/sci/ - Science & Math » Thread #13118715

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Anonymous Wed 12 May 11:01:56 2021 No.13118715 View Reply Original Report

Quoted By: >>13119152 >>13119169 >>13119429 >>13119468 >>13119683 >>13120287 >>13120424 >>13122993 >>13124809 >>13126657 >>13126950 >>13129500

What year in uni did you start using this Euler Lagrange equation? For me, start of 3rd year

Anonymous

Anonymous Wed 12 May 2021 13:15:43 No.13119152 Report

Quoted By: >>13119170

>>13118715
Semester 2 year 1 if I remember correctly. Could be Y2S1.

Anonymous

Anonymous Wed 12 May 2021 13:23:22 No.13119169 Report

Quoted By: >>13119673 >>13120366 >>13127862

>>13118715
Never used this.
>T. Engineer

Anonymous

Anonymous Wed 12 May 2021 13:23:37 No.13119170 Report

Quoted By:

>>13119152
in this form of notation?

Anonymous

Anonymous Wed 12 May 2021 14:19:04 No.13119330 Report

Quoted By:

Last semester of my BSc. No idea who thought it was a good idea not to teach us at least basic analytical mechanics before hitting us in the face with mysterious H's all over the place in quantum mech. Apparently they might put it in the first year mechanics course in a couple of years, which is probably a good thing.

Anonymous

Anonymous Wed 12 May 2021 14:42:49 No.13119429 Report

Quoted By:

>>13118715
Year 1, first semester, that was a wild ride. The profs threw this at us and demanded to understand it even though we didn't even get to the differential equations chapter at the time.

Anonymous

Anonymous Wed 12 May 2021 14:51:23 No.13119468 Report

Quoted By:

>>13118715
We didn't get to continuum mechanics. Is that what this is or fields in general?

Anonymous

Anonymous Wed 12 May 2021 15:33:57 No.13119673 Report

Quoted By:

>>13119169
The absolute state of engineers kek

Anonymous

Anonymous Wed 12 May 2021 15:35:15 No.13119683 Report

Quoted By:

>>13118715
Start of second year

Anonymous

Anonymous Wed 12 May 2021 17:39:00 No.13120287 Report

Quoted By: >>13121189

>>13118715
Yeah, I think it was start of 3rd year with classical dynamics. It's a cool way to do things, but you use it for like one class, then you're in Hamiltonian land.

Anonymous

Anonymous Wed 12 May 2021 17:56:03 No.13120366 Report

Quoted By: >>13121308 >>13121671

>>13119169
same
t.engineer 2
what is it used for?

Anonymous

Anonymous Wed 12 May 2021 18:09:14 No.13120424 Report

Quoted By:

>>13118715
Was a central feature of a module on mechanics I took in 2nd semester of year 2, only to never explicitly use it again.

I can vaguely recall it being somehow relevant to the Hamiltonian and it looks very similar, but at a certain point of writing those out over and over in QM I've forgotten the underlying math and now just take it as axiomatic.

Anonymous

Anonymous Wed 12 May 2021 21:29:23 No.13121189 Report

Quoted By:

>>13120287
I love canonical transformations so much. Just by wangjangling your coordinates you can trivialize your Hamiltonian. Too bad most canonical transformations can't be represented as unitary transformations, quantization is a little too ambiguous because of this.

Anonymous

Anonymous Wed 12 May 2021 21:48:42 No.13121308 Report

Quoted By:

>>13120366
finding the equations of a conservative mechanical problem usually with multiple moving parts, so that the Newtonian formalism would be really hard

Anonymous

Anonymous Wed 12 May 2021 23:07:10 No.13121671 Report

Quoted By: >>13127023 >>13127978 >>13128262

>>13120366
Euler-Lagrange equations for fields.
https://en.m.wikipedia.org/wiki/Lagrangian_(field_theory)
I only know it's useful for general relativity and quantum field theory/standard model. You first encounter them when studying continuum mechanics. I don't actually know if it's used for solving problems or just to derive known equations in a fancy fashion.

Anonymous

Anonymous Thu 13 May 2021 05:28:11 No.13122993 Report

Quoted By:

>>13118715
literally never

Anonymous

Anonymous Thu 13 May 2021 16:49:33 No.13124809 Report

Quoted By:

>>13118715
3rd year of highschool.

Anonymous

Anonymous Thu 13 May 2021 22:53:42 No.13126657 Report

Quoted By:

>>13118715
First upper division mechanics course
We used Taylor

Anonymous

Anonymous Thu 13 May 2021 23:50:26 No.13126913 Report

Quoted By:

Euler Lagrange for 0+1 dimensional field theories aka mechanics: year 1, semester 2.
For 4-d field theories: year 2, Semester 1

Anonymous

Anonymous Thu 13 May 2021 23:59:54 No.13126950 Report

Quoted By:

>>13118715
Never seen it before in my life. What does it mean and why?

Anonymous

Anonymous Fri 14 May 2021 00:23:16 No.13127023 Report

Quoted By:

>>13121671
The Lagrangian is functional. In Calculus of Variations, you ask what functions are maxima or minima of the functional. The Euler-Lagrange equations are necessary conditions for extrema. For example
$\int_{D} \sqrt{1 + u_x^2 + u_y^1} dx dy$
is the functional corresponding to the surface area of the surface defined by $(x,y, u(x,y) )$ . The extrema of this functional are called minimal surfaces. The Euler-Lagrange equation is the minimal surface equation. Another example is the Chaplygin problem
https://en.wikipedia.org/wiki/Chaplygin_problem#:~:text=In%20mathematics%2C%20particularly%20in%20the%20fields%20of%20nonlinear,possible%20area%20in%20a%20given%20amount%20of%20time.
Calculus of variations is used for these types of optimization problems. In physics, you're just looking for the equations that are extrema of the action because those are the ones considered the most physical.

Anonymous

Anonymous Fri 14 May 2021 02:55:03 No.13127566 Report

Quoted By:

BUMP

bbbbbbbbbb

bbbbbbbbbb Fri 14 May 2021 03:54:57 No.13127862 Report

Quoted By: >>13127967 >>13128179

>>13119169
I learned it from YT in my y1s1. Is it really useless? Thought it was fundamental for fluid and thermo.

>t. cheme y1s2

Anonymous

Anonymous Fri 14 May 2021 04:21:52 No.13127967 Report

Quoted By:

>>13127862
Its useful in fundamental physical research, not in engineering so its ok. Different professions and all that.

Anonymous

Anonymous Fri 14 May 2021 04:24:42 No.13127978 Report

Quoted By:

>>13121671
It can be used to easily derive equations of motion in many physical situations but its never used in engineering because deriving equations of motion has never been the main challege of engineering.

Anonymous

Anonymous Fri 14 May 2021 05:12:04 No.13128179 Report

Quoted By:

>>13127862
My entire job is trying different Lagrangians and seeing which one can give good observables.

t. cosmologist

Anonymous

Anonymous Fri 14 May 2021 05:26:40 No.13128262 Report

Quoted By:

>>13121671
you can solve some complicated systems very easily with it.

Anonymous

Anonymous Fri 14 May 2021 11:53:00 No.13129500 Report

Quoted By:

>>13118715
End of 1st year iirc

Anonymous

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Anonymous Fri 14 May 2021 19:08:05 No.13131087 Report

Quoted By:

sorry, I'm a pure math chad

Anonymous

Anonymous Fri 14 May 2021 22:00:14 No.13131983 Report

Quoted By:

I study glorified economics and calculus of variations/optimal control theory is part of our second year

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