Upside down pendulum
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- เผยแพร่เมื่อ 21 ก.ย. 2024
- This is David Acheson talking about the inverted pendulum and other things:
• David Acheson, Surpris...
And here's his book:
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And here he is discussing mathematical curiosities:
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Wouldn't a rope essentially be like an infinite number of pendulums?
Perhaps you can't stabilize a rope in this way.
Nice way to think about it.
2394098234509 But it's the closest thing in real-life to an infinity-pendulum, right?
Technically you'd need a 1D string which can't change length but can change angle at any point, so it can "wrinkle up" indefinitely. As soon as you have *some* width, the constraint of not changing length is probably impossible, since you'd have to compress the string on the inside of a curve and stretch it on the outside.
But as an approximation, that should suffice, shouldn't it?
2394098234509 The approximation should become better (in relative terms) as the length becomes longer and longer versus the width.
So perhaps lets take a very long piece of yarn. Sufficiently long yarn should almost behave like infinite pendulums.
Except, of course, that such a hand-crafted string will always be stretchy to some extend. So of course this will never be perfect. But that's not even what I'm aiming at.
For the purposes of this discussion:
"You can't balance an infinity-pendulum with rapid movement" - This fact should likely be true for even a "real" string with actual thickness and stretch.
I would be surprised if the complications of the real world would somehow make balancing a rope upright easier instead of harder.
All this is saying is that, even with an ideal string, that can't stretch but it can bend at arbitrary angles at each and every point - even under such unrealistic assumptions, it's impossible to balance with rapid movement. Certainly this should be true for a real-life string too, right? Or could you actually do this with a(n arbitrary long) piece of yarn?
But it's not infinite. There is a finite number of molecules and atoms inside the rope so in theory, it should work on a rope too. But unfortunately, it does not because the internal structure of a rope isn't the same as a pendulum.
Derek Leung typically, results "at infinity" mean "this is what is approached when # becomes large". And even in a (macroscopically) short rope, the number of atoms that make up that rope area, for this purpose, as good as (but obviously nowhere near exactly) infinite.
The other concern you have, that of inner structure, I can agree with though.
It would need a very special kind of string that could do this. One which is strictly limited to transformations that do not stretch it at all but that can locally change orientation arbitrarily.
My main point here was, that you could, mathematically speaking, have this actually be the case with a finite-length pendulum, by basically going towards a "multi-pendulum continuum" of sort.
Any exact real-life analogy is always doomed to fail.
However, I'm pretty certain that if you tried to do this with a rope, string, piece of yarn, what ever of reasonably big length:diameter-ratio, especially if you use a material with low stiffness and high stretch-resistance (not sure what the correct physical terms would be, also not sure if such a material exists), you'll probably find it hard to balance it in this way.
you should try this with your signature gizmo: a metal beads chain. The same rigidity of links that allow for the "Mould effect" should have interesting properties with this setup...
One of my earliest "wow" moments in maths was going to a David Acheson lecture somewhere in the region of 15 years ago when I think he had not long made this discovery. I went home and bought his book off Amazon and have always regarded him as a bit of a mathematical hero of mine. So naturally when I saw this video I was reminded of him! I had the pleasure of meeting him at the British Congress of Mathematical Education in 2014 and he's a lovely man too.
Wow, you were just a kid way back then.....5 years ago!!!! Keep on having fun until the end bro!
I just read about inverse floating and also learned about this pendulum. So I searched it on TH-cam and, of course, Steve Mould has a video about it. Perfect.
Precisely the same thing for me 3 years later after reading xkcd 2924. I actually thought "this would be perfect for Steve Mould to do a video on, I wonder...". Lo and behold, I'm 10 years late to the party
I tried to build something like this for my A level physics as an experiment to try and get some maths behind the thinking. This was back in the 1990s and I did a really poor job. Good to see someone doing it waaaaay better nearly 20 years later
What is wrong with people? How can you have less than 40.000 Subscribers. You're brilliant and entertaining, a mixture that is very rare sadly.
78k and counting
Felix Reisch it's not people, it's the algorithm
129k at June 1st.
151k, October 13
188k April 7th 2018
I think the more pendulums the faster the oscillation must be so infinite pendulums means zero period. Which is not possible.
Technically it would be infinitesimal but not zero.
Caleb Shoemaker 1/n when n->oo is 0 tho
@@rokronroff 3.333333333333333333......*3=1, not 9.99999999999999999......
This is how we build the space elevator
Lol
:D
Ah yes, instead of tensile stress you have alternating tensile and compressive stresses. Much easier
@@technodruid it's a joke
Only discovered your channel tonight, great content.
+Steven Coleman thank you!
It's called Kapitza Pendulum and a very interesting and minimal description can be found in Landau-Liftshitz's Mechanics book chapter #30 'motion in a rapidly oscillating field'. Essentially the same principle is used in quadrupolar mass specteometers, ion traps (also know as Paul trap) etc.
Well wouldn't stabilizing an infinite numbers of pendulums require infinite energy (exuding uncountable infinite series).
this what we call a perfect outro
hats off steve
You should do another video on this and explain how it works in a similar fashion to your current videos. Huge fan in general.
Regards,
I could be wrong, but I'm pretty sure the plural form of pendulum is pendula. The red squiggly line that has appeared as I write this makes me less sure, but it just seems like it should be no different to words like momenta (momentum), data (datum), etc. Just thought I'd mention that. Jiggle on.
It's a version, demo of vertical integration quantization cause-effect derived from frequency aligned wavelengths in AM-FM superposition.
Explain why stable orbits are not really accelerating and yet the story has to be related to this arrangement in harmony and metastability. (?)
I would guess this is related to the frequency (or rather wavelenght) of agitation related to the size of the links? Namely if the wavelenght of agitation is sufficiently smaller it works. With an infinite link pendulum you would need more than infinite frequency agitation - which is impossible.
KEEP ADDING LINKS UNTIL THE STABILIZATION STOPS WORKING!!!! =)
then buy faster saw
The physics can be broken down: 1. when the saw blade moves upward, the bottom side of the hinge bearings experiences high friction; 2. when the saw blade moves downwards, the top side of the hinge bearings experiences high friction. 3. gravity contributes higher friction on the bottom side of the hinge bearing, therefore, the bottom side of hinge bearings experience higher friction when the saw blade is moving upwards than the top side of the hinge bearings do when the saw blade is moving downwards. 4. The saw blades moving downwards rotates the bars such that they tend to be line up more (much like rope in tension), but the saw blades moving upwards tends rotates the bars such that they tend to misaligned (much like rope in compression). 5. The weaker friction in the hinge bearing means that the bars are allowed to rotate more to be aligned during which the saw blade is moving downwards, causing bar alignment to be strengthened over each osicllation.
my explanation would be that the up and down movement cause it to sort of pull the pendulum down, the going up part isn't a problem since it happen so quickly it hadn't had a time to make the pendulum fall before it get pulled back again by the down movement
Coming from your latest video!!!😁
Is it because you're putting so much energy into the system that the lower energy states become unavailable? Like, it can't be bent more than halfway down without getting rid of some of it's energy, or somehow getting its potential into downward kinetic?
I'm assuming there's a need for speed, seeing that the faster it is, the more stable it becomes. Thus the reason why is it finite, is because it's impossible for anything with mass to move with speed of light, let alone infinite speed, under current understanding of physics, right?
So if a finite number of rigid pendulums can be made to work. Does it work with a piece of string? If you have a short enough piece of string, it can be made to stand up, making it a rigid pendulum. Extrapolate that out with multiple short lengths of string, then a piece of string should work.
"saw bit", "bit"? "BIT"? The word you are grasping for is blade.
Very cool.
Didn't know that. Stunning.
I was curious if it could stand up on its own at that short length by just turning on the jig, but i assume you cant, as you didn’t show that. So the downward jerking force of the whole assembly had enough force on the upper link to be suffered enough counter its directional force of falling and as a result it swung back upwards. Certainly there are weight limitations of the upper links to be countered by the up and down forces of the motor mechanism. I guess the real question is, How is this going to save us from ourselves.
iirc it would have stood up of its own accord if he had turned it on with it not already being upright
So if we use pendulums as tools and as figuring out more and more about physics, then we can say that it goes deeper right? Well if I'm a senior in high school, and I'm getting taught the "correct information", then doesn't that mean they fall in lines with, and don't quote ME on it, "substances tend to act the same way on a molecular scale"? And if thats true, then doesn't that also include physical actions as well, such as oh, I don't know, vibrating pendulms for example. What I'm getting at is how far molecularly do pendulums go? I don't know maybe I'm just being ignorant and leaving something out. LET ME KNOW.
I think the limit on the number of pendulum elements would be depend on the mass and elastic modulus of the material used for the elements. The stability is likely linked to changes in momentum due to vibration, yes?
that grand illusions crew would love this
I wonder what the critical frequency is for a pendulum of a given mass and length
i'm guessing the problem lies in the limitations of speed. it seems the pendulum is held up by traveling at a certain speed (the vibrations keeping it in place) and since you can't go infinitely fast, you can't have an infinitely tall pendulum. my guess is that each segement increases the required speed maybe.
What map projection is that in the background?
+Emil Malta-Müller dymaxion. My favourite projection!
I went to the store to by an infinite number of pendulums to see what they would do, but the shopkeeper told me he was out of stock and they were on order. So I asked how many days until they arrived.
Infinite, he replied.
Steve was doing that weird tiktok pointing text thing before everyone else
More amazing vids pls. Keep up the great vid!
I love you and your brain and idjfidfhdifi You have saved me several times in my science and math fairs. Thank you very much.
Nice video, but it would have been better if you went into a tiny bit more depth, such as explaining why an infinite number would not work
I know another upside down pendulum you can see in the nature and it's connected with strings. It's called paraglider.
Could it be that increasing the number of pendulums increases the energy needed to vibrate & stabilise so a finite number has a definable energy need and an infinite number requires infinite energy input and so is incalculable ?
An infinite number of pendulums would probably implicate infinite mass so...
I want to see this on a high speed camera.
**shows us a cool thing**
**does not explain why cool thing works**
Infinite pendulums would be stable because it couldn't move. It is equivalent to having an infinite string, a finite change in tension has effectively zero effect on an infinite string.
I probably won't get an answer, but what would happen if you stabilised it, then rotated it onto the horizontal?
It falls. Obviously.
Fresh Rock Papa-E what's so obvious about it? When the top gets knocked over it returns to upright. Who's to say the same doesn't occur in some way on its side?
Have you performed the experiment yourself? How do you know?
I know because I've lived in this universe and understand the laws of motion.
Oh my fucking god, how dense and rude can someone be at the same time.
Dude, I need no evidence, this system is fully described by Newton's laws of motion, I don't need to build this thing and test it to know how it will behave, I can just use my reasoning, and I see that it's an unfamiliar activity to you.
"Maybe its impossible to buy an infinite number of pendulums"
So the human race is confused whether or not purchasing an infinite number of items is possible at this stage?
It was sarcasm.
Can you prove that it is impossible?
We're uncertain at what point China will stop loaning us money.
No, we know that if you never stop buying pendulums you can buy an infinite number of them even though you will always have a finite number of them no matter how many you buy.
That messed my head up. That outro though, clever.
wouldnt an upside down pendulum be a metronome by function?
What happens if you turn the saw on with the pendulum hanging down, and then turn it upside down slowly?
I saw David speak, was pretty good
does this work in 3d?
You mean with ball and socket type joints? Good question. I'm not sure but my guess would be that it does.
Steve Mould
yes. ball and socket
you probably get asked this a lot, but do you get enough sleep?
It comes up once or twice per video! The answer is: that's just how my eyes are. Always have been. But I appreciate your concern.
@@SteveMould Wait, his eyes are just like that?
Always have been.
Pew
The ending had me dying It reminds me of mr beans idk if you were going for that but hysterical
Awesome!
fear not, impotent lads! With the right technique, there's hope after all!
The issue with infinite points would need infinite speed
lol the utro, steve is such a goof xD
Banger BGM
Well you would be limited by the speed of sound through the material.
I like how he's got watchmen in the back
how about doing it with 50cm of a bike chain? or maybe use the bead chain you used in mould effect?
Well, infinite number of pendulum means infinite mass witch means you don't have enough energy to move it
yada yada yada show me the drilldo 0:57
All I want to know, Is, Does it work with different directions? I'm sure it wouldn't, But im not the expert here.
is this similar to what keeps a rolling wheel upright?
An infinite number of pendulums would require an infinite amount of power to make it stable
you'd need an infinite number of vibrations for an infinite amount of pendulum.
Can it be done with a bike or motorcycle chain?
Great video! You should have more subscribers and more views and more likes and more comments because youre great!!!
Thanks Matteo!
Steve Mould also..... MORE VIDEOS!!!! I believe in you steeeeve
Steve Mould 00
U r brilliant
I feel like the finite number comes from the speed of light limiting the vibration to balance it.
This is the fundamental principal of taichi and aikido. =\
How long can you make it and it still be stable?
Put a laser on it and see the pattern it makes on the wall.
Is there any intuitive explanation to this without getting into the maths?
What's the map projection in the background? Cassini?
Pendulum for youtube, sexton in the bedroom
cool outro
proof!
But why?
Why?
Pendulum has got erectile dysfunction
Hi Steve
I want to see this done with a bike chain! :D
Parametric Resonance is weird, isn't it?
Upside down pendulum aka a metronome
EXPLAIN????
1:05 WHAT KIND OF DARK SORCERY IS THIS???
at one point the speed of oscillation needed would violate the speed of light
That's not how any of this works...
0:48 "if you vibrate an upside down pendulum fast enough it becomes stable"
1:35 "im not sure what the issue is there" contextually about how many pendulums you can attach as an upper limit
the "fast enough" part is the one that ultimately becomes the limiting factor as it's limit is the speed of light. an infinitely long one would need infinity fast oscillation which violates the speed of light
also a limiting factor is the strength of the joint between either the first and second pendulum as they would experience the most stress or the first pendulum and the oscillating body
Force is only transmitted at the speed of sound.
What happens with a supersonic bullet? There is no force moving faster than the speed of sound, it's the bullet itself that's moving faster. It doesn't have anything to do with what we are talking here.
Mathematical link to gyroscope ?
Nice
What if you ran it rightside up?
the normal downward vertical is still a stable point, so it could still behave like a normal pendulum for a small enough deflection
Hey Steve join us at JokePit UK ;)
you really should have been wearing safety glasses and gloves...
three years ago.
infinite number of pendulum is basically like a rope its not gonna work
+magicandmagik (10 month later) A rope is not rigid though, if you used some rope like thing that doesn't get compressed, like a steel hose, it might work better
Why aren't a large finite number of pendulums like a rope?
Metronome?
Well someone likes Watchmen!
does it work horizontally?
Of course not.
i bet some people have diffeent uses for that :3
This actually makes a lot of sense. Imagine trying to balance a ruler on your finger. You will find that you constantly move you finger side to side to maintain balance. If you move your finger side to side with a fast enough frequency, you will always maintain balance. Cool!
Except here the oscillations are vertical. You are correct though, it does indeed work with horizontal oscillations too
infinite amount of pendulums is a rope