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Central field - equation

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that in a central force field [tex]\vec{F}(\vec{r})=f(r)\frac{\vec{r}}{r}[/tex] the equation for a body's trajectory in terms of [tex]u=\frac{1}{r}[/tex] is given by:

    where m is the body's mass and L is the angular momentum

    2. Relevant equations

    3. The attempt at a solution

    Transforming Newton's equations for [tex]\ddot{r}[/tex] leads to ab equation for [tex]\ddot{u}[/tex] and [tex]u[/tex] where unfortunately [tex]\dot{u}[/tex] also appears and I don't know how to eliminate it from the equation.
  2. jcsd
  3. Nov 25, 2007 #2


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    can you show us how you did it?
  4. Nov 25, 2007 #3
    [tex]\ddot u=\frac{d^2u}{d\theta^2}[/tex]
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