Proper Velocity Addition Formula
The proper velocity addition formula:
where is the beta factor given by .
This formula provides a proper-velocity gyrovector space model of hyperbolic geometry that uses a whole space compared to other models of hyperbolic geometry which use discs or half-planes.
In the unidirectional case this becomes commutative and simplifies to a Lorentz-factor product times a coordinate-velocity sum, e.g. to wAC = γABγBC(vAB+vBC), as discussed in the application section below.
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