论文标题
非标准的集成且可整合的古典哈密顿系统在非变化磁场中
Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
论文作者
论文摘要
在本文中，我们介绍了所有非标准集成系统在磁场中的构造，其积分具有与定理1（a Marchesiello和lšnobl2022 {\ it J. Phys）相对应的指导顺序结构。答：数学。理论。} {\ bf 55} 145203]。我们发现所得系统可以写为具有多个参数的一个家庭。对于这些参数的某些限制，该系统属于与笛卡尔和 /或圆柱坐标分开的已经知道的标准系统的交叉点，并且独立运动积分的数量增加，因此该系统变得最小化。这些结果概括了[Marchesiello和Lšnobl2022 {\ it J. Phys的第3节所示的特定示例。答：数学。理论。} {\ bf 55} 145203]。
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].
