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A little clarification on absolute values

  1. Sep 29, 2006 #1
    Hello again. I have a (stupid, but I'm not real sure about the answer-type) question. I'm trying to prove that the second order ODE of the simple pendulum y''=-(g/l)sin y is Lipschitz (using norm 1). After doing some evaluating, I came up with

    |u'-v'| + |\frac{g}{l}||\sin u - \sin v|

    All I'm asking is if this is true for all values of u and v:

    |\sin u - \sin v| \leq |u - v|

    All clarifications are appreciated.


  2. jcsd
  3. Sep 29, 2006 #2
    I think you can show that |sin(u)-sin(v)| <= |u-v| using the MVT.
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