Geodesic
Quasi-St\"ackel Hamiltonians and electron dynamics in an~external field in the~two-dimensional case
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 210-217

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In the two-dimensional case, we construct nondegenerate Hamiltonians that describe electron motion in an electromagnetic field and have additional integrals of motion quadratic in momentum. We completely classify the quasi-Stäckel Hamiltonians related to these systems in the cases where the leading approximation in momenta of the additional integral depends quadratically on the coordinates. We consider reductions of such systems that are symmetric under rotation about the $z$ axis.
Keywords: classical electrodynamics, separation of variables, algebraic curve. 
@article{TMF_2019_199_2_a2,
     author = {V. G. Marikhin},
     title = {Quasi-St\"ackel {Hamiltonians} and electron dynamics in an~external field in the~two-dimensional case},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {210--217},
     publisher = {mathdoc},
     volume = {199},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a2/}
}
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V. G. Marikhin. Quasi-St\"ackel Hamiltonians and electron dynamics in an~external field in the~two-dimensional case. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 210-217. http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a2/