Charged Particle Motion
The theory of charged particle motion in a magnetic field can be regarded as an application of classical mechanics. Plasma physics in general, however, and the theory of magnetized motion in particular, make different demands on classical mechanics than other disciplines, such as celestial mechanics. The particles experience additional drifts, however, caused by inertial forces and the interaction of the effective magnetic moment with the equilibrium field. The central result of this theory is that particles behave like magnetic dipoles, or small magnets, aligned with magnetic field and with conserved magnetic dipole moments. Write down the Lagrangian, and find all the constants of the motion. Compare the exact solution to the predictions of guiding center theory. The motion of a charged particle around a monopole was first studied by Poincare in the context of magnetic mirroring in the polar cusp regions.