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  1. The plane wave spectrum arises naturally as the eigenfunction or " natural mode " solution to the homogeneous electromagnetic wave equation in rectangular coordinates ( see also Electromagnetic radiation, which derives the wave equation from Maxwell's equations in source-free media, or Scott [ 1998 ] ).
  2. :\ hat { g } \, and \ hat { h } \, are the base vectors of the rectangular coordinate system in the plane of the reference Kepler orbit with \ hat { g } \, in the equatorial plane towards the ascending node and u \, is the polar argument relative this equatorial coordinate system
  3. With this end in view he expounded to the Berlin Academy in 1849 a mode of determining an elliptic orbit from three observations, and communicated to that body in 1851 a new method of calculating planetary perturbations by means of rectangular coordinates ( republished in W . Ostwald's " Klassiker der exacten Wissenschaften ", No . 141, 1903 ).
  4. Where " C " 1 and " C " 2 are constants that depend on the rotation rates of the cylinders . ( Note that " r " has replaced " y " in this result to reflect cylindrical rather than rectangular coordinates . ) It is clear from this equation that curvature effects no longer allow for constant shear in the flow domain, as shown above.

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