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Recursive function in a physics equation

  1. May 15, 2004 #1
    Hoping someone can point out an example of a recursive function in a physics equation. If this is not a valid step that would be great to hear about too. Also if anyone has even tried to introduce such an equation in the past or how it might be represented. [I'm not the best student of maths].

    I have a form in mind that I can only express with recursion.

    Thanks in advance.
  2. jcsd
  3. May 15, 2004 #2
    What do you mean by recursion? Is it of the form:
    x_{n+1} = f(x_n)
    or is it something like
    y = f(y)
    where f(y) is some nasty integral or something which you can't solve?

    In either case, yes, recursion occurs a lot in physics and is the basis for things like perturbation theory.

  4. May 15, 2004 #3
    Something more along these lines:

    [tex] v(t) = 3 * v(t) [/tex]

    Obviously this equation cannot be solved as there is no terminating condition specified. Trying to solve this when t=1 for instance gives:

    [tex] v(1) = 3* (3* (3 * (3 * (3* ...))))[/tex]

    I have a structure that relies on this form of recursion, but how do I go about specifying the terminating value? For instance, suppose I simply wanted a value > 8 * PI. How is it that I would express this?
  5. May 15, 2004 #4
    Hmm, either something fishy is going on or you need help from a mathematician (which sadly I'm not).

    By my reconing the only 'physical' solution to your equation is zero. My argument would run as follows:

    Assume [itex]v(t)[/itex] has a solution [itex]v(t)>0[/itex].

    [itex] v(t) = 3 v(t) \Rightarrow 1 = 3[/itex]
    This is a contradiction hence [itex]v(t)=0[/itex].

    Unless I am wrong in thinking your symbol [itex]*[/itex] means multiply?

    Ok, as I said before I am not a mathematician so if I've done something stupid please don't hurt me :)

  6. May 16, 2004 #5
    Would you like to explain better what you are trying to do. It is interesting your topic and please give us details. I really don't know what to say about your recursive physics, but I ran into similar ideas, too. Maybe I can help :)
  7. May 16, 2004 #6


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    Aren't fractals recursive?
  8. May 16, 2004 #7
    If by that you mean a great many of them are generated by recursive algorithms, then yes they definitely are.

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