How to export an animation for a numerically solved system

Questions
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1

I’ve been trying to put together a double pendulum animation for my physics project.

forces = {m1* 
     x1''[t] == (\[Lambda]1[t]/l1) x1[t] - (\[Lambda]2[t]/
       l2) (x2[t] - x1[t]), 
   m1* y1''[t] == (\[Lambda]1[t]/l1) y1[t] - (\[Lambda]2[t]/
       l2) (y2[t] - y1[t]) - m1* g, 
   m2* x2''[t] == (\[Lambda]2[t]/l2) (x2[t] - x1[t]), 
   m2* y2''[t] == (\[Lambda]2[t]/l2) (y2[t] - y1[t]) - m2* g};
constraints = {x1[t]^2 + y1[t]^2 == 
    l1^2, (x2[t] - x1[t])^2 + (y2[t] - y1[t])^2 == l2^2};
initialconditions = {x1[0] == 1, y1[0] == 0, x1'[0] == 0, y1'[0] == 0,
   x2[0] == 1, y2[0] == -.6, x2'[0] == 0, 
  y2'[0] == 0}; constants = {g -> 9.8, m1 -> 1, m2 -> 1, l1 -> 1, 
  l2 -> .6}; 
solution = 
 First[NDSolve[{forces, constraints, initialconditions} /. 
    constants, {x1, y1, x2, y2, \[Lambda]1, \[Lambda]2}, {t, 0, 100}, 
   Method -> {"IndexReduction" -> {"Pantelides", 
       "ConstraintMethod" -> "Projection"}}]]; 
Animate[
 Graphics[{{PointSize[.025], {Gray, Point[{x1[t], y1[t]}]}, {Orange, 
      Point[{x2[t], y2[t]}]}, 
     Line[{{0, 0}, {x1[t], y1[t]}, {x2[t], y2[t]}}]} /. 
    solution, {Orange, 
    Line[Map[Function[Evaluate[{x2[#], y2[#]} /. solution]], 
      Range[0, t, .025]]]}, {Gray, Opacity[.5], 
    Line[Map[Function[Evaluate[{x1[#], y1[#]} /. solution]], 
      Range[0, t, .025]]]}}, PlotRange -> {{-1.6, 1.6}, {-1.8, 0}}, 
  Axes -> False, Ticks -> False, ImageSize -> 500], {{t, , "Time"}, 0,
   7, .0000001}, DefaultDuration -> 40, RefreshRate -> 30]

I’ve been trying to export this using

Export["m.avi",%]

But the result I get is a 4 second long video that looks like this the entire time

ScreenShot2013-11-17at5.41.45PM.png
ScreenShot2013-11-17at5.41.45PM.png598×394 35 KB

The output Mathematica gives after the animate command is the kind of thing i’m looking for -- a 40 second video of the double pendulum starting from the initial conditions of rest. Am I doing anything wrong?

2

I generated an animated GIF in code that is here: Animating Optimization with the Gradient Projection Method

circle_packing10.gif

3

Frank, you can easily upload animated GIFs to the community - as we did for your post. It is done in the same way you upload a regular image. To read how please refer to: ** How to type up a post: editor tutorial & general tips **

4

Lucas, it is a beautiful animation, but there is a typo in your posted code that causes the problem - as you can see on the image below you did not specify initial moment of time - it should be zero between those 2 comas. On a general note, the movie you export will be too fast. For precision control I suggest using Table, not animate and control the number of frames - table values - the more frames you have the slower is the movie. Basically this you need this approach, just change GIF to AVI: ** How to export GIFs **

sdf90809830453LKJ.png
sdf90809830453LKJ.png500×135 46.1 KB

5

Lucas, this is a very lovely application and we decided to give its animated GIF below. You may also find it useful to check similar applications at the Wolfram Demonstration Project.

dsfJHKI98797dsf.gif

6

Sam, from my experience leaving a blank space within the manipulate value

{{t,,"Time"},0,10}

will leave the value as default. I just wanted to give the variable a name “Time.”

I modify the speed using

DefaultDuration -> 40

Thanks for the GIF advice though, I think I’ll do that!! It looks so nice, I worked hard getting it right! :smiley:

7

These 2 versions will work as interfaces but 1st will fail on export. My guess is that automated procedure that computes total number of frames and duration need specified initial value to make a movie.

Export["test.avi", Manipulate[t, {{t, , "Time"}, 0, 10}]]

Export["test.avi", Manipulate[t, {{t, 0, "Time"}, 0, 10}]]