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
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.
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
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...
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...