Abstract
As a generalization and extension of Escobar-Ruiz and Turbiner [J. Math. Phys. 54, 022901 (2013)], the classical dynamics of three non-relativistic Coulomb charges (e1, m1), (e2, m2), and (e3, m3) on the plane placed in a perpendicular constant magnetic field is considered. Special trajectories for which the distances between the charges remain unchanged are presented and their corresponding constants of motion are indicated. For these special trajectories, the number of constants of motion is larger than the dimension of the configuration space and hence they can be called particularly superintegrable. Three physically relevant cases are analyzed in detail, namely, that of three electrons, a neutral system, and a helium-like system. The n-body case is discussed as well.
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