Recent content by Rick16

Thank you for making this clearer. I briefly thought about how I should go about finding the force from this momentary potential energy change, but a decided that in any case the force can only be perpendicular to the boundary, and that is enough for me (for now).

I don't understand the last post. I think the situation is much simpler. I forgot indeed to consider that the potential energies are constant. Since they are constant, there is no gradient in the fields and the force is zero on both sides of the partition. The only place where the potential...

I understand the case with a single potential energy field, or perhaps I should rather say force field if I want to speak of the direction of the field. I can orient my coordinate axes such that the force points along one of the axes. The momentum of a particle moving in this field would then...

Problem Statement A particle of mass m moving with velocity v1 leaves a half-space in which its potential energy is a constant U1 and enters another in which its potential energy is a different constant U2. Determine the change in the direction of motion of the particle. Beginning of Landau's...

I just thought about something. I am new to Landau and I am not familiar with his style. When he writes the displacement as ##dl_1^2 =a^2 d\theta^2 + a^2 sin^2 \theta d\phi^2##, perhaps this is not meant to be an intermediate step towards the final solution, but just a helpful statement?

This problem has been addressed before under https://www.physicsforums.com/threads/trouble-understanding-coordinates-for-the-lagrangian.1006528/ I also copied the following problem statement with Landau's very sketchy solution from this old post, because I don't have the English edition of the...

In any case, this is my first reading of the text, and I am satisfied that I can show that ##\vec v## is constant when I assume that the Lagrangian is known. I don't need to show it for an arbitrary function ##L(v^2)## at this point. I may come back to it later, but now I must move on. Thank you...

@Vincf already had a counter example in #5.

The fact that dL/dv is constant was never the question. The question was why v is constant.

This would be my next problem: I don't understand the paragraph before equation 4.1. But like I already wrote, my head is already spinning, mostly because of problem 3, and it looks like I won't be able to understand anything more today.

I also tried out several different functions for ##L(v^2)##, but I found that the velocity was constant for all of them. You apparently found one for which this is not the case. When Landau writes that the Lagrangian can only be a function of the square of the velocity, he actually does not...

Yes, I know, but PeroK's suggestion is one way to see why the velocity would have to be constant (provided I already know the form of the Lagrangian). Landau must have had something else in mind.

I just wanted to ask why on earth the Lagrangian would be ##L=\sqrt {v_x^2 +v_y^2 +v_z^2}##, when I discovered that you had changed that. I spent quite a while this morning trying to work through the problems at the end of chapter 1, and my head was already spinning. This Lagrangian really...

Thank you, that is an interesting trick with the ratios. It is not likely that I would have thought of it. I suppose you know how to do it? Because I don't.

This question does not seem to evoke a lot of interest. Could somebody just tell me if it is legitimate to write ##\frac{d}{d\vec v}(\vec v \cdot \vec v)=2\vec v##? I.e. I wonder if I can take the derivative directly with respect to the vector as a whole or if I must take the derivative...