Contents
Special Relativity
© 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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