Sorry this should be:
... the code the user gives the parameters in lab frame ##S'##. They are then immediately boosted to ##S## frame. All the calculations are done in the co-moving ##S## frame. For some outputs ...
Ok so this is for a simulation code where at the beginning of the code the user gives the parameters in lab frame ##S##. They are then immediately boosted to ##S'## frame. All the calculations are done in the co-moving ##S'## frame. For some outputs at certain required times, we transform back...
Thanks, I couldn't find the guide earlier. Much nicer now.
By third reference frame I meant frame ##S''##, where the particle is at rest.
At ##t'=0## the Lorentz transformation would be ##z = \gamma_0z'##, but this would be incorrect I believe, because you would be be transforming what ##S'##...
A particle is moving in the lab frame ##S'## at ##\beta'_z##. I want to transform coordinates and momenta of the particle to a frame ##S## moving at ##\beta_0##.
At time ##t = t' = 0##:
$$z = \frac{z'} { \gamma_0 (1 - \beta'_z \beta_0) },\,
\gamma\beta_z = \gamma_0 ( \gamma'\beta'_z -...