On the constants of motion governing an electron in a magnetic field constrained by an electrostatic central force
نویسنده
چکیده
Planetary motion mechanics with noncolinear particle forces is a well defined science. The problem considered here is that of an electron constrained by an electrostatic central force in a uniform magnetic field. The problem is of interest because it is the classical limit of the hydrogen atom in a magnetic field, and because there are not enough constants of motion to solve the problem exactly. Discussed in this paper, from a pedagogical viewpoint, are the derivation and use of the constants of motion to predict the orbit of such an electron. A numerical example illustrating the concepts is worked out for the cylindrical magnetron (for which analytical solutions exist).
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