Contrary to a rather widespread belief, the Newton-Lorentz equation of motionmdv/dt  = qv × Bdoes not exclude orbit solutions which represent the trapping of a charged particle which is externally injected into a region of time-independent magnetic field. Specific examples of such orbits are demonstrated. Theorems of Liouville and Poincaré are used to clarify the nature of the restrictions which classical mechanics imposes upon the injection and trapping of charged particles in a static magnetic field.