361(4): Analysis of the New Acceleration Terms in Plane Polar Coordinates

By unit vector analysis it is shown that the new acceleration terms vanish in the plane polar coordinate system, (r, theta), for which partial r / partial theta = 0, giving the result (26) of dynamics unified with fluid dynamics. Eq. (26) shows that the accelerations systematically deduced by Coriolis are due to the Lagrange derivative (v dot del) v if and only if the plane polar coordinate system is used. More generally the Lagrange derivative defines v to be a velocity field, in which v = v(r(t), theta(t), t). In the plane polar system v = v(t), and is a velocity of dynamics, not a velocity field of fluid dynamics. ECE2 unification asserts that the velocity of dynamics can be generalized to a velocity field because the background spacetime or aether or vacuum is a fluid. This generalization implies the existence of many new orbital terms that do not exist in the analysis by Coriolis. One way of developing these terms was given in UFT360. Note carefully that when considering orbits in the plane polar system, a constraint is introduced, so that r becomes a function of theta. So when the orbit is considered partial r / partial theta is no longer zero. An example is the conic sections r = alpha / (1 + epsilon cos theta)). In ECE2 the orbit is the frame of reference itself, as in UFT360. In classical orbital theory the orbit is a function defined by a frame of reference, the plane polar system, a rotating frame. The Corialis forces are due to the frame rotation. In the Cartesian system the frame is fixed, and there are no Coriolis forces. In ECE2 general relativity they are understood in terms of a spin connection.


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