Classical Electrodynamics · Problem 11.3

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · successive-lorentz-transformations

Problem

Show explicitly that two successive Lorentz transformations in the same direction are equivalent to a single Lorentz transformation with a velocity

v = \frac{v_1 + v_2}{1 + (v_1 v_2/c^2)}

This is an alternative way to derive the parallel-velocity addition law.