375(1): Equivalence of Cartesian and Plane Polar Force Laws

This is a note on the equivalence of the Cartesian force laws (4) and (5) and the plane polar force laws (15) and (16). This means that numerical integration in Cartesian coordinates can be applied to several problems, as in Horst’s section 3 of UFT374 just sent over. This has the advantage of being simpler to understand, because the axes are not rotating in the Cartesian frame. In order to extract the centrifugal and Coriolis forces the axese must be made to rotate as in Eqs. (7) and (8). Therefor numerical integration of Eqs. (4) and (5) gives the ellipse (17), which is equivalent to the offset ellipse (18). This has already been demonstrated in UFT374. The analytical integration of Eqs. (4) and (5) to give an offset ellipse is by no means easy.


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