User:Tohline/PGE/RotatingFrame
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NOTE to Eric Hirschmann & David Neilsen... I have move the earlier contents of this page to a new Wiki location called Compressible Riemann Ellipsoids.
Rotating Reference Frame
At times, it can be useful to view the motion of a fluid from a frame of reference that is rotating with a uniform (i.e., time-independent) angular velocity <math>\Omega_f</math>. In order to transform any one of the principal governing equations from the inertial reference frame to such a rotating reference frame, the operator <math>d/dt</math>, which denotes Lagrangian time-differentiation in the interial frame, must everywhere be replaced as follows:
<math> \biggl[\frac{d}{dt} \biggr]_{inertial} \rightarrow \biggl[\frac{d}{dt} \biggr]_{rot} + {\vec{\Omega}}_f \times . </math>
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