In order to define these formulas, the movement of a component B of a mechanical system is defined by the set of rotations [A(t)] and translations d (t) assembled into the homogeneous transformation [T(t)]=[A(t), d (t)]. If p is the coordinates of a point P in B measured in the moving reference frame M, then the trajectory of this point traced in F is given by: P ( t ) = [ T ( t ) ] p = [ P 1 ] = [ A ( t ) d ( t ) 0 1 ] [ p 1 ] . This notation does not distinguish between P = (X, Y, Z, 1), and P = (X, Y, Z), which is hopefully clear in context.