# The differential time operator is put into the rst

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Unformatted text preview: ©§ ¢ ¨¦ ¤ d ,0 dt . 1, r Cos d ,0 dt . 1, R 0, R ¢ £¡ ¢ d ,0 dt ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢ ¤ ¥ & %&& ' . 1, R ,0 . ,0 ¤  & . Newton’s 2nd Law in a Noninertial, Rotating Frame Consider the ”noninertial” case, with the frame rotating at an angular speed omega. The differential time operator is put into the ﬁrst term of the quaternion, and the three directions for the angular speed are put in the next terms. This quaternion is then multiplied by the position quaternion to get the velocity in a rotating reference frame. Unlike the previous examples where t did not interfere with the calculations, this time it must be set explicitly to zero (I wonder what that means?).  ¡1 ¡ V 0, R Operate on the velocity quaternion with the same operator.  A The ﬁrst three terms of the 3-vector are the translational, coriolis, and azimuthal alterations respectively. The last term of the 3-vector may not look like the centrifugal force, but using a vector identity it can be rewritten: 2 If the angular velocity an the radius are...
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## This note was uploaded on 09/30/2010 for the course MAE 123 taught by Professor 123 during the Spring '10 term at École Normale Supérieure.

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