Bertrand theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 18/02/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Bertrand%27s_theorem


00:01:27 1 General preliminaries
00:32:21 2 Inverse-square force
00:32:38 3 Radial harmonic oscillator
00:32:47 4 References
00:36:19 5 Further reading
00:37:16 Radial harmonic oscillator



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SUMMARY
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In classical mechanics, Bertrand's theorem states that among central-force potentials with bound orbits, there are only two types of central force potentials with the property that all bound orbits are also closed orbits: (1) an inverse-square central force such as the gravitational or electrostatic potential

  
    
      
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    {\displaystyle V(\mathbf {r} )=-{\frac {k}{r}},}
  and (2) the radial harmonic oscillator potential

  
    
      
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    {\displaystyle V(\mathbf {r} )={\frac {1}{2}}kr^{2}.}
  The theorem was discovered by and named for the French mathematician Joseph Bertrand (1822–1900).