Recent content by Alexandre

I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out https://people.ifm.liu.se/irina/teaching/sem4.pdf

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First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.

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Oh, thanks, now I understand. I didn't realize that velocity doesn't depend on time and so Lagrangian goes out of the integral here S = \frac{m}{2} ( \frac{x - x_{0}}{t - t_{0}} )^{2} \int^{t}_{t_{0}} d t

On the idealized curve yes, on the actual data no. Besides it's a joke.

I really like the book, its the first physics textbook that I liked actually. But I've found a minor error. On page 8 (chapter 1 The Wave Function) it says that if you sum deviations from average of a random variable you'd get zero because " Δj is as often negative as positive", here's the...

Suppose I have no potential, just the kinetic energy of a free particle wandering around (actually moving at a straight line with a constant velocity), the Lagrangian will be equal to kinetic energy only. I've found out a hint why my derivation might be wrong, there's a thing called abbreviated...

How can show that momentum is the gradient of the action for the free particle? I tried it like this for one dimensional case: s=\int Ldt ds=Ldt ds=\frac{mv^2}{2}dt\: Velocity is constant right? So I should be able to to this: \frac{ds}{dx}=\frac{mv^2}{2}\frac{dt}{dx} I'm not sure about...

Oh, you're right again.

If D is not constant you should have took care of it when writing Euler-Lagrange equation by applying derivative to it too.

Ups, sorry, I did. Did you figure out how to do the numerical approximation?

Nope you can't. Sorry for that, math is not omnipotent.

Yes it's Heun's method, a.k.a. two stage Runge–Kutta method. In my case F is time independent. I don't seem to understand what F1 and F2 are in your algorithm.

Square of derivative is not same as second derivative and parentheses are missing: \int_0^L ( A \left( \frac{ d \phi (x) } {dx} \right) ^2 + (B +C cos( \phi (x)) ^2 \mbox ) {d}x Applying Euler-Lagrange equation which has a form: \frac{d}{dx}\frac{\partial L}{\partial \frac{d\phi...