where we can write the dual Ω Ω of Ω Ω ∗ ∗ as Ω Ω i j ∗ ∗ = ε ε i j k Ω Ω k (and 2 Ω Ω i = ε ε i j k Ω Ω j k ∗ ∗ ), where Ω Ω ( t ) is nothing but the time-dependent rotation of the rotating frame with respect to the inertial frame.