Do you want more? Here is an extended version incl. chapter 5 -> www.patreon.com/braintruffle Thank you for helping fund future videos!

@bbrother92

4 ай бұрын

Hi, do you use manim for animation?

@alexhogwood-wx2nz

4 ай бұрын

@braintruffle No clue what your intuition is here, but I would love to work together and hear your insight on my research into optical transformers. I am fairly certain we may be working on the same problem. Anyways, thank you. These videos have been massively beneficial to me by essentially reinforcing my novel approach to classical mechanics. Seriously, from myself and many others.. thank you! Best Regards

@alexreustle

4 ай бұрын

Is this method based on a particular paper or set of papers? Or anything in the numerical analysis literature? Does this method or class of methods have a name(s)?

@MrAlubenco

4 ай бұрын

May I ask a question? The math used to describe fractional changes in molecular and liquid density composition and projection, along with explaining how gravity wells play their parts... what are the new set of people are the thinkers now? Wow!!!!

@wojciechkalinowski3827

4 ай бұрын

​@alexreustle Hi, I do not know if this video is about any specific paper in general. The video does cover general well studied and known concepts in astrodynamics although a bit quickly and many things mentioned are much deeper. However, some very common things mentioned the Liouville's theorem (Hamiltonian mechanics) where the "volume" stays constant. Of course the video goes into general astrodynamics/orbital mechanics where we see the Jacobi Intergral (or close to it) which is the effective potential (gravitational + centrifugal) minus the kinetic energy. Note the Jacobi Intergral is only in the circular restricted three body problem which is a very common problem. From the effective potential we can find the lagrange points (stationary points) where as from the Jacobi Intergral we can find the enclosed surface where we do not need use any burns. As for the numerical methods I belive that we had mentions of Monte Carlo with the initial varying of velocity or position and statment how that is expensive. We also have statistical physics mentioned which use probability and statistics to see the macroscopic behaviour of systems. Over the past few years there was research into the use of differential algebra using Taylor series polynomials to create a manifolds and see how that manifold propagated through time and space changes for better uncertinty anlysis. But, going back to the video we are looking at the L1 and L2 lagrange points which ahead and behind the moon (Earth-moon-satilte system) or Earth (Sun-Earth-satilite system). Here we saw two rings that the manifolds conformed to these rings are related to the Jacobi Intergral but the orbits created are quasi periodic halo/Lyapunov orbits. I would probably look into astrodynamics uncertinty and the numerical methods use there and statistical astrodynamics. Both of these deal with mathematics and numerics seen here. Also, not related to astrodynamics but in aerodynamics when dealing with molecules we use BGK equations/model where we also have probability distribution rather than numbers. I doubt this answers your question unfortunately but I hope it helps somewhat

This goes horribly fast. And I'm an astrophysicist :S Amazing concept and visuals by the way. So much work in something like this.

@ballisticfox9033

4 ай бұрын

Yeah I thought 5k hours of KSP would save me but nope! :/

@drewbransby4600

4 ай бұрын

Right, thought it could be a interesting add on after taking uni orbit dynamics. But hell nope

@daigakunobaku273

4 ай бұрын

I'm finishing my masters in an unrelated area of theoretical physics, took several courses on numerical methods. Listening to this for the first time on x1, I can kinda vaguely understand what concepts the author is referring to, but all details are lost completely as the pacing is indeed incredibly fast, and lack of coherence doesn't help either. Stunningly beautiful visuals though. This reminds me of our brilliant Statistical Physics associate professor, who tried to pack basically all she wanted us to learn during the four years of uni, from analytical mechanics and quantum mechanics to statistical physics, methods of solving integral and partial differential equations, group theory, quantum field theory, and effective QFT, into a single semester long course "Methods of Second Quantization", which, to add to everything else, consisted of lectures only.

@treborhuang233

4 ай бұрын

Yeah, great idea and great animation, but the presentation needs some improvement.

@devalapar7878

4 ай бұрын

@@daigakunobaku273I had the same problem. The video explains too fast and the explanations are not good enough. A layman won't be able to follow the explanation. The visuals look great! But if you can't follow the explanation, the visuals are for nothing. So if I was him, I would put more effort into the explanation.

i feel like i walked into the wrong classroom and then the door locked good job on the teaching!

@fabiovezzari2895

4 ай бұрын

This psychopath closed us in!!

@ThePowerfox18

4 ай бұрын

True and then the prof says get together in groups work on something and your heart sinks. Yeah… I’m still traumatized

@deniszarubin2920

2 ай бұрын

They say "if you are in a room, where you are the smartest person - you are in the wrong room". Now I feel "damn, I'm the dumbest person now"

Single-handedly one of the greatest data visualisations I have ever seen - this feels like the absolute cutting edge of modern presentation.

@paiggey

3 ай бұрын

agreed on that

@Rose_Harmonic

13 күн бұрын

as beautiful as any art project I have seen, and eight times as stimulating.

Your videos feel like a dream. Beautiful, chaotic, and I forget everything after I wake up

@tach5884

4 ай бұрын

lol

@DevashishGuptaOfficial

4 ай бұрын

lmao yes

This felt like walking into a lecture that started 15 minutes ago. The teacher is brilliant, the teaching material is excellent, but I'm left scratching my head as to what we are talking about exactly. Others have said this too: this video is amazing, *but* really hard to follow. I really believe that you can capture a broader audience by taking the time to explain the setting better. The beginning of the video would for instance feel a lot less abrupt if we knew we were in space with very little fuel left. Keep up the work, though, I love you videos!

@chemplay866

4 ай бұрын

I got lost as soon as the intro ended

@xymaryai8283

4 ай бұрын

i was half on board at multiple points, he would start a new approach and i'm like "yep, okay i know where he's going with this" and i'm right, but it ramps into statistics and higher order probability space so smoothly, i never think i've lost the thread, but at the end i realise i had no clue what just happened, and i'm just piecing together the ghosts of understanding its beautiful, an experience i don't regret, it made me understand what people mean by 'pleasingly whispering sweet nothings into my ear' because thats what that felt like

@Ranged66

3 ай бұрын

To be fair, this is basically a full PhD thesis in 32 minutes lol

@yunarad0ki

3 ай бұрын

@@chemplay866 same

@cubing7276

3 ай бұрын

@@Ranged66which is why it should be longer

“Simple” and “Astrophysics” never belonged in the same sentence until I played kerbal space program. Watching this makes me realize just how much more I’d love to try and learn about it, these animations just look so satisfyingly beautiful

@fabiovezzari2895

4 ай бұрын

Man I want to try the ballistic approach so bad, as soon as I finish my studies and get back to playing

@chemplay866

4 ай бұрын

I think KSP only simulates the gravity of objects you are in the SOI of @@fabiovezzari2895

@xymaryai8283

4 ай бұрын

yeah, KSP and other space games used an approximate physics system called Patched Conics specifically to avoid this complexity you could probably do some approximation of the continuous acceleration one, but it is fundamentally resctricted in ways that make the instantaneous thrust examples impossible, maybe i'm wrong but i don't think even lagrange points even exist in KSP

@ancientcolors

4 ай бұрын

@@xymaryai8283 For KSP you can use the mod "Principia" to get a pretty accurate simulation of n-body physics, allowing the use of lagrange points as well as low energy transfers

@maxi4251

3 ай бұрын

@@xymaryai8283 No they don't in original KSP. There is a mod called Principia which gives you it also more realistic orbital mechanics though. Astrophysics is not my expertise so I don't know the math behind it.

I am really impressed with your methods and visualizations, captivated by your obvious passion on the subject, and appreciative of value that your content offers. That all being said, I feel like this could have easily been a series of many videos that add up to 5 or 10 times the length of this one. I have a bachelor's degree in math, and have taken some orbital mechanics coursework, and this video still feels a bit like trying to drink from a firehose. Respectfully, I would suggest that if you were to slow down the information stream, your channel would easily become one of the most entertaining and effective STEM content sources on the internet. In any case, I really enjoy your stuff, and I hope you keep making great content.

@ianglenn2821

4 ай бұрын

I agree that this video could be expanded to make more sense to a wider audience. But for long time Kerbal Space Program players, this doesn't feel like a firehose. There's even an xkcd, people who worked at NASA for years report a huge boost in understanding from playing KSP. This video is a love story for everyone who's accidentally run low on fuel in the atmosphere of Duna and used Ike to swing home.

@gokuldastvm

4 ай бұрын

@@ianglenn2821 I have to agree with the parent commenter here. I have used software like KSP, GMAT and others, worked professionally on it and have done related simulations as a hobby - probably for decades now. This still feels like drinking from a firehose. I don't think KSP experience alone changes anything. I don't believe KSP gives you enough information on discretization and numerical integration techniques or probability theory. If you still find it easy, you have some amazing and possibly superhuman cognitive abilities. It isn't that all these ideas are too hardcore. Everything the narrator says is familiar - including the mathematical pieces. Even the graphs and the solution approaches look familiar - I have seen them emerge from my own simulations. But he is switching from one concept to the next in a matter of mere seconds. Every single minute of the video probably has a half to a full dozen ideas. It's not easy for people to process ideas that fast - even the ones they're already familiar with. The author himself may have spent months on it - evident from the long gap between his videos. All these would make a lot of sense if it is stretched 6x to 12x or written down as a semi-book, with videos for support. Making good use of this video would take hours of watching and re-watching. None of this is to say that his work is bad. It's an awe inspiring video with a lot of dedication and hardwork. It should go into KZread's hall of fame.

@Nat-oj2uc

4 ай бұрын

Lol another expert in KZread channels

@gokuldastvm

4 ай бұрын

@@Nat-oj2uc Lol! Another person going around mindlessly loling very plausible things.

@Nat-oj2uc

4 ай бұрын

@@gokuldastvm so how many successful channels do you have🤡

This video is so densely packed with ridiculously good information, concepts and graphics. It's epic

Wow. Just...wow. I really struggled to keep up, but at the same time, none of the concepts individually were impossible to grasp - just the information density was absolutely at my limit. It makes me giddy to think of some several-century-from-now starfleet academy students having to grok all of this intuitively so they understand how it works before letting the ship computer take over and do all the maneuvering.

@xymaryai8283

4 ай бұрын

i do not envy the several-century-from-now starfleet engineers that had to include all the simulations needed for emergency multi-body return programs if the ship is ever low on reaction mass...

@thefacethatstares

4 ай бұрын

I'M gonna be one of those starfleet academy students. I'm gonna write the darn textbook on cost effective strategic readiness in the inner asteroid belt heliocentric zone

@RoySATX

2 ай бұрын

I am impressed you struggled to keep up, you are far more talented that I am. I gave up struggling very early into the video and was satisfied to just enjoy the fantastic animations! ¯\_(ツ)_/¯

As someone who is studying Astrodynamics as part of my own project, I am gobsmacked with how detailed and clean your animations are. And while you do go through things relatively quickly, I think you do a great job of appropriately simplifying and rapidly explaining concepts that would usually take weeks to learn all together. In this way, you are able to quickly and efficiently answer the central problem of the video without taking unnecessary detours. Some others complain about the pace and complexity of the video, but the topics at hand cannot be further simplified without leading to inaccuracy or very long explanation; there simply is no way around that tradeoff. That said, I think that including some sources and supplementary materials would be welcome so that the audience can dive deep into the details in their own time. Overall, amazing job!!

I don't have a math degree and only the most basic background in physics. This was the most enjoyable video I've watched in a serious amount of time. And I understood probably only 10 percent of it. And that's honestly part of the appeal - so refreshing to see a video that doesn't promise to get you over lunch break to an understanding of a complex subject people take years to study. Instead it's a gripping, raw illustration of the depths of how much you really don't know, and the joy of finding that out.

I can't remember the last time I've seen another video as packed with amazing visualisations as this. As a KSP player, this is amazing

@xymaryai8283

4 ай бұрын

theres a video about Bezier curves that has the same vibe

This is a gold mine for a motion graphics designer making VFX HUDs for spaceships or AR helmets. This looks so good, it's beyond high budget cinema level because here it's actually scientific on top of looking stunning.

Thank you very much, this tutorial will help me get back home

@hrishikeshaggrawal

4 ай бұрын

r slash unernamechecksout

@RoySATX

2 ай бұрын

It helped me decide not to leave home!

Absolute masterclass presentation as always. It's like someone took Arnold's classical mechanics text and put it on screen.

How the hell do you do so beautiful animation ?? No seriously, I need an answer, your videos are amazing !

This is the most beautiful presentation I have ever seen from a math/physics educational video.

Man these visuals really cleared a lot up for me.

I would love to be able to play around with the code you used to generate this. Not asking for a polished release, just throwing the current state of your simulation code on github would be really nice for any viewers who want to explore some of these ideas without writing a full simulation from scratch.

@xymaryai8283

4 ай бұрын

i suspect the actual code wouldn't produce pretty visualizations, if any visualizations, just numbers they later used to animate in after affects or something, but i would love to be wrong and for them to release it

@AntonDeutsch

3 ай бұрын

I also would really love to play with that simulation

@crimsonninja6995

2 ай бұрын

Seconded!

@pyro.monkey2501

Ай бұрын

​@@xymaryai8283 I would like to know what library's are being used for visualization or if it generates numbers that need to be pasted in to some spread sheet

Your mastery over the concepts, but you're also an incredibly good animator. I just wish i understood the math and the simulation techniques better. You make it look easy!

This is a piece of art disguised as educational content. Its seriously impressive.

The level of detail and animation is ridiculous. This is a true Celestial Mechanic class.

Hi, its an amazing video I am used to pause and ponder while watching such videos and I have built my own simulation similar to yours but I would recommend for general audience encouraging to pause and ponder about what was just shown

It is incredibly dense, I watched it twice, should probably watch a third time after sleeping, but I like it like that

@SkullTecProductions

4 ай бұрын

Me too I agree

this is the best space flight design video that I have ever seen. I am truly amazed at the quality of the simulations that you made, and the visualizations along side them -- while people may say it is hard to follow, I commend you on making content that truly explores and shares your unbridled academic curiosity without polluting youtube with more clickbait videos that barely explain anything more than what a simple google search would uncover.

Why are so many people expecting to understand all of this without having any education on the matters? If he catered to beginners then it would be really boring to the rest of us. That’s why I love this channel, it’s high level without the details that I’ve already studied.

this is by far the most incredible, high quality content science video I’ve seen for a long time. I just can’t imagine the amount of time it took. 32 min of fast paced explanation and simulations, so fast I had to pause to wrap my head around the concepts. Wonderful job from braintruffle.

Love how dense this video is, beautiful illustrations, captivating storyline. Feels like you put your everything into it. Thank you!

The direct intuition for symplectic integrators is just pure joy :) Also nicely hinting that higher order methods (like IAS15) might be preferable, very nice (one reason is that keeping the volume becomes harder when you want to change the stepsize adaptively) :)

Phenomenal motion graphics / data visualisation!

The most valuable content I've come across this year, such a great channel, keep going, CONGRATS!

This is one of the most beautiful videos I've ever seen. I can tell that so much work went into all these manifolds, simulations, images, 4d graphs and everything else. Thank you for making this. I'll definitely need to rewatch it to understand more, but I prefer that to watching a drawn-out video making everything slower than it needs to be. This video could not be any shorter.

I was just amazed and yet scared of all those beautiful mathematical monuments that you showed along. I just whished that you took a bit more time to develop, your videos deserve more attention !

This is literally INSANE QUALITY. love this channel.

I love the video, it became easier to understand the further in the video I got. I'd say the second part is perfect, first part flew out of my orbit

I’m in love with this video, I’ve been studying this topic the past year and seeing it animated so beautifully is amazing.

Incredible video. While I can't help but echo some other comments that the pacing of this video is very fast, it's so gorgeous and well made that I really enjoyed the whole thing

After your explanations about the efficiency of changing energy levels ex. capture burns, suddenly the lines on the graphs made so much more sense! They also make 1000x more sense now playing KSP with Principia installed and looking at the exact same lines for the Kerbol system

As an aerosoace phd candidate, this video has sparked an increadile amount of excitement for the field! The stable/unstable manifolds representation is an increadible tool, and makes me wonder of the ways of using these potentials to a greated advantage, rather than just lumping the forces into disturbances. Would love to see the bibliography for this video!

to the people complaining about the video being hard to follow: have you considered that his primary goal might not be making a video that's understandable to the largest number of people possible? sometimes it feels like almost all of youtube is just optimized for maximal viewer retention and honestly it's really refreshing to see a video that i have to struggle to keep up with. of course the dude is hard to understand; he clearly knows 100x as much as i do about what he's talking about and he's probably significantly smarter than me, too don't listen to the people whining imo; just keep making incredible videos the way you already do. your CFD videos are some of my all time favorite videos ive ever seen on youtube

I'm so excited you made this video. I asked this exact question to one of my computer science professors years ago, identifying how insanely high the dimensionality was per your intro. But the shifts in perspective you show here are exactly what I was looking for back then. The simplifications you make make the problem so much more tractable, and the visualizations are soooo satisfying. I'm in love with this video 🎉🎉.

This is an awesome visualization and overview of orbital dynamics

I've been waiting for years for an explainer, just like this one, to tackle this very topic. Thank you.

Absolutely AMAZING! I think this is the best numerical methods video on orbital dynamics that was ever made and perhaps forever. 99.99/100!

It is the best animation quality I have seen om youtube! Amazing!

These are very advanced topics, thank you for the immense work you put in these videos

Incredible animations and creative detail. More of a magic show than a lecture. Author is fond of complexity. Outlining recommended.

This video is perfect, your English and script writing is totally fine and easy to understand. I like the level that this channel teaches at. Keep doing your thing!

God damn, I love this so much! Have only vague understanding of what's going on but the deep habit holes quick tour feels amazing by giving perspective to appreciate more how intricate this is.

It's fascinating!

The legend is back!

the particle/density/boundary tracing approach is beautifully elegant! simple enough to entice me to play around with it too..

I took a course at my Uni majoring in Physics on "Our and other Solar Systems". We had introductory astrophysics equasions and computed a lot of the "easy" parts of this video. But the part about the transfers between Lagrange point orbit manifolds almost brang a tear to my eye. Mind officially blown. I love it when a concept in physics feels so hard to understand, but at the same time so simple "how couldn't I think of that before". Also, even though I switched major and failed physics, I consider myself adept in Classical Mechanics, this video was WAY above my head. The pretty pictures makes one feel one understands, but I imagine just how much depth there is to every example speeding by. You are an artist for this. 🔥🙏

love the content, love the pace, love the voiceover and the background tracks ❤

This is fantastic! You're a boss! Now I just need to spend a year unpacking the content here.

This video is amazing and the amount of work that has gone into it is just insane

Fantastic project overview video. I think people misunderstand what the purpose of the vid is. Very cool information in this and amazing work.

What an amazing concept, presentation and explanation. Of course I dont understand any of this, but you laid out the conclusions and progression and brought us along on the journey, too. It is extremely clear, concise and creative.

This is genius. Love everything about it, especially your presentation style. Well done.

What a great video! You are wildly knowledgeable!

Absolutely awesome, I've been looking for a video exactly like this!

This is an extraordinary video. Thank you so much for sharing this with us. I can't comprehend the sheer amount of work that went into it. Probably the densest information to time ratio of anything I've ever watched. You go over so many concepts in such a beautiful way. Please keep making content like this. I wished you'd shared resources for further reading (papers, books, etc...) and code for the simulation. Where can we learn more?

There are a million courses where all of this is taught in detail, so what you’re doing is unique and valuable

Simply amazing, thank you for this work

While not understanding 80% of what is happening I still able to pick some conclusions and concepts and having wow effect after. Just the visualization is stunning! Thanks for that hard work and research

Thank you for your time. I am amazed

Thanks for that, great summation 🤍

This is great. Incredible stuff. Now I can apply this to imagine orbit phasing manifolds and boundaries for visualizing trajectories. For art

Congratulations and thanks for sharing soo much knowledge, this video is amazing!

Absolutely amazing video, thanks for putting so much time and effort in making it. Could you please make a video on how you create your video? You do the best scientific animations I have ever seen and would love to learn how you them

This is so good! Do not slow it down the pace is perfect I didn't need to skip any boring sections :)

i just started it, but thank you. The one you made before was also super super good.

Impressive. And quite poetic to dream about orbits

This video caused me to devote (literally) the entire day to trying out similar stuff myself lol. So incredibly cool, and you are so INCREDIBLY smart. I have no idea how you came up with these ideas lol, completely mindblowing :)

this is really cool. thanks for putting this together!

Habe das Abo nach 30 Sekunden hier gelassen. Grandioser Mix aus Wissenschaft und Entertainment.

Wow this is very great. A friend tried to tell me about unstable and stable manifolds and now hete is an application.

Another good topic to break down would be how things get passed the van allen belt and how things propel themselves in a vacuum.

Incredible stuff! Thank you for sharing this!

This is absolutely fantastic. I will share with my friends.

Most of this went over my head, but the visualizations really looked stunning.

That's like the most amazing video i've ever seen, i'm interested a lot in spaceflight and my experience doesn't get further than KSP I already took 2hours to watch that video but I know I can learn new things after 10 rewatch This is amazing

I don't think I understood until this video why people were so into space travel. Amazing job, I can't wait for your Chanel to blow up, this was really good work.

hefty stuff... love it! this one is especially visually pleasing

Absolutely beautiful

I couldn't help but think of electron orbital shapes and probabilities. This was beautiful, and informative! I've wished for a better explanation low energy transfer orbits since I first read about them as a kid in Science News.

I got 7 mins in before I started crying, quit my job and now I mow lawns for a living. I am at peace. Beautiful graphics btw!

I thought it was a game.. loving it, great video!

Extremely underrated Video. So cool!

Since you animate with code, did you make this with opengl or some other API, would love to know the process because every curve or surface seems to be so accurate. As always amazing video!

Great video!! I want to mention at 16:35 the reason firing at higher velocity (lower potential) leads to a greater change in energy is due to the fact that 1/2 m(v+\delta v)^2 is to first order changing by mv \delta v, which is proportional to v, the velocity before the boost. In other words, this is a purely dynamical problem, not a kinematic one (you set \delta t = 0 already).

Phenomenal work, thank you

Don't worry about people saying it wasn't well explained. It's so refreshing seeing science material on yt that is both well produced AND not dumbed down into oblivion. This video gave me the same tingles as PBS Spacetime usually does: I dont fully understand the math, but the bigger picture it creates is wonderful. Keep at it!

@RealTallestSkil

3 ай бұрын

Assuaging these concerns would only require viewers being pointed to prerequisite videos to describe the mathematical concepts used therein more generally. You have to have a basic understanding of phase space, manifolds, and the integration needed for them (maybe an orbital mechanics terminology video, too) to be able to see how they fit together in this one. This video’s great! It’s just not “self-contained” with what it’s discussing.

I am wondering what tools you use to create those stunning visuals! Even tough I didn't understand everything it was still a joy to watch you video!

Everyone whining abt the narration but the density is soooo good. Keeps me 100% locked in

Your videos are great. Don't listen to the critics telling you to slow down, simplify and essentially dumb down your content. Don't follow the current stultifying trend.

this is like finding a gold nugget on the beach of pebbles of content. Amazing

I remember seeing a talk by Emmanuel Trelat where he mentionned that you could consider figure-eight orbits around Lagrange points instead of simple orbits, and that the corresponding manifolds are much more stable.

This video is one of the greatest works of art I've even seen in my life. It makes me proud to be human