Basic Transformation of Coordinates and Measures, Corresponding Axes Parallel, CoLinear xAxes Parallel to β, and t = 0 When Origins Coincide.
Table 1: Transformation of Coordinates of a SpaceTime Point
rest coordinates to moving coordinates 
moving coordinates to rest coordinates 
t_{β} = t_{0}, T_{β} = T_{0} [subscripts superfluous] 
t_{0} = t_{β}, T_{0} = T_{β} [subscripts superfluous] 
In the moving frame we find the angle φ transformed, ; if then . In the rest frame, the absolute span s at any instant of a moving solid rod of length l, (in its proper frame with velocity β,) with the angle φ_{0} (in the rest frame) between β and the axis of the rod, is given by . In the moving system, a point at absolute rest (at rest in the rest frame) will have velocity . Time in all frames of reference is the same as in the rest frame.
Table 2: Transformation of Measure
tan(φ) 

cos(φ) 
, 
sin(φ) 
, 
absolute span of moving length 
,

velocity 
,

ψ dihedral angle between two angles φ_{1} and φ_{2} 
ψ_{0} = ψ_{β} 
θ angle between the vectors β_{1} and β_{2} of two inertial frames 
,

Copyright © 2014 by David Bryan Wallace, Cape Coral, Florida, USA