@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
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)?
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!!!!
@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
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.
@@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.
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!
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
“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
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
@@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
@@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.
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.
@@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 UA-cam's hall of fame.
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.
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...
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
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)_/¯
Your videos are so, so stunningly beautiful, and yet the scripts and the voiceover are so hard to understand. You put so much time into your videos, and yet you are so far from reaching your true potential because of simple surface level things lacking quality. Please, find someone to revise your scripts, work on your pacing, and find someone to review your work before it is published. I really want your channel to succeed, and yet I see why your videos get so, so little attention despite being the most visually advanced on the whole platform.
i mean, you might just not be his target audience - which isn't an inherently bad thing. Despite having an engineering degree and experience in computational science I still don't understand quite everything about this video. I don't find that necessarily bad, it's just high level. I'm impressed and fascinated by his amount of knowledge and it makes me want to learn more. Whereas most science on UA-cam is for the general public and kinda bores me because I already have an understanding of most things they talk about in greater depth than they're describing. I hope this doesn't come off as arrogant, I'm just saying that different audiences will enjoy the same material differently and that's ok!
@@mitchhowe2201 I absolutely agree. To me this type of content is what I like the most unfortunately I doubt most of my other friends would watch this to its entirety, there is some level of familiarity needed to understand the topics which is good thing for me but not for everyone.
@@mitchhowe2201 I perfectly understand the target audience concern, and I was actually going to mention it in my comment, but after some deliberation I decided not to. I am a computer scientist. I have worked on simulations before. I have a good enough background in probability theory and in physics to understand this video. Heck, I tried to optimize the hell out of my maneuvers in Kerbal Space Program. I think I *am* the target audience of that video, but feel free to disagree. I really enjoyed the fluid simulation series, despite it having the same flaws, even when I did not know quantum mechanics on the level I do now. I am impressed by their knowledge too, and I want to learn more, but their approach for making videos makes me consider using different sources in the first place. Of course, I am not saying that youtube video is the pinnacle of education value and should be the only source which must give right enough amount of information about the topic for everyone to become an expert in the field and yet not bore the audience at the same time, but I do think that video should be a good hook and it should give a good overview of the area, and yet their videos fail to fulfill that niche, in my opinion.
Re-reading this actually makes me realize I have made a few assumptions along the way, so feel free to dismiss my argument if you disagree with my position on the topic. I still consider this video to be disappointing.
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
Holy hell, this is an incredibly densely packed video. My background in university orbital dynamics was just enough to barely not get lost in what was presented. I must applaud your visualizations. They are simply incredible, both artistically beautiful and significant. That said, the speed at which items are presented are comparable to compressing university semesters into 15 minutes. It watches like reading the introduction to a PhD thesis. I am delighted to watch this, yet I would be equally delighted to watch an hour long video decompressing every single minute of this video. Thank you for all the effort you put into this.
I am only 4 minutes into the video, and already my head is spinning! The visualizations are soo out-of-this-world beautiful and compress very advanced topics into just a few seconds of rendering. Please consider slowing down your explanations in order to give people the chance to understand what you're saying. Don't get me wrong - your script is great - you have your little protagonist which allows you to have a story overarching your explanations, which is very cute (and quite important to keep people engaged). However, the timing ist just too fast to understand. You could be by far the best Sci-Viz UA-camr, but it's just flying by (no pun indended) too quickly. All the best for your future!
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!!
Seconded, as someone with a degree in computer science. Braintruffle, please don’t lengthen the video by explaining the prerequisites - that would take ages and we’d lose sight of the bigger picture. Although it is hard to follow, that’s because I’ve only been on the problem for 5 minutes. After all, the intended audience is not the casual UA-cam viewer - it’s the spaceship pilot trying to find their way home while minimizing fuel and time! Once you catch up on those topics and put yourself in their shoes, you can start to appreciate the difficulty in trying to solve these problems using traditional methods like Hohmann transfer, interpolation, etc.. This scope is perfect for communicating exactly what was intended - the complexity of spaceflight - keeping the details in view while also focusing on the big picture. I think this video threads the needle perfectly. A little disclaimer in the beginning would be all that could improve it in my opinion. Something like “as a spaceship pilot well versed in multivariate calculus, high dimensional geometry, and basic orbital mechanics, your first thought….” So you can communicate the prerequisites while not ruining the fantasy.
That what learning should be, a fast and simple overview of the entire thing, then if you want to go deeper, you take your time to research and understand accurately. First spark interest, then explain the fine details
Mathematician here. I couldn't follow... you've lost me quite early and you probably would've lost me continuously throughout the video. That's a bummer, because the animations are beautiful! It should pay out to work on the pacing a little more, especially if you plan for this video to be educational. I hope this comment does not take away your motivation... please keep up the good work!
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.
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!
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) :)
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.
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
@@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
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
I think the entire concept of a manifold as a region in phase space that takes you to your destination is so intuitive on for how the pilot would actually think about their mission - they need to get to a certain region of space by a certain time with a certain velocity. And it also communicates that there is a range of acceptable solutions, but changing one variable will affect the others.
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
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
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.
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 🎉🎉.
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 !
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.
Great visual! You have compressed someone's years of career in astrophysics into a video. That's why it will be hard for us to understand the concepts in the video in just one run of watching. I could now appreciate the weird orbit of the Artemis mission to the Moon because of how you laid out how they trace possible flight plan to a given body in the space.
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
Wow these animations are incredible. You can follow the math so well with them. Honestly, if you just slowed the playback speed to 0.5x, this is one of the best astro videos on youtube.
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!
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?
I am so glad others also find this video a difficult to grasp. I struggled to keep up. This video is incredible and so well made. Wish it was a bit slower for people like me.
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.
Oh my god, I thought I lost this video… adding it to my watch later so I never lose it again. Seriously one of the most beautiful videos I’ve ever seen.
You should make a game like kerbal space, but it's purely done with these exact aesthetic diagrams instead of third person view. I think a macroscopic space simulator game would be a great great way to disseminate understanding of orbital mechanics. I love the simplicity of this explanation
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. 🔥🙏
Man, I don't understand a sh*t of what he's saying but the amount of effort and beauty on the visuals makes me want to subscribe and learn everything, and how can i not aprecciate this masterpiece
This is without a doubt the coolest thing I've seen all year. It also made my head hurt more than anything I've seen in the past two. Lemme just put it this way: When information (any information) is optimally compressed into a perfectly digestible format, it enters the brain smoothly. (That's step 1 of learning. Your video here aced that part.) After entering the brain though, it has to be incorporated into the learner's MIND. This doesn't happen automatically! Lots of neurons have to fire across large parts of the brain, and incorporating the learned content requires changing neural connections on a physical level! That's an energy intensive process that scales inversely to the learner's existing knowledge about the subject! (For reference, I have a bachelor's in physics and I'm still digesting this. My wife, who does not have my background in physics or calculus, left the room 5 minutes into the video - even though she liked it a lot.) I recommend mixing up the contents to include more information about what's going on at a low level. You jumped through Newtonian physics in what...ten seconds? Started using Hamiltonians and Lagrangians with no background? Teach those things but with this kind of context! It'd get way more attention than most intro physics videos, and the quality of your visualizations would bridge the abstraction to gap enough to let new learners appreciate what we see in physics after having spent years studying it. For videos like this where you share what I'm sure excites you most, reduce the word count and link back to those other videos for those who don't automatically get what you're describing by the visuals alone. Definitely subscribing though! I'll just have to rate limit myself because my brain isn't going to stop processing this for at least another day, and I'll probably have at least one dream about it. edit: Wait, I'm already subscribed lol. My points still stand though xd
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).
Having a PhD related to dynamics and probabilities, I personally find the video's pace too fast. People who get it, don't need to watch the video and people who would benefit from the video have no chance following along. The animations are amazing and the discussed concepts are cool. If the video emphasizes the key ideas in a slower pace similar to Freya Holmér's video on splines, then this work would be awe inspiring.
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.
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.
Amazing, you should absolutely write a paper on your findings if you aren’t already. Open this up to the academic community. A tool like this could make huge strides in the field of trajectory design for real missions.
This is the first video on youtube that I founf where I understood NOTHING. This is like alientalk to me. I dont know what it is for, what the problem is, what he is doing and how it works. I love it.
A little glimpse of introduction to basic concepts to understand your way of speaking and explaining would be good, Like basic concepts before advanced ones, it'll be more helpful for everyone
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
Wow, it's like wonderful summary of Orbital Mechanics and Astrodynamics with beautiful visualization. 😮 . Great work 👍🏻 . I feel bored and helpless waiting from some youtube video with more than surface level of knowledge of anything. At first, I thought this video is like "Oh, another video about Hohmann Orbit transfer." Now this is something. Hohmann Transfer is only one concept shown in the video. This video explain almost all other alternatives. Beautiful visualization but deep concept. . This is the kind of video I need nowadays to remove my boredom 🔥
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.
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.
I find the prose and cadence of your videos hard to follow, while the visuals are probably the best I’ve seen on the platform. I think thats whats missing for your channel to really blow up :). If you are open to some feedback, I would like you to suggest reviewing the first 50 seconds of the video, there is so much going on there! The second sentence is already a question with no time to the user to think about or answer. A script review and some proper cadence on audio, which channels such as Veritasium does masterfully, would bring you to the next level. I will always appreciate the huge amount of effort your videos take, and so I want you to succeed, thats exactly why I am commenting this.
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.
one of the best videos on the subject. the software he uses should be adapted to an interactive toy for toddlers to develop their neural pathways for this subject in their deep neural functions.
Finally! A video about high level mathematics, fluid dynamics, orbital mechanics, ray tracing and probability analysis? I have no idea what any of that is, but it’s awakening my brain parts!
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!
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.
Prior to watching this video, I was confident that Starfleet Academy courses were a work of science fiction. I have now been persuaded otherwise. I'm not exactly an analytical slouch, but this blew my mind. I think I would genuinely need a few weeks (months? years?) of workshops and lectures to unpack this. Marvelous graphics, and I concur with the comment below that I could see future generations of brilliant minds needing to learn how to intuitively grasp these concepts before using high-powered AI-assisted quantum computing to solve (where brute force is required and generations of more elegant algorithmic tuning can't handle the computation more efficiently, anyway!) Incredible work.
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!
+very good graphics -fitting a degree in 30 min youtube video +interesting concepts -unlabeled plots of something vs something. Sure, you know what they mean. But we can't read minds. It is both very intelligent and very stupid
Do you want more? Here is an extended version incl. chapter 5 -> www.patreon.com/braintruffle
Thank you for helping fund future videos!
Hi, do you use manim for animation?
@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
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)?
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!!!!
@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
Single-handedly one of the greatest data visualisations I have ever seen - this feels like the absolute cutting edge of modern presentation.
agreed on that
as beautiful as any art project I have seen, and eight times as stimulating.
i feel like i walked into the wrong classroom and then the door locked
good job on the teaching!
This psychopath closed us in!!
True and then the prof says get together in groups work on something and your heart sinks.
Yeah… I’m still traumatized
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"
This goes horribly fast. And I'm an astrophysicist :S
Amazing concept and visuals by the way. So much work in something like this.
Yeah I thought 5k hours of KSP would save me but nope! :/
Right, thought it could be a interesting add on after taking uni orbit dynamics. But hell nope
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.
Yeah, great idea and great animation, but the presentation needs some improvement.
@@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.
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!
I got lost as soon as the intro ended
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
To be fair, this is basically a full PhD thesis in 32 minutes lol
@@chemplay866 same
@@Ranged66which is why it should be longer
Your videos feel like a dream. Beautiful, chaotic, and I forget everything after I wake up
lol
lmao yes
“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
Man I want to try the ballistic approach so bad, as soon as I finish my studies and get back to playing
I think KSP only simulates the gravity of objects you are in the SOI of @@fabiovezzari2895
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
@@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
@@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.
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.
@@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 UA-cam's hall of fame.
Lol another expert in UA-cam channels
@@Nat-oj2uc Lol! Another person going around mindlessly loling very plausible things.
@@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.
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...
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
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)_/¯
@@xymaryai8283 I sure do
also, I was barely hanging on up until the manifolds came up
Your videos are so, so stunningly beautiful, and yet the scripts and the voiceover are so hard to understand. You put so much time into your videos, and yet you are so far from reaching your true potential because of simple surface level things lacking quality. Please, find someone to revise your scripts, work on your pacing, and find someone to review your work before it is published. I really want your channel to succeed, and yet I see why your videos get so, so little attention despite being the most visually advanced on the whole platform.
this. entirely this. and it sucks cuz the fluid videos could be so interesting but i just cant follow a single word hes saying
i mean, you might just not be his target audience - which isn't an inherently bad thing. Despite having an engineering degree and experience in computational science I still don't understand quite everything about this video. I don't find that necessarily bad, it's just high level.
I'm impressed and fascinated by his amount of knowledge and it makes me want to learn more. Whereas most science on UA-cam is for the general public and kinda bores me because I already have an understanding of most things they talk about in greater depth than they're describing.
I hope this doesn't come off as arrogant, I'm just saying that different audiences will enjoy the same material differently and that's ok!
@@mitchhowe2201 I absolutely agree. To me this type of content is what I like the most unfortunately I doubt most of my other friends would watch this to its entirety, there is some level of familiarity needed to understand the topics which is good thing for me but not for everyone.
@@mitchhowe2201 I perfectly understand the target audience concern, and I was actually going to mention it in my comment, but after some deliberation I decided not to.
I am a computer scientist. I have worked on simulations before. I have a good enough background in probability theory and in physics to understand this video. Heck, I tried to optimize the hell out of my maneuvers in Kerbal Space Program. I think I *am* the target audience of that video, but feel free to disagree.
I really enjoyed the fluid simulation series, despite it having the same flaws, even when I did not know quantum mechanics on the level I do now. I am impressed by their knowledge too, and I want to learn more, but their approach for making videos makes me consider using different sources in the first place. Of course, I am not saying that youtube video is the pinnacle of education value and should be the only source which must give right enough amount of information about the topic for everyone to become an expert in the field and yet not bore the audience at the same time, but I do think that video should be a good hook and it should give a good overview of the area, and yet their videos fail to fulfill that niche, in my opinion.
Re-reading this actually makes me realize I have made a few assumptions along the way, so feel free to dismiss my argument if you disagree with my position on the topic. I still consider this video to be disappointing.
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
theres a video about Bezier curves that has the same vibe
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
Holy hell, this is an incredibly densely packed video. My background in university orbital dynamics was just enough to barely not get lost in what was presented.
I must applaud your visualizations. They are simply incredible, both artistically beautiful and significant. That said, the speed at which items are presented are comparable to compressing university semesters into 15 minutes. It watches like reading the introduction to a PhD thesis. I am delighted to watch this, yet I would be equally delighted to watch an hour long video decompressing every single minute of this video.
Thank you for all the effort you put into this.
I am only 4 minutes into the video, and already my head is spinning! The visualizations are soo out-of-this-world beautiful and compress very advanced topics into just a few seconds of rendering. Please consider slowing down your explanations in order to give people the chance to understand what you're saying. Don't get me wrong - your script is great - you have your little protagonist which allows you to have a story overarching your explanations, which is very cute (and quite important to keep people engaged). However, the timing ist just too fast to understand. You could be by far the best Sci-Viz UA-camr, but it's just flying by (no pun indended) too quickly. All the best for your future!
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!!
Seconded, as someone with a degree in computer science. Braintruffle, please don’t lengthen the video by explaining the prerequisites - that would take ages and we’d lose sight of the bigger picture. Although it is hard to follow, that’s because I’ve only been on the problem for 5 minutes. After all, the intended audience is not the casual UA-cam viewer - it’s the spaceship pilot trying to find their way home while minimizing fuel and time! Once you catch up on those topics and put yourself in their shoes, you can start to appreciate the difficulty in trying to solve these problems using traditional methods like Hohmann transfer, interpolation, etc.. This scope is perfect for communicating exactly what was intended - the complexity of spaceflight - keeping the details in view while also focusing on the big picture. I think this video threads the needle perfectly. A little disclaimer in the beginning would be all that could improve it in my opinion. Something like “as a spaceship pilot well versed in multivariate calculus, high dimensional geometry, and basic orbital mechanics, your first thought….” So you can communicate the prerequisites while not ruining the fantasy.
That what learning should be, a fast and simple overview of the entire thing, then if you want to go deeper, you take your time to research and understand accurately.
First spark interest, then explain the fine details
Mathematician here. I couldn't follow... you've lost me quite early and you probably would've lost me continuously throughout the video. That's a bummer, because the animations are beautiful! It should pay out to work on the pacing a little more, especially if you plan for this video to be educational. I hope this comment does not take away your motivation... please keep up the good work!
Agreed
Thank you very much, this tutorial will help me get back home
r slash unernamechecksout
It helped me decide not to leave home!
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.
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!
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) :)
seriously the most incredible educational visualizations i've ever seen. This is the future of education.
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.
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
I also would really love to play with that simulation
Seconded!
@@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
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
I think the entire concept of a manifold as a region in phase space that takes you to your destination is so intuitive on for how the pilot would actually think about their mission - they need to get to a certain region of space by a certain time with a certain velocity. And it also communicates that there is a range of acceptable solutions, but changing one variable will affect the others.
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
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
This is the most intuitive, concise explanation of symplectic integration I've ever seen. Excellent video!
This is a piece of art disguised as educational content. Its seriously impressive.
Absolute masterclass presentation as always. It's like someone took Arnold's classical mechanics text and put it on screen.
The level of detail and animation is ridiculous. This is a true Celestial Mechanic class.
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
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.
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 🎉🎉.
Phenomenal motion graphics / data visualisation!
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 !
Best KSP tutorial I have seen so far
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.
I'd seen and used symplectic integrators before but didn't really understand them - your shearing description makes so much sense!
There are a million courses where all of this is taught in detail, so what you’re doing is unique and valuable
Great visual! You have compressed someone's years of career in astrophysics into a video. That's why it will be hard for us to understand the concepts in the video in just one run of watching. I could now appreciate the weird orbit of the Artemis mission to the Moon because of how you laid out how they trace possible flight plan to a given body in the space.
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
This is literally INSANE QUALITY. love this channel.
Wow these animations are incredible. You can follow the math so well with them. Honestly, if you just slowed the playback speed to 0.5x, this is one of the best astro videos on youtube.
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!
Absolutely AMAZING! I think this is the best numerical methods video on orbital dynamics that was ever made and perhaps forever. 99.99/100!
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?
Incredible animations and creative detail. More of a magic show than a lecture. Author is fond of complexity. Outlining recommended.
Perhaps this should be split into a series, too much information is shown at once.
I am so glad others also find this video a difficult to grasp. I struggled to keep up. This video is incredible and so well made. Wish it was a bit slower for people like me.
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.
Oh my god, I thought I lost this video… adding it to my watch later so I never lose it again. Seriously one of the most beautiful videos I’ve ever seen.
You should make a game like kerbal space, but it's purely done with these exact aesthetic diagrams instead of third person view. I think a macroscopic space simulator game would be a great great way to disseminate understanding of orbital mechanics. I love the simplicity of this explanation
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 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. 🔥🙏
Man, I don't understand a sh*t of what he's saying but the amount of effort and beauty on the visuals makes me want to subscribe and learn everything, and how can i not aprecciate this masterpiece
This is without a doubt the coolest thing I've seen all year. It also made my head hurt more than anything I've seen in the past two.
Lemme just put it this way: When information (any information) is optimally compressed into a perfectly digestible format, it enters the brain smoothly. (That's step 1 of learning. Your video here aced that part.) After entering the brain though, it has to be incorporated into the learner's MIND. This doesn't happen automatically! Lots of neurons have to fire across large parts of the brain, and incorporating the learned content requires changing neural connections on a physical level! That's an energy intensive process that scales inversely to the learner's existing knowledge about the subject! (For reference, I have a bachelor's in physics and I'm still digesting this. My wife, who does not have my background in physics or calculus, left the room 5 minutes into the video - even though she liked it a lot.)
I recommend mixing up the contents to include more information about what's going on at a low level. You jumped through Newtonian physics in what...ten seconds? Started using Hamiltonians and Lagrangians with no background? Teach those things but with this kind of context! It'd get way more attention than most intro physics videos, and the quality of your visualizations would bridge the abstraction to gap enough to let new learners appreciate what we see in physics after having spent years studying it. For videos like this where you share what I'm sure excites you most, reduce the word count and link back to those other videos for those who don't automatically get what you're describing by the visuals alone.
Definitely subscribing though! I'll just have to rate limit myself because my brain isn't going to stop processing this for at least another day, and I'll probably have at least one dream about it.
edit: Wait, I'm already subscribed lol. My points still stand though xd
Love how dense this video is, beautiful illustrations, captivating storyline. Feels like you put your everything into it. Thank you!
This video paired with hours of playing KSP really make the subject more intuitive and practical
Fantastic project overview video. I think people misunderstand what the purpose of the vid is. Very cool information in this and amazing work.
Man these visuals really cleared a lot up for me.
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).
Having a PhD related to dynamics and probabilities, I personally find the video's pace too fast. People who get it, don't need to watch the video and people who would benefit from the video have no chance following along. The animations are amazing and the discussed concepts are cool. If the video emphasizes the key ideas in a slower pace similar to Freya Holmér's video on splines, then this work would be awe inspiring.
Ok you showed off your degree online now stop scrolling tiktok and your concentration will improve!
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.
This is fantastic! You're a boss! Now I just need to spend a year unpacking the content here.
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.
Couldn't understand most of the math language, I have limited knowledge of orbital mechanics, but this was one of the most satisfying videos to watch.
the visuals are sooooo beautiful! 🎉 ❤ and so are the ideas. wish i could understand the concepts more!
Amazing, you should absolutely write a paper on your findings if you aren’t already. Open this up to the academic community. A tool like this could make huge strides in the field of trajectory design for real missions.
This is the first video on youtube that I founf where I understood NOTHING. This is like alientalk to me. I dont know what it is for, what the problem is, what he is doing and how it works. I love it.
A little glimpse of introduction to basic concepts to understand your way of speaking and explaining would be good,
Like basic concepts before advanced ones, it'll be more helpful for everyone
He should start by explaining basic maths I think, multiplication and addition etc
Everything goes over top of my head but... Nicely done! Makes me appreciate Math and Computer Simulation more
Wow this is very great. A friend tried to tell me about unstable and stable manifolds and now hete is an application.
This video is one of the greatest works of art I've even seen in my life. It makes me proud to be human
Impressive. And quite poetic to dream about orbits
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
Wow, it's like wonderful summary of Orbital Mechanics and Astrodynamics with beautiful visualization.
😮
.
Great work 👍🏻
.
I feel bored and helpless waiting from some youtube video with more than surface level of knowledge of anything.
At first, I thought this video is like "Oh, another video about Hohmann Orbit transfer."
Now this is something.
Hohmann Transfer is only one concept shown in the video.
This video explain almost all other alternatives.
Beautiful visualization but deep concept.
.
This is the kind of video I need nowadays to remove my boredom 🔥
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.
Everyone whining abt the narration but the density is soooo good. Keeps me 100% locked in
This is an awesome visualization and overview of orbital dynamics
I’m in love with this video, I’ve been studying this topic the past year and seeing it animated so beautifully is amazing.
this is like finding a gold nugget on the beach of pebbles of content. Amazing
Another good topic to break down would be how things get passed the van allen belt and how things propel themselves in a vacuum.
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.
I find the prose and cadence of your videos hard to follow, while the visuals are probably the best I’ve seen on the platform. I think thats whats missing for your channel to really blow up :). If you are open to some feedback, I would like you to suggest reviewing the first 50 seconds of the video, there is so much going on there! The second sentence is already a question with no time to the user to think about or answer. A script review and some proper cadence on audio, which channels such as Veritasium does masterfully, would bring you to the next level. I will always appreciate the huge amount of effort your videos take, and so I want you to succeed, thats exactly why I am commenting this.
Probably only absorbed 1/3rd of all the knowledge in this video, but it was FANTASTIC nonetheless
OUTSTANDING PRESENTATION! I've never seen anything THIS beautiful on a free medium!
How the hell do you do so beautiful animation ?? No seriously, I need an answer, your videos are 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.
one of the best videos on the subject. the software he uses should be adapted to an interactive toy for toddlers to develop their neural pathways for this subject in their deep neural functions.
It is the best animation quality I have seen om youtube! Amazing!
Oh my GOD, seeing the lagrange points just pop out when adding the centrifugal potential with the gravitational potential was mind blowing
Finally! A video about high level mathematics, fluid dynamics, orbital mechanics, ray tracing and probability analysis?
I have no idea what any of that is, but it’s awakening my brain parts!
It is incredibly dense, I watched it twice, should probably watch a third time after sleeping, but I like it like that
Me too I agree
I've been waiting for years for an explainer, just like this one, to tackle this very topic. 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!
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.
Awesome Video. Please make more videos on robust and efficient probabilistic modelling. Thank you so much 🎉
Prior to watching this video, I was confident that Starfleet Academy courses were a work of science fiction. I have now been persuaded otherwise. I'm not exactly an analytical slouch, but this blew my mind. I think I would genuinely need a few weeks (months? years?) of workshops and lectures to unpack this. Marvelous graphics, and I concur with the comment below that I could see future generations of brilliant minds needing to learn how to intuitively grasp these concepts before using high-powered AI-assisted quantum computing to solve (where brute force is required and generations of more elegant algorithmic tuning can't handle the computation more efficiently, anyway!) Incredible work.
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!
+very good graphics
-fitting a degree in 30 min youtube video
+interesting concepts
-unlabeled plots of something vs something. Sure, you know what they mean. But we can't read minds.
It is both very intelligent and very stupid