Calculate, to first-order in beta, the way the coordinates transform when velocity is a function of time.
Poisson-bracket relations for Poincare group? Also: expression of any dynamical variable as an n-applied Poisson-bracket in a Taylor-series.
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??