Legea compunerii vitezelor.

Legea compunerii vitezelor

Pornind de la transformările Lorentz se deduce legea compunerii vitezelor în următoarea formă:

$$\begin{gathered} u_x`=\frac{u_x-v}{1-{\displaystyle \frac{v}{c^2}}{u}_x} \\ {u}_y`=\frac{u_y}{\gamma \left(1-{\displaystyle \frac{v}{c^2}}{u}_x\right)}=\frac{u_y\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}{1-{\displaystyle \frac{v}{c^2}}{u}_x} \\ {u}_z`=\frac{u_z}{\gamma \left(1-{\displaystyle \frac{v}{c^2}}{u}_x\right)}=\frac{u_z\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}{1-{\displaystyle \frac{v}{c^2}}{u}_x} \end{gathered}$$