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Thread: Parametric equations of a particle

  1. #1
    Junior Member
    Jun 2009

    Parametric equations of a particle

    Consider the motion of a particle of mass m in a 3D isotropic harmonic oscillator potential V(r)=\frac{1}{2}kr^2 where k > 0
    Determine the parametric equations for the orbit of the particle using the general differential equations of motions
    and \dot{\theta}=\frac{L}{mr^2}
    Assume that E>E_{0}\equiv{E_{min}},r(0)=r_{max},\theta(0)=0 and L is not zero.
    The final answer should not contain r_{max}; the final result should be given in terms of the parameters m, k, E and L.
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  2. #2
    Junior Member
    Jun 2009
    Ok, i need find the r(t) and \theta(t) for the parametric equations.
    First, i tried to find r(t) from f(r)=\frac{-dV(r)}{dr} from the range( r_{0}, r)? but the integral is so hard to be solved, i think i get something wrong here.
    Then i tried to find it from E=\frac{1}{2}mv^2+V(r) where v^2=v_{r}^2+v_{\theta}^2 and v_{r}=\dot{r},v_{\theta}=\dot{\theta}
    The integral still owned me, could someone help me or give me some advice?
    Btw, do we need to know about the turning points of radial motion r_{min},r_{max}? I think it helps a lot for the integral.
    Last edited by zorop; Jul 23rd 2009 at 04:24 PM.
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