|XXXVII Workshop on Geometric Methods in Physics||1-7.07.2018|
|VII School on Geometry and Physics||25-29.06.2018|
Pedal coordinate, dark Kepler and other force problems
We will make the case that pedal coordinates (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test particle under the influence of central and Lorentz-like forces can be translated into pedal coordinates at once without the need of solving any differential equation. This will allow us to generalize Newton theorem of revolving orbits to include non-local transforms of curves. Finally, we apply developed methods to solve the ``dark Kepler problem'', i.e. central force problem where in addition to the central body, gravitational influences of dark matter and dark energy are assumed.
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