Anonymous at Thu, 12 Sep 2024 19:35:40 UTC No. 16377434

>>16377410
>WTF is a Lagrangian?
A shortcut to the relevant equations of motion. You're going to love it. It really does make things much, much easier.
>L=T-U? WTF? Why does this quantity have so many mysterious properties?
Nature prefers full conversions from potential to kinetic or vice-versa. It doesn't like to hover in the realm with a little of each. So if you take the exchange difference between the two forms of energy, and optimize with respect to position and speed, you will correctly predict the path of motion.

Anonymous at Thu, 12 Sep 2024 19:41:26 UTC No. 16377440

>>16377410
The Legendre transform of the Hamiltonian

Anonymous at Thu, 12 Sep 2024 19:46:08 UTC No. 16377450

>>16377440
wrong. the hamiltonian is the legendre transform of the lagrangian

Anonymous at Thu, 12 Sep 2024 19:56:19 UTC No. 16377459

>>16377410
If you understand basic calculus there is nothing mysterious about it. Probably your questions is really about the principle of least action, and not the actual Lagrangian.

Anonymous at Thu, 12 Sep 2024 20:07:59 UTC No. 16377478

It is magic. Assumption. Nobody has made well good proof that links this theory to newtonian physics, even though they are the same, yielding always the same results.

Anonymous at Thu, 12 Sep 2024 20:16:05 UTC No. 16377488

>>16377478
t.brainlet

Anonymous at Thu, 12 Sep 2024 20:49:14 UTC No. 16377528

>>16377410
>L=T-U? WTF?
The way I always thought of it is that the time derivative of either T or U changes in general, but since energy is conserved, a linear combination of the two is a constant. Lagrange could have defined a*T+b*U and we could have the same equations of motion (up to an arbitrary constant). It's just that taking a =b=1and T-U=0 (at any time T) is the simplest approach. That could be bollocks tho. Just my way of trying to understand what Lagrange was trying to do.

Anonymous at Thu, 12 Sep 2024 20:52:29 UTC No. 16377531

>>16377528
>but since energy is conserved, a linear combination of the two is a constant
>bollocks

yup

Anonymous at Thu, 12 Sep 2024 22:25:34 UTC No. 16377653

Nobody really knows. It just works and physicists keep using it but we don't fully understand yet why it works.

Anonymous at Fri, 13 Sep 2024 00:05:42 UTC No. 16377753

>>16377528
>but since energy is conserved, a linear combination of the two is a constant
Yes but not just any linear combination. The sum T+U is constant. The Lagrangian T-U is not constant but it's time integral obeys a stationary action principal. They are different things

Anonymous at Fri, 13 Sep 2024 00:13:07 UTC No. 16377764

>>16377410
>Why does this quantity have so many mysterious properties?
The action (the time integral of the Lagrangian) is natural from the perspective of quantum mechanics. It comes from the path integral representation of the time evolution operator e^{-iHt}. The principal of least action follows from the ordinary method of steepest descent applied to path integrals.

Anonymous at Fri, 13 Sep 2024 00:17:04 UTC No. 16377769

>>16377410
Spared... For now.

Anonymous at Fri, 13 Sep 2024 08:52:33 UTC No. 16378224

>>16377459
But no one in the history of physics nor mathematics nor engineering has ever understood basic calculus...

Anonymous at Fri, 13 Sep 2024 09:36:46 UTC No. 16378248

>>16377488
Show the proof

Anonymous at Fri, 13 Sep 2024 10:27:26 UTC No. 16378294

>>16378248
Are you serious? You either have not taken a single mechanics course in your life, or you are that stupid. First please tell me what would you accept as a "proof that links this theory to newtonian physics", or what is missing from our understanding of their connection.

Anonymous at Sat, 14 Sep 2024 17:04:22 UTC No. 16380255

>>16378294
If everyone knows it, you should have no trouble providing it.

Anonymous at Sat, 14 Sep 2024 17:06:54 UTC No. 16380259

>>16377528
Bot hallucinating?

Anonymous at Sat, 14 Sep 2024 17:20:14 UTC No. 16380271

>>16380255
Well I'm not gonna give you a lecture on mechanics. Answer the question I asked here >>16378294, telling me what you think we are missing in their connection, and I will tell you why you are wrong, saving us both some time

Anonymous at Sat, 14 Sep 2024 17:21:33 UTC No. 16380276

[math]λ[/math]
[math]\flat\lambda[/math]

Anonymous at Sat, 14 Sep 2024 17:29:43 UTC No. 16380291

>>16378248
Proof?
On the internet?

Anonymous at Sat, 14 Sep 2024 17:39:26 UTC No. 16380304

>>16377434
Anon, minimizing the lagrangian means minimizing the difference which means to have the split in energies be about equal. This is how the virial theorem works too, which is part of thermodynamics which is physics most sacred cow

Anonymous at Sat, 14 Sep 2024 18:17:02 UTC No. 16380377

>>16380304
>minimizing
EXTREMIZING. You clearly don't know how lagrangians behave in spacetime.

Anonymous at Sat, 14 Sep 2024 21:00:08 UTC No. 16380695

>>16380304
>minimizing the lagrangian
Who gives a shit about minimizing the lagrangian?

Anonymous at Sat, 14 Sep 2024 21:07:36 UTC No. 16380706

>>16377410
idk man

Anonymous at Sun, 15 Sep 2024 03:24:13 UTC No. 16381196

>>16377410
Aside from the rather good answers on this thread, one could also see Lagrangian mechanics as a method for determining the “path of least resistance” that a system will naturally take. It relies on such a path-based intuition to start. Ofc, this is a very informal and analogy-based description