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Perturbed circular orbit under central force motion?

  1. Mar 11, 2015 #1
    I am self studying Kleppner and Kolenkow's an Introduction to mechanics. But i have one doubt about how they got in to the equation no 3 of the example problem 9.3 in Central Force Motion.
    Please clarify my doubt.
     
  2. jcsd
  3. Mar 11, 2015 #2

    mathman

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    I suggest you quote it or give a link.
     
  4. Mar 15, 2015 #3
    Here i have attached the photo graph of that page.
     

    Attached Files:

  5. Mar 15, 2015 #4
    Seems pretty straight forward. Differentiate [itex]U_{eff}[/itex] twice, evaluate it at [itex]r=r_0[/itex] and replace [itex]l[/itex] by the one we obtained earlier. This should equal k, which is related to beta.
     
  6. Mar 15, 2015 #5
    Omg. I am so dumb. I just calculated the second derivative and then used to sit brooding over what to do next without plugging the value of l from equation 1. I am feeling embarrassed.

    Anyway,,, thank you. I got it. Better late than never.
     
  7. Mar 16, 2015 #6
    No problem :) This is just the peeking-over-the-shoulder effect.
     
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