These are all incorporated automatically in the ECE2 field equations of gravitation and dynamics, because the field equations are based on Cartan’s general spin connection. The 1835 Coriolis velocity and accelerations are due to the rotation of a plane polar system. They have caused many students and teachers to clean around the bend, trying to understand them. They are vaguely described in many textbooks as “pseudo-forces”. ”
They are usually called ‘fictitious forces’, because that is what they are. They were conjured-up, mainly by D’Alembert, in order to simplify the mathematics associated with movement within a rotating system. They have no reality outside of the system. They cannot, for instance, be used to propel a rotating system from within … even though there exist hundreds of patent applications for devices which supposedly do that very thing. We know that Ron does not understand centrifugal force, for a start, as he once claimed that a thrown hammer moves radially away from the thrower*. Fictitious forces are therefore handy for treating an isolated rotating system but say nothing useful on the (literally) universal scale. One loony who thought that mere rotation could replace gravity altogether was of course the late and unlamented Viv Pope; another Welsh loony from the Swansea area. He said that Newton was hit on the head not because of gravity but because the apple was ‘orbiting at the wrong height for its speed’. He almost made Ron look sensible in comparison!
“Anyone who has gone around a bend (for example a string theorist or those who have fallen in to a black hole and emerged miraculously as white haired raving maniacs) knows that they are real. This was first realized in the sixteen thirties, when correcting cannon fire trajectories. As just seen in Note 362(2a) the use of an elliptical polar coordinate system is self consistent with orbital theory, and produces new velocities and accelerations. For a long time I have realized that there is a self contradiction in the use of a plane polar system for an elliptical or conic section orbit. The latest note resolves this contradiction. Hooke obviously did not understand the Coriolis forces, neither did Newton or Leibnitz or Euler or Lagrange. The latter edged towards an understanding, finally achieved by Coriolis in 1835, long after the time of Hooke, Newton and Leibnitz. My ancestral cousin John Aubrey (online “Brief Lives” or short biographies) had no grasp of mathematics but did write the truth and was a highly intelligent man. Hooke guessed that the inverse square law gives an elliptical orbit, but neither Hooke not Newton could have proven it because they had no grasp of a rotating or moving coordinate frame.”
Newton and Hooke did not need to consider fictitious forces, because they used incremental geometrical methods; ones which were still used by students until the advent of computers. As a schoolboy, one of us used to treat the unconstrained three-body problem by means of slide-rule, ruler, pencil and acres of scrap wallpaper; such problems are unsolvable only in the analytical sense. Hooke and Newton used to challenge each other to derive orbits under all sorts of conditions … including the precession of an elliptical orbit within a hollow Earth. One of the best-known fallacies concerning the Coriolis force is that it makes draining water swirl in opposite directions in the Northern and Southern hemispheres. Yes, it should … theoretically; but in practice its effect is drowned-out by other factors. The supposedly clear-cut effect is almost impossible to detect experimentally, but fraudsters on the equator make a pretty penny out of fooling tourists (such as Michael Palin) into thinking that it is easily demonstrated. Finally, we point out yet again that Ron makes no mention of tidal effects. He does not mention them because his contrived reasoning cannot be twisted that far!