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Celestial mechanics with symplectic integrators

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem is that I just don't understand how the algorithm described here in section 2 hangs together... I have to present this on Thursday morning and that sensation of 'I'll never understand this soon enough' is growing ominously.

    2. Relevant equations

    Equations 2,6,7 and 8 are a mystery to me. I could write them out here but they're already in the paper and without their context it wouldn't help much I think.

    Why is there a sum from 1 to n in equation 2? What is n? It doesn't say...

    And, how is q(t) = exp(tau * F) * q(t-tau) a general solution to dq/dt = Fq ?

    Shouldn't it be q(t) = q(tau) * exp(Fq) ?

    How does one knows in which order to apply the exponential operators in equation 6?

    Where does equation 7 fit in with anything introduced previously?


    3. The attempt at a solution

    My attempt at a solution is asking for help here... I've googled but my questions are far too specific for that to help. =(

    Please please help!


    Masklin
     
  2. jcsd
  3. Apr 2, 2013 #2
    Equ. 2 is an application of the chain rule and then Equ. 1. n is the number of the degrees of freedom.
     
  4. Apr 3, 2013 #3
    Degrees of freedom - what does that mean in this context? The dimensionality of x and p, or the number of bodies? Or something else?
     
  5. Apr 3, 2013 #4
    The dimension of x.
     
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