Timeline for Is there a high level reason why the inverse square law of gravitation yields periodic orbits without precession?
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| Nov 30, 2019 at 1:53 | comment | added | Francois Ziegler | Also: Taub-NUT geodesics (Cordani, B.; Fehér, L. Gy.; Horváthy, P. A., Kepler-type dynamical symmetries of long-range monopole interactions, J. Math. Phys. 31, No. 1, 202-211 (1990). ZBL0712.53032) and generalizations (Iwai, Toshihiro; Katayama, Noriaki, Multifold Kepler systems – Dynamical systems all of whose bounded trajectories are closed, J. Math. Phys. 36, No. 4, 1790-1811 (1995). ZBL0832.70010). | |
| Nov 18, 2019 at 16:00 | comment | added | Francois Ziegler | Thus also Kepler in elliptic/hyperbolic geometry (Liebmann et al.: 1903, 1992, 2009), Kepler with a monopole (MICZ 1970,...), etc. Another Dahl paper: 1997. | |
| Nov 18, 2019 at 16:00 | comment | added | Francois Ziegler | Yes... While the thrust of Albouy’s paper that I quoted is to largely downplay the role of symplectic geometry in solving the Kepler problem (and so maybe disappoint the OP), what symplectic geometry does is provide a framework wider than the narrow “mechanics = Hamiltonians (or potentials) on cotangent bundles,” where Bertrand question, Runge-Lenz integrals, etc., become less isolated. | |
| Nov 18, 2019 at 9:16 | history | answered | Zurab Silagadze | CC BY-SA 4.0 |