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Particle motion in a Penning trap

The motion of a charged particle in an ideal Penning trap (ion trap with static electromagnetic fields) can be analysed by a large variety of methods of analytical mechanics, similar to the Kepler problem and the harmonic oscillator exact solutions can be provided. For this reason and because of its great relevance for experimental techniques the problem represents a topic of high pedagogical value for a course in theoretical mechanics. The paper briefly sketches the essential steps of various theoretical approaches.