We have uniform thin rigid disc rolling without slipping on a horizontal rigid plane. A force is applied to its center of mass in a direction along the motion, 30 degrees out from the disc plane. What are a good choice of generalized coordinates for this system in order to furnish Langrages equations? I was thinking (x,y) for the center of the mass of the disc and theta for the angle the central axis of the disc makes with the x-axis for its orientation, but I don't know how to proceed. Thoughts?
We have uniform thin rigid disc rolling without slipping on a horizontal rigid plane...
Leo Turner
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Austin Morgan
That doesn't fucking make sense. How the fuck do you apply a force to the center of mass of a disc? Unless you're applying that force normal to the flat sides of the disc, but then it would fall over. Otherwise, you're going to be applying force to the round side of the disc, but that isn't the center of mass obviously.
Leo Ortiz
I have no idea what you are talking about, and feel offended the first person to respond didn't offer any advice about this problem. If you have a problem visualizing this situation in reality, note that the rigidness of the plane and other such cues clearly define it as a hypothetical exercise. Perhaps you could think of it as a small man or fly hovering close to the center of mass of the disc at the prescriped angle to the disc plain constantly holding a special device that attracts the central atom of the disc in his direction.
Levi Nguyen
>hypothetical exercise
>hypothetical
So in other words a big fat fucking meme?
Justin Sullivan
If I could ban you from the board and kill you instantly for wasting my time, note I would do so with the greatest of speeds.
Christopher Sanchez
why do you have fanart of fucking code lyoko on your computer
Ethan Moore
why the hell are those heads were bih
Xavier Peterson
kek is that force times a distance.
Hudson Johnson
Yet, you can't. So keep wishing, faggot, and I'll keep shitposting
Caleb Gutierrez
Veeky Forums exposed for a bunch of brainlets who talk above their belt on shit like quantum mechanics but cant find the motion of a disc rolling
Ryder Davis
Why would you need a lagrangian for this? I mean, sure, you could use (x, y, theta) system, but since there's no change in potential energy you could literally do the same with highschool level approach of just writing out the equations via F=ma.
Thomas Wood
I believe the way your problem is set-up means your constraint (rolling without slipping) is nonholonomic. I've only dealt with a specific class of nonholonomic problems (skates) so I can't help too much. However, setting it up is trickier than just finding the traditional Lagrange equations. If you are interested in finding a motion through numerical approximation, you can simply use maximal coordinates and a differential algebraic equation approach.
Matthew White
Really, could you do it for me?
I'm aware setting it up is the hardest part which is why my question is about the choice of coordinates and how the kinetic energy (Lagrangian here) changes with it.
Joshua Hill
Are you assuming that disk changes direction under the influence of the force or does it just move in the direction of x axis?
this makes it kinda confusing how much are we handwaving
Colton Fisher
Here is a reference for the problem you are trying to solve, page 21. The mathematical description is unnecessarily dense but the equations of motion and set-up are there.
pdfs.semanticscholar.org
Charles Parker
I'm not sure whats confusing about the force apart I never had a problem understand this. Regardless of the disk's orientation in space, the force is being applied at its center of mass, and points 30 degrees out from the disc plane in the direction the disc moves. The force is therefore changing in direction relative to a stationary origin, but its direction does not change with respect to the reference point of the disc center. I will add that the force is vector is parallel to the xy plane as well. We are now handwaving nothing save for the approximation that the graviational force is uniform on all particles of the disc.
>Are you assuming that disk changes direction under the influence of the force or does it just move in the direction of x axis?
There is no assumption of any kind regarding this, something like that would be derived from the answer to the problem.
Angel Bailey
Assuming L=T
L = 1 2 m ˙ x 2 + 1 2 I ˙ θ 2 − V ( x ) L 1 2 m x 2 1 2 I θ 2 V x
Assuming L = T - V...
d d t ( ∂ L ∂ ˙ q j ) − ∂ L ∂ q j = 0 d d t ∂ L ∂ q j ∂ L ∂ q j 0
(w/ basic notation on the right. Sorry about the spacing.)
It is important to note that this is the Lagrange set for (x,y) on a horizontal plane encountering a parallel force at com. You have 30 deg, so just change the theta of the initial L set.
Isaac Taylor
Oh sorry i forgot to mention, the first set is left in its L form, while the second considers ALL forces and is in the derivative form.
Alexander Allen
>pdfs.semanticscholar.org
That is indeed exactly what I am looking for and in fact looking at this I know realize why the problem I have written actually just asks one to describe the motion of the disc as opposed to deriving it. Thanks. Also for that fellow who said he could solve this using highschool mechanics dont waste your time that aint happening.
Jason Roberts
I'm not against trying to read this but this typesetting is just incomprehensible.
Dominic Cook
No problem, and good luck with the rest of your problem sets.
As a quick comment, I would point out that when facing nonholonomic constraints, it is sometimes (with some practice) simpler to find the equations of motion using Newtonian methods rather than Lagrange methods. I have worked with a few leaders in the subject, and they share this opinion.
Kayden Lee
You are handwaving the part when the disk tips pretty much instantly. How the fuck are we supposed to know which part is a magic model and which isn't?
Jackson Hughes
What a total retard you are. The solution to a many body problem with external forces is an external force applied to the centre of mass
Carson Rivera
You need X,Y, and 3 (or maybe 2) angles. One angle is the rotation of the disc and one is angular about the z axis
Camden Bell
The text in the OP says "If only I had found the courage to tell him what I feel" according to google translate, in case you're wondering too.
Jordan Brooks
>the disc tips pretty much instantly
You have some math to back that up? Why cant it just turn?