Trawler Problem

Author

Eric W. Weisstein
May 23, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialGeometry/TrawlerProblem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TrawlerProblem.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Trawler problem animation created by
Michael Trott
July 25, 2006
For NUMB3RS episode 302, Spree, Part 2

Animation

Manipulate

Tfog = 0.26;

trawlerIntercept[t_] := Graphics[{
{If[t < -Tfog/2, {}, {GrayLevel[1 - 0.3 (Tfog+t)/Tfog ], Disk[{0,0}, 2.4]}],
Blue,Thickness[0.005], Line[{{2.5, 0}, (-t){2.5,0}+(1+t){2/3, 0}}],
 Disk[(-t){2.5,0}+(1+t){2/3, 0}, 0.05]},
{Red,Thickness[0.005],
Disk[{1/3, 0} +  1.1(1-t){-t, 1t^2}, 0.05],
Line[Table[{1/3, 0} + 1.1(1-τ){-τ, 1τ^2}, {τ, t,-1, -1/100}]]}
      }//N, PlotRange -> {2.75 {-1, 1}, 2.3 {-1, 1}}, Frame -> True, FrameTicks -> False,Background ->RGBColor[0.5263294422827497, 0.8741283283741512, 1.]] /; t≤0

star[n_] := {Yellow, EdgeForm[Black], Polygon[
Table[{2.054265625889302`,0.021627011402711883`} + 
      (  0.1  + 0.05 (-1)^k){Cos[2Pi k/n], Sin[2Pi k/n]},{k, 1, n}]]}

trawlerIntercept[t_] :=
With[{t1 = If[t > 0.08, t - 0.08, 0]},
 Show[{trawlerIntercept[0]/. l_Line :> Sequence[Opacity[0.33], l],
  Graphics[{{Blue,Thickness[0.01], 
Disk[t1{3,0}+(1-t1){2/3, 0}, 0.05],Line[{{2/3, 0}, t1{3,0}+(1-t1){2/3, 0}}]},
{Red,Thickness[0.01], 
 Disk[{1/3, 0} + (Exp[0.159 3 Pi t]-1) {Cos[3 Pi t],Sin[3 Pi t]}, 0.05],
Line[Table[{1/3, 0} + (Exp[0.159φ]-1) {Cos[φ],Sin[φ]},{φ,0,3 Pi t,2Pi/120}]]},
 If[t==0.668, star[12] , {}] }     ]  }  ]]  /; t>0

man=Manipulate[trawlerIntercept[t],{{t,-1}, -1,0.668},SaveDefinitions->True]

Animation

GraphicsGrid[Partition[Table[trawlerIntercept[t],{t,-1,.668,1.668/8}],3],ImageSize->400]