Message Boards Message Boards

13
|
15639 Views
|
1 Reply
|
17 Total Likes
View groups...
Share
Share this post:

How to juggle 10 balls

Posted 10 years ago

We stumbled upon this nearly 20 years old (according to author) web page titled Wie man mit 10 Bällen jongliert which in German means "How to juggle 10 balls". With the kind permission of the author Felix Holderied I am reproducing here the code and animation slightly changed. Enjoy ;-)

enter image description here

n = 5;
T = 1;
b = 20;
tw = t /. 
   FindRoot[
    1 == Pi/T Tan[2 Pi t/T] ((2 n - 1)/2 T - 2 t), {t, 0.9 T/4}];
r = 5 ((2 n - 1)/2 T - 2 tw) T/(2 Pi Cos[2 Pi tw/T]) // N;

SHL[t_] := r {Cos[2 Pi t/T], Sin[2 Pi t/T]} // N;
SHR[t_] := {-1, 1} SHL[t + T/2];
VH[t_] := r {-2 Pi Sin[(2*Pi*t)/T]/T, 2 Pi Cos[(2 Pi t)/T]/T} // N;
SB[t_] := SHL[tw] + VH[tw] (t - tw) - {0, 5 (t - tw)^2} // N;

hw = SHL[tw][[2]];
h = VH[tw][[2]]^2/20 + hw;
la = n/2;

jglr = ParallelTable[

  Bll = Table[If[SB[t + (b - 1) T][[2]] > hw,
     {RandomColor[], Disk[SB[t + (b - 1) T] - {la, 0}, 1]},
     {RandomColor[], Disk[SHL[t] - {la, 0}, 1]}], {b, n}];

  Blr = Table[
    If[SB[t + (b - 1.5) T][[2]] > hw, {RandomColor[], 
      Disk[{-1, 1} SB[t + (b - 1.5) T] + {la, 0}, 1]}, {RandomColor[],
       Disk[SHR[t] + {la, 0}, 1]}], {b, n}];

  Show[Graphics[{
     Bll, Blr,
     Thick,
     Line[{{la, 0}, SHR[t] - {-la, 0}}],
     Line[{{-la, 0}, SHL[t] - {la, 0}}],
     Line[{{la, 0}, {0, 1}}],
     Line[{{-la, 0}, {0, 1}}],
     Circle[{0, 3}, 1],
     Line[{{-la, -2 r}, {-2/3 la, -2 r}, {0, 
        1}, {2/3 la, -2 r}, {la, -2 r}}]}], 
   PlotRange -> 1.1 {{-(h + 2 r)/2, (h + 2 r)/2}, {-2 r, h}}], {t, 0, 
   T (1 - 1/b), T/b}]

Export["jglr.gif", jglr, ImageSize -> 500]
POSTED BY: Vitaliy Kaurov

Your post was trending on Reddit ! It is very cool that the juggling patterns can be programmed, thanks for sharing! It is interesting if more or less systematic approach can be applied using Wolfram Language to do other patterns - for examples these from the Library of Juggling (maybe this could be interesting for kids):

Reverse Mills Mess

enter image description here

N-Box

enter image description here

POSTED BY: Marina Shchitova
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract