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Physics
Classical Physics
Mechanics
Hooke's law, Bertrand's theorem and closed orbits
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[QUOTE="Kashmir, post: 6559413, member: 692174"] Bertrand's Theorem says : [I]the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force[/I]. I'm looking at the hookes law ##f=-k r## and try to see explicitly that the orbit is indeed closed. I use the orbit equation ##\frac{d^{2} u}{d \theta^{2}}+u=\frac{-m}{l^{2} u^{2}} f\left(\frac{1}{u}\right)## with the force given as ##f=-k r## ,therefore I get ##\frac{d^{2} u}{d \theta^{2}}+u=+\frac{mk}{l^{2} u 3}## as the equation defining the trajectory. However neither can I solve this nor can I see that the equation implies a closed orbit. Can you please help me. [/QUOTE]
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Forums
Physics
Classical Physics
Mechanics
Hooke's law, Bertrand's theorem and closed orbits
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