*Coordinate Transformations with t*

*r* = space coordinate, *t* = time coordinate, *v* = velocity, *u* = pace

Galileian transformation

speed: *r´* = *r* – *vt* and *t*′ = *t*, pace: *r´* = *r* – *t/u* and *t*′ = *t*.

Co-Galileian transformation

speed: *t´* = *t* – *r/v* and *r*′ = *r*, pace: *t´* = *t* – *ur* and *r*′ = *r*.

Light: *c* := speed of light, *ç* := pace of light.

speed: *r* = *ct* or* r/c = t* and *r′* = *ct′*, or *r′/c* = *t′*,

pace: *çr* = *t* or *r* = *t/ç* and *çr′ *= *t′* or *r′ *= *t′/ç*.

Lorentz transformation

speed: *γ* = (1 – *v*^{2}/*c*^{2})^{–1/2} with *r′* = *γ* (*r − vt*) and *t′* = *γ* (*t* – *rv/c²*),

pace: *γ* = (1 – *ç*^{2}/*u*^{2})^{–1/2} with *r′* = *γ* (*r* – *t/u*) and *t′* = *γ* (*t* – *rç²/u*),

which applies only if |*v*| < |*c*| or |*u*| > |*ç*|.

Co-Lorentz transformation

speed: *λ* = (1 − *c*^{2}/*v*^{2})^{–1/2} with *t′* = *λ* (*t − r/v*) and *r′* = *λ* (*r* − *t* (*c*^{2}*/v*)),

pace: *λ* = (1 – *u*^{2}/*ç*^{2})^{–1/2} with *t′* = *λ* (*t* – *ur*) and *r′ *= *λ* (*r* – *t* (*u/ç²*)),

which applies only if |*v*| > |*c*| or |*u*| < |*ç*|.