Recent content by Zeroxt

Okay, thanks you so much for your help, you help me a lot.

Yes I found angles in term of these condition that you say, so I have two possible values for theta one of them greater than theta0 and the other equal to theta0...

I think that I found the angle, because I compute the Energy with the initial condition and then I compute the Energy in the moment when the velocity in theta is zero, so the energies have the same value therefore I found an angle with these condition... Now I have a doubt, the minimum angle is...

I write you the problem: A spherical pendulum it's build with a rod of length, massless and inextensible, which in the extreme of the rod put a punctual mass m under the gravity acceleration. In a initial moment the particle it's shifted an angle theta0 respect to the vertical and it's impulse...

In the problem appears that the condition initial is theta0 <<1. So the value of theta that I found is a constant times theta0, this constant can take two possible values depending of the large of the pendulum, g and the velocity initial (w0) in fhi (which is constant too). In case that lw0>g...

I found this value of theta assuming that the velocity in theta (theta dot) was zero and I use the condition of the energy to find these theta. So in this angle the momentum will be zero...

Yes, I didn't see it, excuse me for that

But so, how can I define the limits? Because for action of theta, you have to do a line integral, so you have to integrate in a period... For this I suppose that the limits are -theta0 to theta0... In other case I don't know which are the possible limits

Yes, I did that, I integrate with the substitution and then I come back to the original variable and evaluated the result of integral, but in the result I only have squares variables, so the result of the evaluation is zero.

Thanks vela, I guess that work... But only if the terms of phase in the solution are equals or zero, because with that the element would be a constant.

I have the same problem, but in my case the integral I express in other way and for small angles, so in my case the integral was from -theta0 to theta0 ∫±(1/θ)√(-α+Eθ^2 -mglθ^4)dθ. So I did a sustitution with y=θ^2, and the integral was the form ∫(1/y)√(-α+Ey-mgly^2)dy, and that integral is in...

The terms in the diagonal of A are the energies of the two oscillators, and there are a constant of motion. So I have to find the other two terms of the matrix (A12 or A21) in terms of the constant of motion that I found early (E1, E2, Lz), I tired but I don't see how can I produce the term P1P2...

Yes, just like you say that was the answer to the problem to separate in two oscillators, the part of isotropic was a mistake because when C=0 the system was isotropic and therefore Lz is a constant of motion. Summarizing, H=H1+H2 was the answer, so my two constants was E1 and E2, and...

I have to apply some transformation that make the problem convert into a problem of two isotropic harmonic oscillators. I guess that the Lagrangian is the sum of two terms, just like you say, but I don't know if is right the way that I used.

1. A bidimensional oscillator have energies: With C and K constants a) show by a transform of coordinates that this oscillator is equivalent to two isotropic harmonic oscillators. b) then find two independent constants of motion and verify this using: with "a" the constant. I tried to do...