Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
In this paper we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of Theorem 1 in [A Marchesiello and L Šnobl 2022 {\it J. Phys. A: Math. Theor.} {\bf 55} 145203]. We find that the resulting s...
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| description | In this paper we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of Theorem 1 in [A Marchesiello and L Šnobl 2022 {\it J. Phys. A: Math. Theor.} {\bf 55} 145203]. We find that the resulting systems can be written as one family with several parameters. For certain limits of these parameters the system belongs to intersections with already known standard systems separating in Cartesian and / or cylindrical coordinates and the number of independent integrals of motion increases, thus the system becomes minimally superintegrable. These results generalize the particular example presented in section 3 of [A Marchesiello and L Šnobl 2022 {\it J. Phys. A: Math. Theor.} {\bf 55} 145203]. |
| doi_str_mv | 10.48550/arxiv.2212.05338 |
| format | Article |
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| subjects | Cartesian coordinates Cylindrical coordinates Hamiltonian functions Integrals Magnetic fields Mathematics - Mathematical Physics Parameters Physics - Mathematical Physics |
| title | Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields |
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