The Lorentz Transformation of dax/dt

The Lorentz Transformation of da_x/dt

G.R.Dixon, 6/23/2006

As A.P.French demonstrates in his book, SPECIAL RELATIVITY: given inertial frames K and K’, with relative speed v, the Lorentz transformation of a_x is

. (1)

(u_x’ is the velocity of an accelerating particle relative to K’.) Taking the differential of Eq. 1:

. (2)

And since

, (3)

. (4)

Dividing Eq. 2 by Eq. 4:

. (5)

Similarly,

(6)

and

. (6)