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Central force integral

  1. Jul 10, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\int dr \left[\alpha + \frac{\beta}{r^2}\right]^{-1/2}[/tex]

    How can I get started on this? Thanks.
  2. jcsd
  3. Jul 10, 2008 #2
    Multiply numerator and denominator with r and use substitution rule.
  4. Jul 10, 2008 #3
    so if [itex]\alpha = 2E/\mu[/itex] and [itex]\beta = L^2\alpha^2/\mu^2[/itex] (not the same alpha, sorry) and bounds [r0,r] I should get:

    [tex]\frac{\mu}{2E} \left[\left(\frac{2E}{\mu}r^2 + \frac{L^2\alpha^2 }{\mu^2}\right)^{1/2} - \left(\frac{2E}{\mu}r_0^2 + \frac{L^2\alpha^2 }{\mu^2}\right)^{1/2}\right][/tex]

    and this is equal to time so solving r(t) gives a quadratic. Does this make sense for central force motion where [itex]r = ke^{-\alpha\theta}[/itex]?
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