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© The scientific sentence. 2010


Galilean transformations



1. Preliminary

We will use the followings arguments:
- The noun "flash", used here, can be replaced by anything 
we want that travels incredibly fast, with a speed written "c".
It is not necessary light, but it should be a wave.
- This incredible speed "c" is constant in all reference frames.
- Recall that an inertial frame is a frame at rest or moving at 
constant velocity (not accelerated).

2. Galilean transformations



In the frame o'x'y'z' moving at velocity v with respect to
the frame oxyz; the object is at the position x'y'z', and moves 
at velocity u.
But, in the frame oxyz at rest (or moving at velocity - v 
with respect to the frame o'x'y'z'); the object is at the 
position xyz, and moves at velocity u + v.
The Galilean transformations are written as:

x = x' + vt
y = y'
z = z'
t = t'

From which, by first derivation, we get:

Vx = dx/dt = dx'/dt' + v = Vx' + v = u + v
Vy = Vy'
Vz = Vz' 


  


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