Convective Derivative in Terms of Spin Connections

This is the next stage of UFT361, expressing the convective or material or Lagrange derivative in terms of spin connection matrices in the plane polar system. The spin connections are related to rotation matrices. So everything is derivable from Cartan geometry, as is required in ECE2 unified field theory. This gives a great deal of insight to the origin of the Coriolis forces, often known as the non Newtonian forces. Any observed orbit is a constraint on the coordinate system. In the coordinate system itself, partial r /partial theta is zero because r and theta are, by construction, the independent variables of the plane polar system. The orbit introduces a functional relation between r and theta, For the conic sections this is r = alpha / (1 + epsilon cos theta)). For the first time, hydrodynamics has been unified with gravitation theory and orbital theory.

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