Perturbed circular orbit under central force motion?

  • #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.
 

Answers and Replies

  • #2
mathman
Science Advisor
7,870
450
I suggest you quote it or give a link.
 
  • #4
165
14
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.
 
  • #5
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.
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.
 
  • #6
165
14
No problem :) This is just the peeking-over-the-shoulder effect.
 

Related Threads on Perturbed circular orbit under central force motion?

  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
773
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
9
Views
3K
  • Last Post
Replies
11
Views
7K
Top