This is given by the 3 x 3 matrix in Eq. (28), it is an antisymmetric rotation matrix in three dimensions. It can be used to describe a three dimensional orbit, and in general can be used for any problem in dynamics. This proves for the first time that the spherical polar coordinate system is a special case of Cartan geometry. Note that theta and phi are the same as the theta and phi Euler angles. Any curvilinear coordinate system is a special case of Cartan geometry.

a369thpapernotes4.pdf

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