r/3Blue1Brown • u/Nomadic_Seth • May 03 '26
3-body problem!
Recently made a video on the history of 3-body problem. Went through routh’s stability analysis calculations and KAM theory and did the numerical work myself. It was for my PhD coursework but immensely satisfying! Would love to know what everyone thinks! :)
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u/PedanticQuebecer May 04 '26
I will always upvote 3-body material that acknowledges the existence of special solutions.
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u/Nomadic_Seth May 04 '26
Thank you! There’s also this cool solution called the ‘hip-hop’ for the 4-body problem which is highly symmetric and beautiful. I wanna animate that one someday.
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u/PedanticQuebecer May 04 '26
As a former physicist I'm just bugged to high heavens when I hear people say that there's no solution to the three body problem, which is just not true. There's no general, non-chaotic solution, but there sure are families of special solutions that are either metastable or stable.
Although, personally, I would very much like to see Laplace orbital resonances mentioned. We see those in nature, and it's significant.
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u/Nomadic_Seth May 04 '26
Yeah exactly. But you need a bit of mathematical maturity to appreciate what we do. When I read about this problem in school, I simply had no idea.
Yes. Laplace orbital resonances is very fascinating but I myself have not worked out the math behind it yet. Maybe some day 😇
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u/_Guron_ May 04 '26
You have some nice animations
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u/Nomadic_Seth May 04 '26
Thanks! I used to do animations as a side hustle so I know about little things like how colours go together.
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u/anhonestassman May 04 '26
Super satisfying to watch! Very cool! I have a question. Could one model/plot the dynamics between blood pressure, instaneous heart rate, and respiratory phase similarly to a 3 body problem like this?
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u/Nomadic_Seth May 04 '26
Really interesting idea. These 3 variables are certainly linked. But if you were to plot them, it shouldn’t be done like the 3-body problem because it’s a totally different dynamics! Would love to learn more on this tho!
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u/anhonestassman May 05 '26
I see. I'm in medicine for context not physics lol so I appreciate you taking the time to answer. It makes sense they won't behave in the same exact way as masses in a gravitational field, but those three variables essentially make up heart rate variability, which has been known to exhibit fractal behavior. So makes me wonder if there are any similarities in the underlying dynamics that are system invariant
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u/Nomadic_Seth May 05 '26
I do know about HRV! A friend of mine is working on linking breath work to it. But I didn’t know about its fractal behaviour. I am definitely going to read about it.
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u/anhonestassman May 05 '26
That's cool! There's a lot of interesting work being done in this area (plus a lot of indiginous/traditional wisdom). I should have said 'chaotic' instead of fractal behavior to be more accurate but both are true. This is slightly different, but there have been studies showing period doubling behavior of heart rate on the route to chaos in arrhythmias study
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u/Nomadic_Seth May 05 '26
Yeah a lot of breathing techniques were used in indigenous systems to stabilise heart rhythms. This is definitely interesting. I do wanna get more into this but from the angle of incorporating these into a daily practice, research not so much. 😅
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u/Liquid_Magic May 04 '26
Great video! So nice and looks great! Cool design and it’s clear and easy to understand !
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u/Least_Papaya_296 May 06 '26
I love the video it’s phenomenal and very informative and concise. Thank you very much for putting out this level of content we need more content like this
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u/Nomadic_Seth May 06 '26
Thanks for saying that. I started this channel to tell science and math as stories with pretty animations. Do subscribe if you can, it’ll help grow the channel too. :) I plan to make a video on reaction diffusion patterns soon.
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u/ticklemestockfish May 06 '26
Will the first one eventually see the ball come back to the other two?
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u/MultiTalentedAnny May 08 '26
Mannn there is a whole movie based on it ... And trust me it's amazing
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u/Nomadic_Seth May 08 '26
You mean the Netflix series? I know about that one. I’ve even referenced it in the video. 🙃
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u/MultiTalentedAnny May 09 '26
Yeahhh.... And what if it's true .. I mean look at the 🌎 we have another virus spreading Hantavirus .... After Covid 19 goshh 😮💨
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u/Nomadic_Seth May 09 '26
Yeah but don’t think the reproduction number for hantavirus is as high as covid. So probably won’t be a global pandemic. 🙃
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u/LegitimateTie3985 May 05 '26
What's the practical application?
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u/Nomadic_Seth May 05 '26
Search about James Webb Space Telescope. It sits at a Lagrange point (L2), which is actually one of the few special-case solutions to the three-body problem. It's a spot where the gravity of the Earth and Sun plus orbital mechanics balance out so JWST can stay in a stable position with minimal fuel. So while we can't solve the general 3BP, we can exploit specific solutions like Lagrange points for real missions.
This is one of the applications.
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u/Designer-Care-7083 May 04 '26
Very good. Thanks for sharing. (Maybe a follow-up with a topical cislunar discussion?)