Earlier in this article a distinction was introduced between two terminologies, the fictitious forces that vanish in an inertial frame of reference are called in this article the "state-of-motion" fictitious forces and those that originate from differentiation in a particular coordinate system are called "coordinate" fictitious forces. Using the expression for the acceleration above, Newton's law of motion in the inertial frame of reference becomes: F = m a = m ∑ ∑ k = 1 d ( v ˙ ˙ k + ∑ ∑ j = 1 d ∑ ∑ i = 1 d v j Γ Γ k i j q ˙ ˙ i ) e k , where F is the net real force on the particle. No "state-of-motion" fictitious forces are present because the frame is inertial, and "state-of-motion" fictitious forces are zero in an inertial frame, by definition.