A Rope Sliding Down a Table [Lagrangian Formalism Approach]
ฝัง
- เผยแพร่เมื่อ 10 ก.ค. 2024
- Video Sponsored by Ridge Wallet: www.ridge.com/PAPAFLAMMY
Use Code “PAPAFLAMMY” for 10% off your order :)
This STEMweek: 10% Off the WHOLE brand new Nonlinear Dynamics & Chaos Collection :0 stemerch.com/collections/nonl...
Physics Playlist: • Newtonian mechanics: R...
Collab with @vcubingx • Calculus of Variations...
Today we be doing what the title says :v Enjoy! :D Video sponsored by Ridge btw! :3
Help me create more free content! =)
stemerch.com/
/ mathable
Merch :v - papaflammy.myteespring.co/
www.amazon.com/shop/flammable...
shop.spreadshirt.de/papaflammy
Become a Member of the Flammily! :0 / @papaflammy69
2nd Channel: / @npcooking69
--------------------------------------------------------------------------------
Wanna send me some stuff? lel:
Postfach 11 15
06731 Bitterfeld-Wolfen
Saxony-Anhalt
Germany
--------------------------------------------------------------------------------
Twitter: / flammablemaths
Instagram: / uncomfortably_cursed_m...
Flammy's subreddit: / flammybois
Facebook: / flammablemaths
Want to know more about me? Watch my QnA! =D • Question and Answer Ti...
#physics
![Exact Solution of the Nonlinear Pendulum [No Approximations, engis gtfo]](http://i.ytimg.com/vi/efvT2iUSjaA/mqdefault.jpg)
![Exact Solution of the Nonlinear Pendulum [No Approximations, engis gtfo]](/img/tr.png)
Flammy: Forgets to put a tiny dot boi on x at the last.
His viewers: *So you have chosen death*
Ugh when are we ever gonna USE this stuff
xD
mathematicians: *T R I G G E R E D*
You're supposed to be the physicist and notice that he made a mistake in 20:26 :'(
Unfortunately you didn't Andrew :'(
@@eulermed8068 No I think the mistake was actually at 22:01
T R I G G E R E D
YES more lagrangian stuff
Lagrangian mechanics, one of the greatest achievements of mankind :D
agreed!
dude, this is way overrated; Newton's equations deserve all the credit; and by writing them in any coordinate system, considering the covariant components, u get what is called the D'Alembert equations; if only conservative forces act in the system, u get the Lagrange equations, which are equivalent to Hamilton's principle of stationary action (at least for unconstrained or holonomic constrained systems);
20:26 thats supposed to be x double dot right
Yup! Gladly It was right the line before then! =)
WHAT IN THE NONLINEAR DYNAMICS?! ANDREW AND PAPA POSTING VIDEOS ALMOST SIMULTANEOUSLY??
I love it when you do physics stuff.
:)
9:41 "I can use a force and let it act on my wife, for example, smash her against the wall.” LMAO!
:D
This video was absolutely incredible, I adore Lagrangians and Mechanics Stuff!!
:)
*2 is indeed the ODDEST prime!*
More mechanics please!!!
Hi Flammy! PLEASE keep making more physics videos! There is a serious untapped market on TH-cam that is ripe for the taking.
One small comment as a physics student though. Since the whole point of Lagrangian mechanics is to eliminate forces and replace them with energies, really work wouldnt be mentioned at all in a pure Lagrangian approach. It actually complicates the analysis of the potential energy significantly. You can immediately apply the constraint M=(m/L)x to the potential energy U=Mgx to obtain a cleaner solution.
Please make more physics videos!
I know you can only do so much in 20 minutes, but it would have been interesting to include an angular deflection at the table-corner and a state-dependent friction force for the table-top, similar to a pendulum with a state-dependent mass and cord-length. The resulting dynamics would be nonlinear, and thus quite interesting regarding its solutions. Nonetheless, great video!
very good! Really good !! you are an inspiration! whenever i think about giving up making math videos i come to you! thank you for existing 🤙🏾❤️
Hey man. I really appreciate your channel. You clearly have a passion for math and want to share what excites you with others, and let me tell you, I am 100% here for it. Keep it up man :)
In one of your previous videos... in one way you plugged in a square matrix into gamma function!!!! You actually extended the domain of *inputs* for a function!!!!
Which can't be covered up by even complex nos.!!
Can you try to do the same for other functions like sin, cos, log etc.???
New inputs, New outputs, New domains, New results!!!!!!! Totally different!!!
things that make me cry: when papa uses the same symbol for the Laplacian and the length of the rope :""(
;_;
@@PapaFlammy69Oh no! well anyway
Lagrangian. The laplacian is another thing (is a differential operator).
Another way to introduce that spiral 🤣🤣🤣
Need more Lagrangian Physics
Yesssss, more classical mechs pls!
What an amazing video!
thx José! :3
This will come in handy, next time a cobra asks me whats the differential equation describing the relationship of him falling off a table :)
xD
MORE PHYSICS MORE PHYSICS
I remember watching the original video in german when I learnt about theoretical mechanics in university, those were the times
good ol' 3 years ago :D
Hey i saw your videos in my recommended again :)
YES more lagrangian stuff(2)
Nice video
Great!
Very cool. When is the video on Hamilton Jacobi coming out?
There is a better way to think about de equivalence of those derivatives (r'=x'). If all of the rope bits wasnt "glued" together, any of them could have some different speed, but they are, in fact, glued, so that implies on the |speed| of any of them beeing the same. The amount of kinectic energy of the system is, in any case, the \integral{(v^2)/2dm} but the speed does not deppend on that little piece ("dm") of the rope you're looking at, so you could take any point and use as the |speed| and it is, in fact, easier to just get the tip point.
yup!
"moves down in x-direction" me with cartesian co-rodinate system: bruh
xD
Came for maths but got physics.... I ain't even mad
Ja, mehr Probleme, mehr Lösungen, papa flammy löst wirklich wie fast alle Probleme! Was für ein außergewöhnlicher Papa and please don't think I'm dumb, coz I can speak English too, lol 😂
:)
wait, it's all harmonic oscillators?
always has been
:^D
This comment really... resonates... with me
I’ll see myself out
It's not an harmonic oscillator, the - sign screws it up.
Lets see... at every moment, the mass on the table is (1-x/l)m, and it moves right with a velocity dx/dt. Likewise the mass hanging down is xm/l and moves down with velocity dx/dt. The friction above slows the whole system down by a force of (1-x/l)mp, and gravity pulls snek down with the force xmg/l. m, l, p are constants, and we want to know x as a function of time, from small x > 0 up to x=l. p is a constant of the form force per mass, and may depend on velocity as well.
9:45 just.... XD
*so finally your video came in my recommendation*
nice!
Shouldn't the DiffEq you got at the end have the second (time) derivative of x, not the first?
Seems like I forgot a tiny boi hehe^^
@@PapaFlammy69 who would win, one papa flammy or a smol boi?
the boi always wins! :D
@@pR0stYp3 the swole boi
are you going to do a video on lagrange equations of the first kind? I’ve been trying to do those but haven’t figured out how to do it
The last differential equation (but there is x 2 dots instead of 1 dot) looks like harmonic oscillation's equation, but it does not oscillate at all. So here we gotta just believe to formulas instead of intuition, like everywhere in physics
Nah, not oscillating. The frequency is not imaginary
Damn, there is a minus, not plus
Papa you've finally mastered the "Heloo my fellow mathematicians" ;)
:D
Try with fly chain from a cup like fountain
I'm planning on doing this problem with friction using Lagrangians on my website. If anyone would like to see it, plz comment here and I'll be sure to share the link once it's ready!
You should consider doing a video on the Markowitz portfolio theory. It's an awesome application of Lagrangian optimisation where it's centred around linear algebra.
Do some IPhO mechanics problems!
That meme though...superb daddy xd
BTW I am getting ur recommendation...
Disclaimer - No snake was harmed during making of video..
gladly!
Clear explanation even I managed to understand everything lol
nice! =)
A little mistake at last bro, it's mx DOUBLE DOT in the last equation.
Love how u swear while solving. Gr8 vdo❣️
Papa flammy everywhere
Ugh, so complicated, I will stick with Abstract Algebra only. Love you, Papa :D
:D
[Insert clips of papa kicking all sponsors away here]
xD
Ok, but can you use lagrangians to solve the motion of a free particle in flat space in 1d?
So interesting that like 9 times out of 10 your equation of motion for a classical dynamics problem turns out to be the Harmonic Oscillator
Everything's a harmonic oscillator if you're brave enough! :D
Very difficult😏 😂
What did you use to draw the problem in the thumbnail? Love the videos btw.
Simple photoshop^^
@@PapaFlammy69 even for the table and rope?
@@SWL061
Are you surprised?
dachte der tisch ist ein großes pi und dann dachte ich da kommt was geiles
xD
It seems like I have such a tolerance that I stay more than 20min in videos I don't really understand
:D
So solution is c1exp(kt)+c2exp(-kt) {k^2=g/L} which is some kind of sinh(t) or cosh(t)
yup!
Kannst du mal ne Videoserie machen wo du die Lagrangemechanik erklärst?😅
So ne kleine Einführungsserie.
Hard to beat Tim Dillon's Ridge Wallet advert
Flammy ma boi u say ur feeling a bit better but ur doing physics... I think u might still be sick lmao
;_;
I think now Jens is gonna hit lagrangian mechanics badly 😅😅
:D
After integration, should we add some initial x0? Maybe i did something wrong, but my final equation seems to be:
e^(t*root(g/L)) = x.
Which is unit-wise wrong
yoyoy Papa flammy do u have discord?
yes!
@@PapaFlammy69 würdest du mit deinen Namen+Tag geben?
20:07 x-double-dot
I found a very good application for lagrangian. there are 2 chains and they are connected with a rope. and they are moving on a pulley. The mass of the chains that accelerates the system is changing because if one of the chains falls, then a part of it stands on the ground and it's weight does not contribute the force which moves the system. and when a chain rises, then the weight of that chain which contributes the net force of the system is increasing.And system is doing a simple harmonic motion.It is a very different system and very good. I have a photo of the system and I want to send it to you. Do you have an E-mail adress? It is very suitible to make it's lagrangian analysing video. Please reply this comment. Thank you.
What kind of psychopath writes the kinetic energy with m/2 instead of (1/2)m
xD
Papa Flammy, you forgot to make a final point where x marks the spot, but that's okay by me, cuz I always finish my sentences with a triple period just in case you need a spare or two...
I have a question respect to the last limits of integration...i think that last integral must go from L-x to L because you are derive respect to dx and not respect time.
Best regards,
Newton? Nah boi, all my homies using Lagrenage fr
xD
can i use lagrangian mech to describe my own snek?
What kind of physic is this? I wanna to learn more on my own because it seems interesting
Lagrangian Mechanics :)
@@PapaFlammy69 thx❤️❤️❤️
15:16 shooting self are we
Are we assuming no friction?
ye
9:45 Is Mama Flammy alright?
she ded
@@PapaFlammy69 me sed
Good morning fellow physicists
Its snake on an ice cube.
Nice meme in the beginning 😀, great video by the way.☺
Hope you don't apply to much force on wife or she is or that at least she developed some kind of durability and thoughness by now.😆
:'D
sup
is this variational calculus?
yup!
@@PapaFlammy69 awesome! I still don't understand what functionals are but it's awesome
btw love ur vids
also plz sign this petition to get andrew dotson out of some weird german guy's basement
the only thing I didn't understand was why you integrated to x instead of L
seems like integrating from 0 to L should work
Hey! On the video where you solved this with Newtonian mechanics, I left a comment about solving this with the Euler-Lagrange ‘cause I was bored. You stole my idea! 😤.
jk (not Rowling), Love you papa flammy. I mean you probably don’t even remember
Can we say that he second derivative of x is g to simplify the equation?
lel
SNEK
I think you missed the double dot in the end for the second therm
ye, my bad ^^'
Kinda late but that's a tasty stuff
Hi. I got a question. Ask wolfram alpha to find the derivative of (sinx+cosx)/(sinx-cosx). And there will be a huge problem! Wolfram gets it wrong (well kinda)
For the algorithm
that x double dot at the end :(
dropped it ;_;
Maybe u should try some diff way to advertise ur sponsors....! That may increase ur views....
Review jee advanced exam paper please
By newton mechanics it's WAYY easier
Let's say our snecc has mass M and length L (linear mass density i = M/L).
If it is already hanging 'x' distance from the table, then the force pulling it down is (ix)g.
acceleration = force applied / mass of body
a = ixg/M
Now, if v is velocity, then dv/dt = a = ixg/M.
NOW, since I'm not well-versed in the formalities of calculus, I'm going to commit a hate crime!
multiply and divide by dx in the LHS (sorry),
(dv*dx)/(dt*dx) = ixg/M
Group up dx/dt as 'v', we get v dv/dx = ixg/M
v dv = ig/M x dx
Integrating both sides
limits: v_initial = 0, v_at_some_moment = v,
x_initial = 0, x_at_some_moment = x,
(v^2)/2 = Mg(x^2)/2ML
=> v^2 = g/L * x^2
EDIT: WTF why I'm getting a different answer? Can somebody point out the mistake?
EDIT 2: Dumb mistake didn't realise my answer is right and what the video calculated was basically the loooong version to reach at the very first statement I take as a given.
I think your a=ixg/M which can be written as a=xg/L or in notational form: ẍ = xg/L . or, xg/L - ẍ = 0. So, the answer you got at last was you basically solving the given equation. To get the final answer we need to solve this differential equation.
Poor snek :(
_The fysicists_
:D
Last equation it must be acceleration double dot rather single dot
X double dot at the end, not x dot
Wait hold up. I don't think this solution covers the horizontal movement the rope gains during the process of sliding of the table.
Langrangian perturbation of solar system is it works because we living in it :), but Langrangian method not suited for this task :) Or "lazy man: approach solar system is wrong :)
One mistake: answer should have m*x double dot instead of m*x dot
yup, my bad!