Results 1 to 2 of 2

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 $\displaystyle V(r)=\frac{1}{2}kr^2$ where k > 0
    Determine the parametric equations for the orbit of the particle using the general differential equations of motions
    $\displaystyle f(r)=m(\ddot{r}-\frac{L^2}{m^2r^3})$
    and $\displaystyle \dot{\theta}=\frac{L}{mr^2}$
    Assume that $\displaystyle E>E_{0}\equiv{E_{min}},r(0)=r_{max},\theta(0)=0$ and L is not zero.
    The final answer should not contain $\displaystyle r_{max}$; the final result should be given in terms of the parameters m, k, E and L.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Jun 2009
    Ok, i need find the $\displaystyle r(t)$ and $\displaystyle \theta(t)$ for the parametric equations.
    First, i tried to find $\displaystyle r(t)$ from $\displaystyle f(r)=\frac{-dV(r)}{dr}$ from the range($\displaystyle r_{0}$, $\displaystyle r$)? but the integral is so hard to be solved, i think i get something wrong here.
    Then i tried to find it from $\displaystyle E=\frac{1}{2}mv^2+V(r)$ where $\displaystyle v^2=v_{r}^2+v_{\theta}^2$ and $\displaystyle v_{r}=\dot{r},v_{\theta}=\dot{\theta}$
    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 $\displaystyle r_{min},r_{max}$? I think it helps a lot for the integral.
    Last edited by zorop; Jul 23rd 2009 at 03:24 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find Parametric Equation for Moving Particle
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 11th 2010, 08:59 AM
  2. Replies: 1
    Last Post: Nov 29th 2009, 11:07 AM
  3. Parametric equations to rectangular equations.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Apr 5th 2009, 10:39 PM
  4. Replies: 3
    Last Post: Dec 2nd 2008, 10:54 AM
  5. Replies: 1
    Last Post: Sep 1st 2007, 06:35 AM

Search Tags

/mathhelpforum @mathhelpforum