# Lorentz transformation conclusion with rotation of axis

1. Nov 13, 2007

### TheDestroyer

Hi Guys,

I've attached 2 pages from the book of landau "The Classical Theory of fields", I have a question about the lorentz transformations in pages 10,11

after reaching the step:

tanh(psy)= V/c

How did he split the latter into sinh(psy) and cosh(psy) and added the "gamma" constant which is 1/sqrt(1-V^2/c^2) ????

Can we add any constant we want? of course there is a reason

anyone can explain?

I know the Einsteins way of concluding these transformations but I want to understand the rotation of axes method

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2. Nov 13, 2007

### robphy

Think about a [Minkowski-] right-triangle... and its associated Pythagorean theorem [the square-interval]:

write:
$$\cosh^2 \psi - \sinh^2\psi = 1$$
as:
$$\cosh^2 \psi(1 - \tanh^2\psi) = 1$$

Last edited: Nov 13, 2007
3. May 30, 2008

Thanks