The Inclined Plane - Derivation using Lagrangian Mechanics!
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- เผยแพร่เมื่อ 1 ธ.ค. 2019
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Today we are going to derive the equations of motion for the inclined plane with fixed inclination :) Using lagrangian mechanics is the tool right here and it's going to work absolute wonders! Hangabtriebskraft ahoi, enjoy! =D
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![A Rope Sliding Down a Table [Lagrangian Formalism Approach]](/img/n.gif)
okay so basically you should do more of these furshur
@@PapaFlammy69 Yes pls, moar
Andrew... Can you help also congrats with the plaque...
f(z)=z^3+mz^2+nz-52
Given that the roots of the cubic equation f(z)=0 are a, 1/a and a+13/a+46 find the roots of the equation f(z)=0
@@matthewcapstick6242 I think there is a typo in your question. Can you check it again?
Agreed 💯💯💯💯
Solve this inclined plane problem again but in curved space time I dare you
Do it no balls
How dare you
>makes operator theory videos
>doesn't want to solve nonlinear DE's
@@PapaFlammy69 using Lie-Trotter or smm here might be as much of a nuke as using the Lagrangian. Glad to see the physics content tho, the simple example of the complex method always helps
And here ladies and gentleman we have a man cutting cardboard with a chainsaw
It is like asking the robot to bring the two stowaways to the bridge #h2g2
That's like using an angle grinder to cut a piece of paper
Or a samurai sword to cut your sandwich
Pretty much yeah xD
If the paper wasn't there it wouldn't get cut in the first place
Exactly what Lagrangian mechanics is.
@@generalizedkyle Ok but try solving a double pendulum problem without lagrangian
6:19 Didn't expect to see one of Grant's pi creatures!
Xd same
Subhasish Mukherjee omg hi i also was watching this video
Lagrangian mechanics is love, Lagrangian mechanics is life.
Papa, even though the force is downwards, I believe the coordinate y should still be positive r*sin(phi). This would give a U=+mg*r*sin(phi) and you end up with r(t)= -t^2/2 which makes sense because the radius should be decreasing.
For the negative sign to appear in the y-coordinate you have to define your y-axis the other way!
I was looking through the comments to see who else noticed!
Wait wtf your username is Lagrange just noticed lmao
In order to get the minus sign on the y component you should have chosen the opposite direction for y. If you do that, the potential energy is -mgy (if y=0 is your zero potential energy) and you correctly get that r decreases, as it should.
Lagrangian Mechanics are really fun to do man! Always a pleasure to tune in
@@PapaFlammy69 Ahh definitely my man!
When u use the infinity stones to order a pizza
You just combined all my freshman year engineering classes.
>mfw dotson and papa upload at the same time
@@PapaFlammy69 bruh momento numero dos
Yes, I too always thought they were the same person.
@@HAL-oj4jb😳
Just goes to show how mathematics is the language of science and how physics is the purest of all the applied sciences.
*Angry biologists scream in the corner*
DNA methylation rate is basically the only thing, ever
Tfw you nuke a fly.
thanks, really I appreaciate because in most books and classes only the newton approach of that problem is used. I learn something new
Thanks man. Been waiting for quite a while for this thing.
By the way, papa Newton is proud for using his dots.
I love Lagrangian mechanics. Beautifully done! You work so hard to bring us die vergnugung. I’m gonna buy some of your merch.
idea: calculate force on an inclined plane *relativistically*
Doesn't work: newtonian gravity leads to contradictions in special relativity, and in general relativity you would get a nonlinear differential equation (the geodetic equation with constraints), and as flammy said in this video, he doesn't like those.
Please don’t stop these lectures
Papa and Dotson in harmony with each other!
coolest physics channel on youtube imo.
That feeling when you're at work and can only comment and like and not watch the video until tonight. HAPPY SECOND DAY OF ADVENT! #fpadventcalendar
@@PapaFlammy69 Hiyaaaa \o/ Got to watch the video last night while working more (and eating ice cream WOOOO!) but didn't get to follow along too closely so hopefully I can get my hanabtriebskraft on today and pull out that notebook XD Looking forward to day 3! #pfadventcalendar
This is the first time ever i knew exactly what u were going to do in a vid
How dare you make a physics video after making fun of Richard feynman. I'm still waiting for you to apologize to feynman. HAIL RICHARD FEYNMAN. Good video tho
Idk if one is specifically supposed to look for polar coordinates, but great video all around! Thank you!
Love the physics content!
According to the ssystem x =-r cos and y=r sin , if we define x=r cos y=-r sin clearly the particle velocity will point upwards, the particle will climb upwards (dr/Dt < 0 )
Ah finally, some flammy mechanics
Seems like Papa has made a deal with the devil to get brilliant at math, but now he can't use Newton's second law.
Two pendulums of masses m1 and m2 and lengths l1 and l2 hang from the ends of a bar with no weight of length 2L, which is suspended in its center O. Both the pendulums and the bar can rotate freely around the suspension points: P1, P2 and O. Assuming that all the movements are carried out in the vertical plane, analyze the constraints and determine the degrees of freedom of the system.
You are a really mad scientist ! 😉🤣😂
Thank you for that.
Verry good! 👊
A German boi pronouncing *L A W H U U N J* perfectly, who could've thought. Cool video btw, I'm a math major secretly wishing to take Analytical Mechanics next year but also sort of scared.
Ótimo vídeo. 😎👨🏫
OMG I never knew you were kind of a physics boi!
I would have chosen coordinates u and v where v measured the distance from the plane (which stays a constant zero), whilst v measures the distance falls along the plane
Nice finally some physics :D
1:57 Close Lagrange Encounter of the Second Kind
Great video
Fuck yes! More of this papa flammable
"this mess right here" yeah
Papa Laplace would be proud
A particle of mass m slides under its own weight and without friction on the inner surface of an inverted vertical cone of semi-angle α. Use the Lagrange multiplier method to find the constriction force. Express your result in terms of the energy and the z component of the particle velocity.
I just wonder, if you intentionally pronounciate "mass" as "mess" (ca. 2:00). Yes, physics and math can become a mess :) Love your brute-force derivation!
A body of mass m slides without friction on an inclined plane that forms an angle θ with the floor of an elevator. If the lift goes up with uniform acceleration α:
a) Describe the inertial system.
b) The natural coordinates and,
c) Explicitly describe the holonomic constriction on the body.
Two masses m1 and m2 are suspended from a rope of length l1 that passes over a pulley. Two other masses m3 and m4 are simultaneously suspended by a rope of length l2 that passes over another pulley. These two pulleys hang from the ends of a rope of length L that passes over a third fixed pulley. Write down the constraints explicitly and determine the degrees of freedom of the system.
Papa Flammy goes all "Least Action" on us!
WHOOT!!
I can't wait for the Quantum Mechanical version!
Can we have a series on some 🆎️stract stuff + flying 🆎️ creatures (mohamed's profile pic)
Physics yay
Here's a tough one for ya, Flammy: Does there exist a curvature of the plane k such that neither k nor the circumference of a unit circle on said plane are transcendental?
I appreciate physics content.
TBH Langrangian Mechanics was the easiest part of Classical Mech. for me, since it's just solving a DE. The rest of CM was pretty hard!
yes some mechanics!
Could you please make video on orbital mechanics?
More physics videos please!
I'M STILL GETTING THESE RECOMMENDED
Yay some physics again! Please do more papa, love u bruh (no homo)
You have forgotten include de force due to friction as a generalized force in the motion ecuation.
please do more mechanics !!
Oh flammy it was almost perfect, 5:18. 😂
Hey I have a final in this sort of thing on Monday can you maybe cover all of Lagrange's and Hamilton's equations next time?
I learned a little bit of LaTeX last night for honors homework. {/bf :D} = *:D*
I love you
Papa can you do some spicier systems in lagrangian mechanics thanks ly
Wer kennt schon HANGABTRIEBSKRAFT nicht?
i bought some more flammable merch :3
@@PapaFlammy69 cant wait for it to arrive eeee
Lagrange and Hamilton walk into a bar...later they leave at 1.41421...the speed they walked in at, because they are now both broke.
L=g_{kl}*x'^k*x'^l
g_{kl} are functions of the coordinates, and g_{kl}=g_{lk}. x'^k is the derivative of the kth coordinate with respect to some arbitrary parameter, and there is automatic summation for k and l (lets say we are in a 4 dimensional space, so summation from 0 to 3). Calcukate this one, and you obtain the geodesic equation, which would describe a free falling point particle in general relativity. You could make a video out of this.
I just watched papa flammy set the house on fire to cook a instant ramen.
This shit is amazing
Calculus of Varations for an inclined plane? Noice
bazooka to kill a fly
Pappa Flammy, I'm having trouble with a complex integral to find the solution of a PDE using Laplace transform. Would you like to help me and publish our findings together?
Hey Jens! I wanna send you an Integral. where should I send it for you?
Seriously? My analytical mechanics midterm was litteraly 6 hours ago, why oh why didn't you post this yesterday?
@@PapaFlammy69 I forgive you😋
one lagrangian boi
please remake Feynman lectures in physics
Shit I was looking for that like a couple days ago and couldnt find much. Is this on demand service papa?
Btw you know that shirt implies sinx=x right?
Can anyone help...
f(z)=z^3+mz^2+nz-52
Given that the roots of the cubic equation f(z)=0 are a, 1/a and a+13/a+46 find the roots of the equation f(z)=0
Now do it with a perfect circle rolling down xd.
Ciao :D
it is a mass not a mess, ..... but if a mathematician does physics that is what you get! 🤣 Let's solve the spherical chicken in a vacuum!
Sry that was a cheap joke! Actually I love the simplisity of this basic concept that cover many questions in GR and is jet somehow connected to the Hamiltonian Formalism that works in the quantum world. There is more to it than the math!
0:26 Is it a JOJO REFERENCE BOIIII?!
Solve double pendulum with F=ma
Now work out the two-body problem where the incline itself has mass M and can move!
that's gonna be a bill gates with a giant paddle and small ping pong ball from me.
So, in short, if you note that the effective acceleration a is g*sin(phi) (the component of gravity "down" the incline) then the solution to Newton's equation is (wait for it!) s(t) = s(0) + v(0)*t + a*t^2. WHODATHUNKIT?
Man, you're just shooting a mosquito with a cannon
“If we remember correctly from 3rd grade physics > T=m/2r^2” ahhh of course.... 3rd grade physics
OK, smart boy, I modify the problem slightly to make it harder to solve. Suppose the slope is given by a triangle block that is sitting on the smooth surface and it moves freely. What will happen to the acceleration of the mass, m, placed on such a triangle block? Assume the triangle block mass is capital M. That is MIT level.
You should have told g = -pi^2 because otherwise the mass would be moving uphill.
That's like killing a mosquito with a bazooka
On your integral you forgot the double dot r.
he says Lagrange like how la croix looks like it’s pronounced
The kind of things you read to your kids before sleep
3b1b_oid
Phi=theta? :0
In 0:19 - 0:20, what is that phrase?
you made a mistake i think because de potential is mgsin(phi) actualy and the you get r(t) = - sin(phi)*t^2 + ... as it would be expected to go to a smaller radius héhé
That’s cool and all, but did you know F = ma? hA
@@PapaFlammy69 :'3