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How to transform velocities of an accelerating frame?

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Calculate, to first-order in beta, the way the coordinates transform when velocity is a function of time.


    2. Relevant equations
    Poisson-bracket relations for Poincare group? Also: expression of any dynamical variable as an n-applied Poisson-bracket in a Taylor-series.


    3. The attempt at a solution
    - Tried to integral[(d/dt)(dx'/dt')]*dt. Mess.
    - Tried H(beta(t)) = H(beta(0)) + t*H(beta(0)) + (1/2)*H(beta(0)) + ... mess, even when truncated to first order. (Note: dF/dt = (F, H), where F is any function of "q" and "p" (canonical variables), and H is the specific function of q and p called the Hamiltonian)
    - ???


    I guess this problem is supposed to make me appreciate how mathematically-complicated general relativity is??
     
  2. jcsd
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