361(5): Matrix and Spin Connection Format of the Lagrange Derivative

In plane polar coordinates the convective or Lagrange or material derivative is the Cartan derivative with spin connection matrix (7). The latter is the sum of two matrices, the second of which is the antisymmertic matrix generated by the angular velocity of the rotating frame of the plane polar or cylindrical systems of coordinates. This angular velocity matrix does not exist when the static Cartesian system is used. In general both matrices of Eq. (7) exist, and their properties will be developed in the next note. The origin of the both fluid dynamics and gravitation is Cartan geometry.


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