@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
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
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.
“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 TH-cam's hall of fame.
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 TH-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
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.
man, this is magic. i myself doing a phd in statistical surrogate modelling for dynamical systems, but for the first time in my life i see such a complex and advanced topic explained so nicely and pretty... you are a magician, honestly.
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!
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)_/¯
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
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.
God... if ever, if just ever you were strategic; well paced, convincing, not shy of pauses,,, with your content... I say cuz I almost love it, but almost
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
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 TH-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.
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
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
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.
I appreciate this video for providing a technical overview, which is useful for identifying gaps in understanding and for contextualizing these topics together. This video is esoteric and I can’t say I gained any understanding or intuition of any particular topic but the overview is interesting and the visualizations are entertaining! I hope you make a series where you introduce and elaborate on these topics in a broadly accessible way.
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 !
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!
Yeah, he assumes a lot of people already know the concepts he's talking about. He might say X doesn't work so we have to do Y (example particle simulation vs probability cloud). Without really explaining how X and Y work, only giving a one second summary of what they mean. Show me some code, show me how a point is calculated with an example. The animations are nice, but that isn't enough to give an understanding of the concepts that we could apply to other situations.
Gee, I'm not even a mathematician, and I managed to follow along. Please consider using the tools available, such as slowing playback. Pausing and/or replaying until the concept you're stuck on sinks in. MANAGE YOUR OWN LEARNING instead of whining that the video didn't hold your hand. Because this is an absolutely incredible presentation EXACTLY AS IT IS. I wouldn't have changed its delightful density, economy and brevity one iota.
Yeah. As someone in a previous video commented, what's this channel's target audience? It's beautiful and clearly detailed, but the amount of jargon it throws at you and the assumptions it makes about the viewer make me feel like I'm reading a textbook.
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
As a programmer and video maker myself, I understand how much work was put into this video. The visualizations and montage are astonishing. However, I didn't understand the theme and the problem of the video from the very beginning, and therefore felt lost and disconnected. As a result, I couldn't view the video to the end or recommend it to my friends. You should consider doing demo viewings of draft videos with your friends or viewers to get early feedback, to create a more understandable video. Also, I got some grasp of the idea of the video, and it's very interesting: simulating the probability of space trajectories using a grid.
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
Anyone else come back to this channel from time to time just to stay intellectually humble? I check back periodically and go “yeah, I still don’t understand math as well as I thought”
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 TH-camr, but it's just flying by (no pun indended) too quickly. All the best for your future!
Please consider using the tools available to you, such as slowing playback. Pausing and/or replaying until the concept you're stuck on sinks in. MANAGE YOUR OWN LEARNING instead of whining that the video wasn't tailored to your needs (which would have made it way too long). Because this is an absolutely incredible presentation EXACTLY AS IT IS.
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.
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.
This is the best content I have ever seen. As an aerospace engineer, this should not surprise much but I was blown away! many ideas I have just understood but not pondered upon. this is very good man! thank you.
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'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 🎉🎉.
Thank you for reminding me why i fell in love with math 40 years ago. And thanks for one of the most concise, clear, tight scripts I've ever had the joy of listening to.
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.
These are the best videos on TH-cam that inform about space in 3D way, instead of 2D and filling in the blanks with voice over. Prove me wrong (please do)
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. 🔥🙏
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.
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?
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!
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.
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!
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.
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 understand every single word but understanding what is being communicated..not so much so. It super fascinating though, like walking into the wrong lecture room but something keeps you sat there. The graphics are spectacular!
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.
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.
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.
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
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
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).
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 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
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.
“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.
This video is so densely packed with ridiculously good information, concepts and graphics. It's epic
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 TH-cam's hall of fame.
Lol another expert in TH-cam channels
@@Nat-oj2uc Lol! Another person going around mindlessly loling very plausible things.
@@gokuldastvm so how many successful channels do you have🤡
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 TH-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
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.
man, this is magic. i myself doing a phd in statistical surrogate modelling for dynamical systems, but for the first time in my life i see such a complex and advanced topic explained so nicely and pretty... you are a magician, honestly.
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
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!
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
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
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.
God... if ever, if just ever you were strategic; well paced, convincing, not shy of pauses,,, with your content...
I say cuz I almost love it, but almost
This is a piece of art disguised as educational content. Its seriously impressive.
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
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 TH-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.
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
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!
seriously the most incredible educational visualizations i've ever seen. This is the future of education.
Extremely glad you simplified your methodology several times.
Might have to flick through this again to make it stick.
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) :)
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
I loved this. Usually videos in youtube are too simple and inaccurate. This was about about beautiful ideas with beautiful animations.
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
r slash unernamechecksout
It helped me decide not to leave home!
I appreciate this video for providing a technical overview, which is useful for identifying gaps in understanding and for contextualizing these topics together. This video is esoteric and I can’t say I gained any understanding or intuition of any particular topic but the overview is interesting and the visualizations are entertaining! I hope you make a series where you introduce and elaborate on these topics in a broadly accessible way.
Love how dense this video is, beautiful illustrations, captivating storyline. Feels like you put your everything into it. Thank you!
Absolute masterclass presentation as always. It's like someone took Arnold's classical mechanics text and put it on screen.
This is literally INSANE QUALITY. love this channel.
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 !
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
Yeah, he assumes a lot of people already know the concepts he's talking about. He might say X doesn't work so we have to do Y (example particle simulation vs probability cloud). Without really explaining how X and Y work, only giving a one second summary of what they mean. Show me some code, show me how a point is calculated with an example. The animations are nice, but that isn't enough to give an understanding of the concepts that we could apply to other situations.
Gee, I'm not even a mathematician, and I managed to follow along. Please consider using the tools available, such as slowing playback. Pausing and/or replaying until the concept you're stuck on sinks in. MANAGE YOUR OWN LEARNING instead of whining that the video didn't hold your hand. Because this is an absolutely incredible presentation EXACTLY AS IT IS. I wouldn't have changed its delightful density, economy and brevity one iota.
Yeah. As someone in a previous video commented, what's this channel's target audience?
It's beautiful and clearly detailed, but the amount of jargon it throws at you and the assumptions it makes about the viewer make me feel like I'm reading a textbook.
Learned a some of these concept intuitively playing outer wilds. Would recommend if you want the feeling of flying a spaceship around a solar system
This is the most intuitive, concise explanation of symplectic integration I've ever seen. Excellent video!
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
Phenomenal motion graphics / data visualisation!
As a programmer and video maker myself, I understand how much work was put into this video. The visualizations and montage are astonishing. However, I didn't understand the theme and the problem of the video from the very beginning, and therefore felt lost and disconnected. As a result, I couldn't view the video to the end or recommend it to my friends.
You should consider doing demo viewings of draft videos with your friends or viewers to get early feedback, to create a more understandable video.
Also, I got some grasp of the idea of the video, and it's very interesting: simulating the probability of space trajectories using a grid.
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
Best KSP tutorial I have seen so far
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
YES! This is a rare gem amongst pablum.
Anyone else come back to this channel from time to time just to stay intellectually humble? I check back periodically and go “yeah, I still don’t understand math as well as I thought”
I just come back to see if he's posted anything new. He has no socials so I worry he's deceased or something..
The level of detail and animation is ridiculous. This is a true Celestial Mechanic class.
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 TH-camr, but it's just flying by (no pun indended) too quickly. All the best for your future!
Please consider using the tools available to you, such as slowing playback. Pausing and/or replaying until the concept you're stuck on sinks in. MANAGE YOUR OWN LEARNING instead of whining that the video wasn't tailored to your needs (which would have made it way too long). Because this is an absolutely incredible presentation EXACTLY AS IT IS.
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.
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.
This is the best content I have ever seen. As an aerospace engineer, this should not surprise much but I was blown away! many ideas I have just understood but not pondered upon. this is very good man! thank you.
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'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 🎉🎉.
Another good topic to break down would be how things get passed the van allen belt and how things propel themselves in a vacuum.
Absolutely AMAZING! I think this is the best numerical methods video on orbital dynamics that was ever made and perhaps forever. 99.99/100!
Everyone whining abt the narration but the density is soooo good. Keeps me 100% locked in
Incredible animations and creative detail. More of a magic show than a lecture. Author is fond of complexity. Outlining recommended.
Thank you for reminding me why i fell in love with math 40 years ago. And thanks for one of the most concise, clear, tight scripts I've ever had the joy of listening to.
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.
These are the best videos on TH-cam that inform about space in 3D way, instead of 2D and filling in the blanks with voice over. Prove me wrong (please do)
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. 🔥🙏
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.
There are a million courses where all of this is taught in detail, so what you’re doing is unique and valuable
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?
This is fantastic! You're a boss! Now I just need to spend a year unpacking the content here.
I'd seen and used symplectic integrators before but didn't really understand them - your shearing description makes so much sense!
the visuals are sooooo beautiful! 🎉 ❤ and so are the ideas. wish i could understand the concepts more!
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 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!
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.
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!
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.
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.
OUTSTANDING PRESENTATION! I've never seen anything THIS beautiful on a free medium!
I understand every single word but understanding what is being communicated..not so much so. It super fascinating though, like walking into the wrong lecture room but something keeps you sat there.
The graphics are spectacular!
I've been waiting for years for an explainer, just like this one, to tackle this very topic. Thank you.
The most valuable content I've come across this year, such a great channel, keep going, CONGRATS!
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.
This video paired with hours of playing KSP really make the subject more intuitive and practical
Man these visuals really cleared a lot up for me.
this is like finding a gold nugget on the beach of pebbles of content. Amazing
Oh my GOD, seeing the lagrange points just pop out when adding the centrifugal potential with the gravitational potential was mind blowing
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.
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.
It is the best animation quality I have seen om youtube! Amazing!
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
Fantastic project overview video. I think people misunderstand what the purpose of the vid is. Very cool information in this and amazing work.
Habe das Abo nach 30 Sekunden hier gelassen. Grandioser Mix aus Wissenschaft und Entertainment.
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 an awesome visualization and overview of orbital dynamics
These are very advanced topics, thank you for the immense work you put in these videos
This video is amazing and the amount of work that has gone into it is just insane
The legend is back!
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).
My life's mission is to understand this video
the particle/density/boundary tracing approach is beautifully elegant! simple enough to entice me to play around with it too..
This is great. Incredible stuff. Now I can apply this to imagine orbit phasing manifolds and boundaries for visualizing trajectories. For art
Impressive. And quite poetic to dream about orbits
Video is excellent , content is good summary, which allows you to research and learn off line etc
This is probably the most impressive work I’ve ever seen on TH-cam omg… like 3Blue1Brown got a job at NASA 10/10
This amazing video finally manages to visualise how our parents got to school every morning