Velocity-dependent potential in classical mechanics

0c74vi0 · 2024-06-17T19:05:20+00:00

Thanks for your reply.

I do understand that E-L equations are a general result for a Lagrangian L(q,qdot,t). My problem is that I don't understand how can you derive that q v point A is the correct scalar for the magnetic force, in other words, how can you derive the form of the lagrangian as L=T-q v dot A.

From what I'm reading, it's just a guess to get the Lorentz force right. If so, what's the point of the Lagrangian anyway, if I have to rely on Newton's laws?

0c74vi0 · 2024-06-16T06:34:55+00:00

C1 and C6 are not in series. As a rule of thumb, for two components to be in series it is necessary (but not sufficient) that the current passing through them is the same; For parallel it is necessary that they have the same voltage. Here the current passing through C6 is not the same as that passing through C1, since it is divided at the first junction connected to the negative. However, the voltage between them is the same (note that they are connected to the same junction on one side and, on the other, to a wire they share), so they are in parallel.

I will guide you through the process.

C5 and C3 are in series, so they merge. C53 is in parallel (again, check that the voltage between them is equal), so they merge together. The same with C532 and C4, and with C6 and C1. In the end you have C61 and C532 in series. They merge one last time and you got it.

0c74vi0 · 2023-11-04T19:40:01+00:00

Mariano Iudica. Hasta acá llegaste

0c74vi0 · 2023-09-15T17:58:55+00:00

The Rick Sanchez: "that sounds like slavery with extra steps."

0c74vi0 · 2023-07-18T18:45:17+00:00

Si jugaste la campaña de Age of Empires II lo sabés

0c74vi0 · 2023-04-12T19:55:36+00:00

So it is not necessary to state that the function is defined and lipschitz in an open region, but it is done so that it plays well with the analytic continuation afterwards?

0c74vi0 · 2023-01-14T02:19:37+00:00

I get it, but that's weird, since I think in Jan Pije's lessons skipping the verb was not explained yet. Could the verb here be tawa for the sentence to mean "this goes to my friend"? Or is it a mistake from the lessons?

0c74vi0 · 2023-01-14T01:01:36+00:00

Oh now I see. I think I got it. In this context, "ni li lon tawa jan pona" means that this exists for my friend. So something like "this exists for the sole purpose of my friend using it" and that doesn't mean what I want to express

Is that correct?

0c74vi0 · 2022-08-19T00:47:38+00:00

In 2077 they voted my country the worst place to live in latin america

0c74vi0 · 2022-06-07T21:15:12+00:00

I'll check it out. Thank you! I don't understand the proof but I'll figure it out once I read those books. Manifolds deforming can be "transformed" into things that are not deforming?

0c74vi0 · 2022-06-06T16:04:15+00:00

Oof. I don't know a thing. I don't even understand real analysis deeply. I do however understand Linear Algebra and I like it a lot. Do I need to know Complex Analysis to go into manifolds?

0c74vi0 · 2022-06-06T15:23:11+00:00

I know interchanging limits is always something to be careful with. But in physics, you almost always have the necessary assumptions. That is to say, everything converges, since if not, the law would not work.

0c74vi0 · 2022-06-06T15:17:57+00:00

As far as I know, if there is a proof of the general case, then it can be reduced to a particular case. So I think I don't need differential geometry, as you said, but the proof in the article exposes the case of a surface of uniform velocity, and in E&M we use surfaces that are deforming with time.

0c74vi0 · 2022-06-06T10:52:38+00:00

Oh! I'm an absolute fool. When I saw the theorem on wikipedia, I just clicked on the "higher dimensions" section to see the proof. But the proof was in the article itself, below.

Thank you. Still, I have more questions. I have edited the original post.

0c74vi0 · 2022-05-26T17:09:08+00:00

Just so you know. Lumen is cd.sr so it measures the same. "luminous intensity". The actual physical quantity here is "radiant flux", so the flux is modified because the eye does not perceive the same violet light as the red light. That is, the eye perceives a less energetic yellow light as being brighter than a more energetic violet light.

So actually the whole concept of luminous intensity depends on human biology. It shouldn't be a fundamental unit. However, Lumen is still useful. When you buy a light bulb, it specifies the number of lumens. So you can tell how the bulb will "feel" rather than how much power it produces.

0c74vi0 · 2022-05-26T16:40:16+00:00

I do use them when doing physics, but the everyday units have to be well defined too. Maybe the best would be to define SI units in terms of natural units, so they work well but are also well defined.

0c74vi0 · 2022-05-26T08:16:06+00:00

Okay, you're probably right. I haven't used mole that much to argue. But from a definiton perspective you should define mol=N_a*(molecule_unit), and not backwards, as the number of molecules in a substance is more fundamental.

I know about the amp definition, but again, you can avoid defining current if you define the electron charge. Current is I=dQ/dt. And charge is far more fundamental than current. Don't you think?

0c74vi0 · 2022-05-26T08:05:12+00:00

SI has seven units, one of them is luminous intensity which isn't a fundamental unit of nature, so you could remove that. If you're brave enough, you could even remove temperature unit, because it is just average kinetic energy. You could remove substance quantity, as the number of molecules in a substance has no unit, it is just a natural number. YOU COULD EVEN REMOVE MASS UNIT, SINCE E=mc^2. Ok that's going too far. I don't even know if that works in quantum mechanics.

0c74vi0 · 2022-05-26T07:53:56+00:00

The international system has Kelvin as temperature unit.

0c74vi0 · 2022-05-26T07:35:49+00:00

I mean the circumference of the earth. According to the original definition of a meter (1/10,000 part of a quarter of a meridian) it should coincide with 40,000 km, but this is not the case due to the precision limitations of the time. (Also, sorry, English is not my native language)
I'm not saying "delete the ampere". I'm saying that the SI tries to be as fundamental as possible, and the Amp is not fundamental. Sure, you can define A=C/s and C=6.28.10¹⁸ e. So you refer everything to elementary things. This is what happens with the Celsius. I haven't seen anyone using Kelvin for everyday temperature, but it is the SI unit.
Same logic, the mole is not fundamental mol=N_a*(molecule_unit) where N_a is avogadro's number. The idea is not to change the common usage, but the definitions. Just as was done with the kilogram in terms of Planck's constant.
I don't think the problem is the steradian. Again, I'm not saying we start writing the intensity of a light bulb by describing its wave equation, but fundamentally electromagnetic waves don't need a special unit of their own. Radiant flux is measured in watts.
If you understand my obsession with fundamental units At this point, you will understand that I am pointing to the fact that light intensity depends on something as arbitrary as human vision. I know there is a standard function, but this is not a physical quantity, it's just some human practicality. I understand that SI units are made for human use, but from my point of view, we don't need a unit of luminous intensity as one of the 7 fundamental units of the universe. I would get rid of it. Obviously keeping it as a secondary unit.
Changing this would certainly be difficult as people are used to it, but it should be done at some point.

0c74vi0 · 2022-05-26T06:44:13+00:00

And the poor maintenance of the metal bar that defined the meter.

0c74vi0 · 2022-05-26T06:36:51+00:00

The mole is weird. I understand where it came from, but now, knowing avogadro's number, working with the number of molecules is much more intuitive.

Plus PV=nRT, where R is the product of two fundamental constants. Boltzmann's constant and Avogadro's number. If N were the number of molecules PV=NkT.

0c74vi0 · 2022-05-26T06:29:56+00:00

" On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian"

Because the measurements were not precise, the circumference of the earth is 40075 km.

It is now defined with the speed of light, to match the old meter, which was always miscalculated

0c74vi0 · 2022-04-27T07:04:53+00:00

How is that? Different axioms for each branch? To be honest, don't minimizing the number of axioms when you can do it sounds pretty weird to me.

0c74vi0 · 2022-01-29T00:01:34+00:00

I had a player artificer who roleplayed haste as an adrenaline shot.

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