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Is the Coulomb potential, 1/r, the only one that produces a periodic motion?

If no, is there a condition for periodicity to occur?

Thanks,

Michel

- Thread starter lalbatros
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- #1

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Is the Coulomb potential, 1/r, the only one that produces a periodic motion?

If no, is there a condition for periodicity to occur?

Thanks,

Michel

- #2

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There's a list in Goldstein "Classical Mechanics" of the force-laws that give closed orbits, IIRC.

- #3

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You gave me the idea to check in Landau-Lifchitz. (I don't have Goldstein unfortunately).

He states that there are only two potentials that result in closed trajectories: 1/r and r² . That's already good to know. However, I don't see where this magic comes from. The algebra is simple and clear, but it does not indicate some more "fundamental" reason.

Michel

PS: In other words, can a property of an integral be understood in another way?

- #4

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I've never had any deeper insight than the mathematical demonstration you've already seen, sorry.

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