# Special relativity - frames of reference

1. Feb 25, 2009

### qoqosz

1. The problem statement, all variables and given/known data
We have two frames of reference: K (x,y,t) and K' (x',y',t') such that initially x=x'=y=y'=t=t'=0. Now let K' move with a velocity $$\vec{v} = v [\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}}]$$
Write Lorentz transformations in such a case.

2. Relevant equations

3. The attempt at a solution
My try is:
$$t' = \frac{t - (\vec{v} \circ (x, y))/c^2}{\sqrt{1 - \frac{v^2}{c^2}}}, \; x' = \frac{x - v_x t}{\sqrt{1 - \frac{v^2}{c^2}}}, y' = \frac{y - v_y t}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $$v_x = v_y = \frac{v}{\sqrt{2}}$$

Last edited: Feb 25, 2009
2. Feb 26, 2009

### jambaugh

Looks good to me.

3. Feb 26, 2009

### qoqosz

Great, thank you!