Kepler motion on single-sheet hyperboloid
classification
🧮 math-ph
math.MP
keywords
hyperboloidmotionboundedcirclesclassicalclosedellipsesequation
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The classical Kepler-Coulomb problem on the single-sheeted hyperboloid $H^{3}_1$ is solved in the framework of the Hamilton--Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.
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