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I am wondering if there are any studies of a single (classical) particle trajectory in quadrupole potential:

$$ V(x,y,z)=A\sqrt[]{\frac{x^2 + y^2}{a} + \frac{z^2}{b}} $$

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  • $\begingroup$ You mean like this? And where did you get your expression for the quadropole potential? There shouldn't be a square root. $\endgroup$ – Michael Brown Sep 3 '13 at 14:16
  • $\begingroup$ This potential is a magnetic quadrupole trap, similar to this link $\endgroup$ – user29165 Sep 3 '13 at 14:59
  • $\begingroup$ I guess what I like to find out is if this system is an integrable system. If so what are the other constants of motion? $\endgroup$ – user29165 Sep 3 '13 at 19:31

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