberg <murray@math.umass.edu>