/sci/ - Science & Math

[Anonymous No.12053812]

Trying to learn physics and I'm stuck here. Any help appreciated.

I understand that in the Lagrangian the first component is the kinetic energy, and the second is the potential energy, and together they give the you the trajectory of the object

[math]L = 1/2 m\dot{x}^2 - V[/math]

The integral of this with respect to time gives the action of the object

[math]A = \int_{t_0}^{t_1} 1/2 m\dot{x}^2 - V \,dt[/math]

Now I'm supposed to find the stationary point of A using the Euler-Lagrange equation

[math]\frac{d}{dt} \frac{\partial{L}}{\partial{\dot{x}}} - \frac{\partial{L}}{\partial{x}} = 0[/math]

This is where I get stuck. Why am I applying this? And to what? And what does the stationary point give? Apparently you can derive F = ma from this but I'm confused as to how and why.

[El Arcón No.12053825]

>Why am I applying this?
This is merely a postulate, or an axiom, of classical mechanics called Hamilton's principle. The consequence of Hamilton's principle is that the Euler--Lagrange equation generates the correct equations of motion. However, fundamentally it is just a guess that turned out to be correct. All theoretical frameworks rest on axioms: the theory is that the axiom is correct.

[El Arcón No.12053834]

In the way that F=ma is an axiom of Newtonian mechanics, the Euler--Lagrange equation is an axiom of Hamiltonian mechanics.

[El Arcón No.12053837]

In the way that F=ma is an axiom of Newtonian mechanics, the Euler--Lagrange equation is an axiom of Hamiltonian mechanics. You can also derive the Euler--Lagrange equation in other ways, directly from F=ma for example, but it nicely pops right out of Hamilton's principle.

[Anonymous No.12053846]

>>12053825
I get this. I'm not questioning the foundations of physics. I'm asking what the stationary point of the action of an object actually represents. Can you explain this please?

[Anonymous No.12053861]

Here's a bump, I wouldn't get too down on yourself if you're having trouble with analytical mechanics it's not the worst thing to get filtered by.

[Anonymous No.12053876]

>>12053861
Fuck I didn't realise it but it's true... getting filtered feels bad man.

Gonna work through a calculus textbook I think the maths here is too unfamiliar for me anyway.

[Anonymous No.12053886]

>>12053846
>>12053812
Just posting some advice.
El Arcon, real name Jonathan Tooker, is the /sci/ boards resident schizo
I would take whatever he says with a grain of salt, especially around math and subjects that depend on math. The guy thinks he has solved the Riemann hypothesis and some big questions in physics, so he has the ability to convey ideas that seem correct to non-experts, but are actually incorrect.

If you want to see evidence of his schizo-ness go on a third party 4chan archive and search for posts by el arcon

[El Arcón No.12053887]

>>12053846
The stationary point of the action is such that the variation of the action is restorative (in the stationary minimum.) Overall, the derivative of the action at the stationary point is equal to zero. For the minimum of the action, less energy is expended along the stationary action than the action along any nearby path. So, in that way that physics always wants to minimize the energy, the stationary action is associated with the minimum energy path.

[Anonymous No.12053891]

>>12053886
>thinks he has solved the Riemann hypothesis
surely this is enough to warrant an actual diagnosis of schizophrenia?

[El Arcón No.12053900]

[Anonymous No.12053899]

>>12053887
I see. Why isn't the path of minimum energy just a straight line? And has anyone checked your proof for the Riemann hypothesis? (Not that this is relevant but the other poster brought it up.)

>>12053886
Hmm his answer above seems to make sense...

[El Arcón No.12053909]

>>12053899
Free particles do move on straight lines. Massless photons even move on straight lines in gravity. Many people have criticized my solution to RH but I don't believe anyone has shown a flaw in my paper. Pic related, the main criticism is that my solution must be considered inadmissible because I have introduced a new technique.

Here is the best paper I wrote about it:
Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://vixra.org/abs/1906.0237

[Anonymous No.12053923]

>>12053899
I’m not saying he is wrong, just that you shouldn’t take his word alone as fact. You can take what he says and look at sources that are reputable. But you should honestly do this for anything an anon on 4chan says. You shouldn’t even take my word as infallible. Always check that you haven’t been eulered (as Alexander Scott would say)

[El Arcón No.12053927]

>>12053899
>Hmm his answer above seems to make sense...
My parents are two of the three authors of the video Daisy's Destruction and they do that sort of thing professionally for the USA. Because I will call attention to their crimes if I even become a classically public person in the way that successful scientists are often public persons, the USA orchestrates a smear campaign against me.

[Anonymous No.12053931]

>>12053923
You're right, thanks.
>always check that you haven’t been eulered (as Alexander Scott would say)
I was about to go check out what Eulered meant on SSC but then I remembered I don't have 45 minutes to read a blog entry. Will save it for a rainy day.

[Anonymous No.12053937]

>>12053927
your father is peter scully?

[El Arcón No.12053942]

>>12053937
TheSolipsist is Joseph Kuklinski
The Woodman is Helene "The Woman" Gutrfreund, Joseph's wife.
Jacob666 is Carlos "The Jackal" Cavalcanti

[Anonymous No.12053947]

this is some /x/ tier shit itt

[El Arcón No.12053948]

>>12053947

[El Arcón No.12053951]

>>12053947
yes

[Anonymous No.12054001]

>>12053846
It was originally derived from light propagation in which it represents the actual path of a light ray.
In the more general geometric formulation it is basically the equation determining a geodesic.
This is most clear when you're looking at the free relativistic action which is just the interval, and then your statement is literally that particles propagate along geodesics in spacetime.

[Anonymous No.12054940]

https://www.youtube.com/watch?v=zhk9xLjrmi4

[Anonymous No.12055706]

When you define the variation of A and set it to 0, it will follow by generality requirements the Lagrange equations [this should be easily seen in whatever text you have.]. If you apply the equation, get ma+∂V/∂x=0. If a force is given by potential, -∂V/∂x = F and so we have F=ma.