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Пікірлер
@mochen9282 16 сағат бұрын
It is more elegent to use inertia tensor
@larzcaetano 8 күн бұрын
Hey, Peeter! Is there a way I can get in touch with you? I’m currently graduating in electrical engineering but I have always been a math enthusiast. I have a few questions after going through one of your books.
@PeeterJoot 8 күн бұрын
My email address should be in any of my books, but if you want to math chat specifically, I'd recommend using this discord: discord.gg/nfuB5B2BRt It has a latex bot that makes math communication much easier.
@Pluralist 25 күн бұрын
👏
@helehex Ай бұрын
unknown wood
@helehex Ай бұрын
neat
@jackdragon5353 Ай бұрын
Is I (capital i) the unit pseudoscalar?
@PeeterJoot Ай бұрын
Yes
@rodbarrack7815 2 ай бұрын
Worked for me 🎉
@SuperDeadparrot 4 ай бұрын
What frame is d/dt being taken in?
@PeeterJoot 4 ай бұрын
This isn't a relativistic discussion, so any time derivatives do not depend on the motion of any observer frame... but please consider the origin fixed for this discussion.
@Pluralist 5 ай бұрын
👏
@MinMax-kc8uj 5 ай бұрын
I think this is something else entirely. I think time is in the exponent, and waves are time thing. So, that means there are infinite answers because a negative 1 can always be factored out. e^t=(-1)^t*(-e)^t e^t=e^(i*pi*(t+2*pi+k)*e^t, or something like that. So, that would make it a surface, wouldn't it? It revolves around [t, Re(f(t)), Im(f(t))], or [t, f(t)] where f(t) is a complex number.
@PeeterJoot 5 ай бұрын
It's not clear to me what you are trying to illustrate here. I suggest you visit my discord server: discord.gg/nfuB5B2BRt where you can pose your question with LaTeX formatted mathematics for additional clarity, as well as provide any additional context needed to understand your point.
@MinMax-kc8uj 4 ай бұрын
@@PeeterJoot no need. I think I figured it out. I'm pretty sure there is also a general solution to the quintic, now that I know how to look at everything. I'm sure someone else will figure it out at some point.
@NorthMoon.666 5 ай бұрын
😂😂😂 This is one of the best ending chases from Benny Hill i have ever seen. Go Canada! 🤣🤣🤣
@malcolmpowell9164 5 ай бұрын
Was that how Harry froze his todger? 👍🤔
@sleepyheadsleeps 5 ай бұрын
Was he a mental patient or just bonkers ?
@PeeterJoot 5 ай бұрын
I'd guess that this was surely related to self or prescribed medication, but don't know the details.
@hotbit7327 5 ай бұрын
"Let i = e1e2" ... WHY? What I'm looking for is understanding, instead, usually people juggle words (like i, e1 etc.) according to some syntax rules and that's it. Therefore, it's some playing within linguist8ics system. Also, in 10 min. video, talking fast, people pack a tonne of information, as if they (and viewers) are so smart. But I don't see this cleverness in the real world. That's why I don't like your video.
@PeeterJoot 5 ай бұрын
"Let i = e1e2". Why? Because i^2 = -1, just like complex numbers: e_1 e_2 e_1 e_2 = (e_1 e_2) (e_1 e_2) = (-e_2 e_1) (e_1 e_2) = - e_2 (e_1^2) e_2 = - e_2 (1) e_2 = - e_2^2 = -1.
@glennbrymer4065 5 ай бұрын
It is a unique item. Very nice looking and certainly different. 1st time I believe I've ever seen one. The idea reminds me of the old magnetic holstersfor pistols.
@PeeterJoot 5 ай бұрын
I got the magnets for a little router box project with a sliding lid that I'm planning to start soon. I was initially annoyed that I had to buy those in a set of 20, when I only needed 4, so perhaps I was searching mentally for something to do with some of the rest of them. I'm pretty pleased with the final product.
@Pluralist 5 ай бұрын
@juliavixen176 5 ай бұрын
It seems like that sheath would pop apart with a slight twist of the handle. It would probably pop apart in low velocity collisions, too... which defeats the safety purpose of using a sheath at all.
@PeeterJoot 5 ай бұрын
This is for static circumstances (it's not going to be used on a belt). I don't think the risk of it popping open when it's just sitting on a surface, is a big risk.
@mandrake3899 5 ай бұрын
It's a kitchen knife
@mandrake3899 5 ай бұрын
Nice work man
@juliavixen176 5 ай бұрын
Nice work! I hope I didn't sound like I was critical previously.
@Pluralist 5 ай бұрын
👍
@stoicsceptic8420 6 ай бұрын
So he refused the jab then ?
@adrianellis4497 6 ай бұрын
The mind boggles 😂
@Pluralist 6 ай бұрын
👍
@Pluralist 6 ай бұрын
@samaustin9720 7 ай бұрын
'Promo sm' 😊
@Pluralist 7 ай бұрын
😯
@guidosalescalvano9862 7 ай бұрын
Is it me or are you rotating in "dimension space" itself? Because the dot product is the cosine of the lengths, and the cross product is the projection of the vectors on higher dimensional surfaces, but also a sine of the angle of the vectors.
@PeeterJoot 7 ай бұрын
There is a fundamental relationships between the geometric product and the projection and rejection operations. The projection has the cosine factor that you mentioned and the rejection has the sine factor. The geometric product can also be expressed in a "complex exponential" form, which has both of those cosine and sine terms built in. See kzbin.info/www/bejne/fn66e3ybqJ2mnpo but a brief intro to projection and rejection and for the complex exponential form of the geometric product, see my book, which has a free PDF available for download at peeterjoot.com/gaee
@sz5876 7 ай бұрын
So many Masktards and it's basically 2023
@linuxp00 8 ай бұрын
The development at 4:47 seems a little confusing, I'd just callback for the definition ûv = û⋅ν + û∧v, so û∧ν = ûv - û⋅v. That makes the solution much more obvious and straighforward: rej(v,u) = (v∧û)û = (vû - v⋅û)û = vûû - (v⋅û)û = v||û||² - (v⋅û)û = v*1 - (v⋅û)û = v - (v⋅û)û = v - proj(v,u) or following from 0:56, you could just subtract the projection from both sides and get the same result without much ado. Also, I think there is no need for a grade selection operator at 5:17, as û × v is orthogonal to û, so their dot product is zero, anyways: û⋅(û×v) = û⋅[(û₂v₃-û₃v₂)ê₁-(û₁v₃-û₃v₁)ê₂+(û₁v₂-û₂v₁)ê₃] = (û₁ê₁+û₂ê₂+û₃ê₃)⋅[(û₂v₃-û₃v₂)ê₁-(û₁v₃-û₃v₁)ê₂+(û₁v₂-û₂v₁)ê₃] = û₁(û₂v₃-û₃v₂)ê₁⋅ê₁ - û₂(û₁v₃-û₃v₁)ê₂⋅ê₂ + û₃(û₁v₂-û₂v₁)ê₃⋅ê₃ = (û₁û₂v₃ - û₁û₃v₂) - (û₁û₂v₃ - û₂û₃v₁) + (û₁û₃v₂ - û₂û₃v₁) = û₁û₂v₃ - û₁û₃v₂ - û₁û₂v₃ + û₂û₃v₁ + û₁û₃v₂ - û₂û₃v₁ = (û₂û₃ - û₂û₃)v₁ + (û₁û₃ - û₁û₃)v₂ + (û₁û₂ - û₁û₂)v₃ = 0v₁ + 0v₂ + 0v₃ = 0 + 0 + 0 = 0 and the triple cross product yield a vector, while I² is a real scalar factor as shown in the video.
@PeeterJoot 8 ай бұрын
Yes, those are both good approaches. That said, the trick of encoding a no-op grade selection around a multivector expression is a really useful trick, so it's worth showing it in action.
@ruicastanho4273 8 ай бұрын
😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂
@spdyrzr01 8 ай бұрын
Face down, naked in the snow. Can we name him "Frozen Willy"?
@Connowot387 5 ай бұрын
Chilly Willy rolls off the tongue better.
@spdyrzr01 5 ай бұрын
@@Connowot387 it does.
@reynardbizzar5461 5 ай бұрын
You could do , but it doesn’t look like he had a Willy to freeze😂😂
@overlordprincekhan 9 ай бұрын
One mistake here is that e must be greater than zero. If it isn't, then we will get a pair of straight line which would be nonsense in this context.
@PeeterJoot 9 ай бұрын
It definitely doesn't make sense to write -L^2/G m^2 M = e d, if e = 0. However, before the introduction of that scaling constant d (directrix?), the solution with e = 0, is r = -L^2/G m^2 M (i.e.: constant positive), which is a circle.
@Pluralist 9 ай бұрын
@Pluralist 9 ай бұрын
@Pluralist 9 ай бұрын
@Pluralist 9 ай бұрын
@Pluralist 9 ай бұрын
@alexeyl22 10 ай бұрын
Good effort )). But you obviously had to skip a lot of explaining to fit this in 10 min. Impossible to follow as is.
@PeeterJoot 10 ай бұрын
Sorry about that. I have some other videos that describe the background material, and I had assumed those would have been watched first. Or see my book, available in pdf form for free here: peeterjoot.com/gaee/
@errantis 10 ай бұрын
Great video. Can you recommend a book for further exploration of geometric Algebra that also includes physical applications?"
@PeeterJoot 10 ай бұрын
For some very theoretical applications, the Doran and Lasenby's book "Geometric Algebra for Physicists" is unparalleled. Hestenes' book "New Foundations for classical mechanics" has many applications spelled out. The Hestenes book is very expensive, but you can probably find a copy at a university library if you have access to one.
@andy_lamax 10 ай бұрын
why does my man sound like Wilson Fix from marvel's daredevil??
@PeeterJoot 10 ай бұрын
I did get a better microphone after some complaints. Maybe I won't be emulating Fisk in future videos
@therealeleadi7000 11 ай бұрын
This is like a bunch of npcs lol
@samin3997 11 ай бұрын
MHD is the way
@PeeterJoot 11 ай бұрын
Magneto-Hydro-Dynamics?
@alanoneill3065 11 ай бұрын
????????????????????????????????????
@SirTravelMuffin 11 ай бұрын
Thank you for such a great demonstration of the power of GA!
@pochotom2834 11 ай бұрын
Why is it not taught this way in engineering universities?
@PeeterJoot 11 ай бұрын
Geometric algebra is currently still very obscure, and not known by many engineering instructors. What I've shown in this video would probably be taught using complex variables, or matrices in engineering classes, which can both be used very effectively for this planar material (but generalizing to the 3D spherical coordinate case is not as nice.)
@leokovacic707 11 ай бұрын
Do you have some insights into a geometric algebra interpretatioon of the aharonov bohm effect in any formulation .
@PeeterJoot 11 ай бұрын
Understanding the connections between quantum theory and electromagnetism is one of the things I'd really like to understand, but I don't currently have any good insights for you. In particular, the Aharonov-Bohm effect appears to make the vector potential a first hand citizen, but I don't understand how that effect isn't perturbed by a gauge transformation of the potential. I once asked my Professor in an engineering electromagnetism class about this, and only got a startled blank stare. I haven't tried to do a literature search for an answer, but expect there is one or many available. If somebody could point me to one, I'd appreciate it.
@leokovacic707 11 ай бұрын
@@PeeterJoot I mentioned this to my CED prof and he was bewildered as well never heard of it . I think the catch is that irrotational fields need not be integrable (gradients/ conservative) . The basic calculation uses the Schrödinger eq , plugging in a trial solution of the form e^ig where g is the path integral of A - the vector potential which is curl free but not conservative and even though it's curl( the magnetic field is zero ) you get a different value for different path and hence a phase shift . Basically the point being that the potential although only determined up to a gauge , is more real than the concep of a field. But I'm sure GA could give a different SPIN on this pun intended, especially in something akin to hestenes approach to electron theory m
@BongoFerno 11 ай бұрын
How do you use nilpotent versors ε²=0 to get the velocity and acceleration for free?
@PeeterJoot 11 ай бұрын
I'm not sure, but it sounds like you might? If you know, perhaps you can demonstrate, or point to a reference.
@dsgowo 10 ай бұрын
@@PeeterJoot This sounds like something you might be able to do in PGA? Not entirely sure.
@PeeterJoot 10 ай бұрын
@@dsgowo Perhaps. I haven't spent much time on either PGA/CGA, so I'm not in a good position to comment on that.
@alanthayer8797 11 ай бұрын
THIS IS easier ta grasp than HIS BOOK called GA for electric engineering!Do videos based on applications! But jst know this is mainstream engineering until u study OLIVER HEAVYSIDE, Jj thompson , Steinmetz , Tesla ! Speed up to POLYPHASE Electric engineering by checkin out ERIC DOLLARD who's on Murikambi energy KZbin channel that do Non Mainstream Energy conferences! In Non Mainstream MAXWELL was an IDIOT compared to da names & Otha's I didn't name! Maxwell IS BILL GATES great uncle on his MOM SIDE it's y u here of MAXWELL ! It's not cuz HE WAS DA BEST ! Eric dollard book 📚 called polyphase & 4 quadrant will display world of NON MAINSTREAM electric engineering such as NON 3 phase systems which is DEADLY Em field electric man made crap which is what ALL ELECTRIC ENGINEERS textbook teaches ! I'm gonna contact PETER JOOK n c cn he do GA books on NON MAINSTREAM Energy engineering!
@erykpakula 11 ай бұрын
Thank you for video
@PeeterJoot Жыл бұрын
typos @5:58, in the "Check Recovering Maxwell's equations" slide. I write out a set of grade selection operations, one for each grade, but all the grade selections on the left are written as scalar selections.
@tsrgoinc Жыл бұрын
See Benny Hill, way ahead of his time! 🤣
@realedna Жыл бұрын
Neat, but you could also have added an interpretation of the result: By multiplying with d_1_bar you're rotating 2 "vectors", so they become relative to d_1 being real-only or horizontal. So here the triangle out of z_1, z_2 and Z gets rotated clockwise with line_1 being horizontal at the top. z_1-z_2 is the "vector" from z_2 to z_1 and d_2 is the vector from z_2 towards Z (negative if facing the other way). The ratio between the imaginary parts of these rotated vectors is beta (at point Z), because from z_2 (the origin here) both (z1 and Z) have equal vertical (imaginary) distance to line_1. So from the ratio you get beta as the scalar that scales d_2 to the full distance of z_2 to line_1 (which is Im[(z_1-z_2)*d_1_bar]). The rotated vectors get also scaled by the magnitude of d_1, but as we take the ratio it cancels out anyways. This way it's probably easier to understand the result and to reconstruct the formula from memory.
@PeeterJoot Жыл бұрын
Nice. This reinterpretation works even better if you let d_1, d_2 be unit "vectors", so if you divide through by d_1 you are doing a strict rotation, finding an equation where d_1 lies on the horizontal: z_1' + \alpha = z_2' + \beta d_2' so now it's obvious that to eliminate \alpha, we just take imaginaries.