RELATIONSHIPS FOR MOTION DESCRIBED IN ANY TWO ROTATIONAL REFERENCE FRAMES

In this paper the definitions of the relative derivatives of a vector with respect to time in any reference frame by using the notation of vectrix are proposed. It is further shown that with the help of vectrix one can treat the relative derivatives more clearly and more rigorously when multiple reference frames are concerned. Very useful relationships between the first order relative derivatives described in any two reference frames are derived. Relationships for the second order relative derivatives are also presented in detail. A new concept called "rotation induced acceleration" which is caused by the rotation of two reference frames when motion is necessarily described in them is presented. The result obtained in this paper is the generalization of the acceleration theorem given in conventional theoretical mechanics.