50 double pendulums, whose initial velocities differ only by 1 part in 1000pic.twitter.com/3b75BDkwF1
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50 double pendulums whose initial velocities differ by only 1 part in 1 Million
#WaitForItpic.twitter.com/sHZUaFPzSC14 replies 313 retweets 1,127 likesShow this thread -
Replying to @InertialObservr
So satisfying. Do you think it's possible to take the end state of this simulation, reverse the velocities, and watch the 50 pendulums (pendula?) come together again, or do chaotic dynamics + floating point rounding errors make that impossible?
1 reply 0 retweets 15 likes -
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Replying to @AndrewM_Webb
but to answer your question newtons equations of motion are invariant under time reversal, so yes it's totally possible
1 reply 0 retweets 14 likes -
Replying to @InertialObservr
Sure, but what I'm wondering: say the original sim goes from t=0 to t=10. Then reverse velocities, with the new sim's time going from t'=10 to t'=0. Due to floating point rounding errors, the state at say, t'=5 is going to be very slightly different from the state at t=5...
2 replies 1 retweet 20 likes -
Replying to @AndrewM_Webb @InertialObservr
that slight difference will be magnified by the chaotic dynamics and the pendulums (maybe) won't come together again at t'=0
1 reply 0 retweets 12 likes -
Replying to @AndrewM_Webb @InertialObservr
Here's an e.g. of what I meant: two pendulums started with a diff of 10⁻⁸ in one of their angles. In the forward sim they stick together from t=0 til t=15. At t=22 I reverse the velocities. In the reverse simulation they're together from t=15 til t=10pic.twitter.com/vLc5aMgX3B
4 replies 8 retweets 58 likes
Ever since you showed me this I always use this locally as a check to make sure everything is accurate
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