The time derivative of vectors depends on the coordinate frame in which the vector is expresses and the coordinate frame in which the derivative is taken. By redefining and expanding the Euler’s derivative transformation formula, we introduce the general theory of derivative and coordinate frames using a proper notation method. Introducing three coordinate frames, we show that the Coriolis acceleration is actually the addition of two different accelerations. Furthermore, a new acceleration term appears that we call it Razi acceleration.

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