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Can somebody show me a non-trivial exmple of Noether Theorem?

  1. Dec 8, 2009 #1
    Can somebody show me a "non-trivial" exmple of Noether Theorem?

    Noether Theorem states that if the Lagrangian of a system is invariant under some continuous coordinate transformation, then there's a conserved quantity.But does it simply mean the Lagrangian has to have a cyclic coordinate? Or a cyclic coordinate is just a special "trivial" case of Noether theorem? If so could somebody show me a "non-trivial" example? I mean a Lagrangian with no cyclic coordinates but we can apply Noether Theorem on.
     
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  3. Dec 8, 2009 #2

    Vanadium 50

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    Re: Can somebody show me a "non-trivial" exmple of Noether Theorem?

    You can show the Runge-Lenz vector is a conserved quantity in a 1/r potential. However, I warn you - after wrestling with this derivation, you might wish for the trivial examples again.
     
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