In this paper, we analyze a noncommutativity error that is not able to be compensated with integrating gyro outputs in RLG-based INS. The system can suffer from some motion known as RLG dithering motion, coning motion, ISA motion derived by an AV mount and vehicle real dynamic motion. So these motions are a cause of the noncommutativity error, the system error derived by each motion has to be analyzed. For the analysis, a relation between rotation vector and gyro outputs is introduced and applied to define the coordinate transformation matrix and the angular vector.