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Retarded Central Force Problem in Classical Physics

  1. Apr 14, 2012 #1
    There are many good treatments of the classical central force problem in many undergraduate and graduate text books. But I was unable to find a similar treatment of the retarded central force problem. I am looking for the classical treatment of the potentials of type:
    [tex] \delta(t'-t + |\mathbf{x}-\mathbf{x}'|/c) V({|\mathbf{x}-\mathbf{x}'|}) [/tex]
    I will be also happy with the treatment of a special case with:
    [tex]V({|\mathbf{x}-\mathbf{x}'|}) = \frac{1}{|\mathbf{x}-\mathbf{x}'|} [/tex]
    Can anybody recommend a good book or a published article?

    Thank you. :smile:

    PS: Please do not refer me to the Lienard-Wiechert potentials in classical electromagnetism. They only treat the case when one of the particle's position (path) is given (and unaltered by the other particle.) I am looking for the dynamic interaction of a two-body-system.
  2. jcsd
  3. Apr 14, 2012 #2
    I just finished Spivak's Mechanics for Mathematicians, and there was a good treatment of central force / two-body problems, and of wave propagation (presumably you mean this central "force" is derivable from a central potential that propagates from sources as a wave?)...but as far as the full retarded two-body problem goes, I don't think I have seen any treatments of that (even neglecting energy loss through radiation)...my understanding is it would be a highly non-linear equation, if an analytic solution could even be derived.

    In fact, I don't think I've ever even seen a full treatment of the retarded *one* body problem; when researching another question here I did track down a long-OOP text book on Google books that gave a pictorial analysis of what it would look like, and showed how the self-field forces would cancel for a rigid sphere with zero jerk, but nothing like an equation of motion.

    I would be really interested in hearing if you find anything, though (provided I properly understand the question).
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