Re: pursuit curve (differential equations)

*To*: mathgroup at smc.vnet.net*Subject*: [mg72858] Re: [mg72843] pursuit curve (differential equations)*From*: "Josef Otta" <josef.otta at gmail.com>*Date*: Tue, 23 Jan 2007 04:23:04 -0500 (EST)

Hi, i think that you have some missing arguments in your equation. I tried to repair it (q->q[t], p->p[t] etc.)and here is the output: p[t_] := Sin[t]; q[t_] := Cos[t]; k = 10.; t0 = 0; t1 = 6Pi; poc0 = {1, 2}; soln = {x[t], y[t]} /. NDSolve[{x'[t] == k* Sqrt[p'[t]^2 + q'[ t]^2]*(p[t] - x[t])/ Sqrt[(p[t] - x[t])^2 + (q[t] - y[t])^2], y'[t] == k* Sqrt[p'[t]^2 + q'[t]^2]*(y[t] - q[t])/ Sqrt[(p[t] - x[t])^2 + (q[t] - y[ t])^2], x[t0] == poc0[[1]], y[t0] == poc0[[2]]}, {x[t], y[t]}, {t, t0, t1}][[1]] Regards, Josef Otta http://home.zcu.cz/~jotta 2007/1/22, Trijezni Pijanac <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? > >