The classical non-relativistic problem of the motion of a charged particle in an external central force field and a weak uniform magnetic field is revisited to show that the motion of the kinetic angular momentumL = r × p of the particle, in the so-called Larmor approximation, is not a simple precession but is actually a composite motion involving precession as well as a high frequency nutation. The precession-nutation motion ofL is discussed in the Larmor approximation when the Larmor-frame-orbit of the charged particle is an ellipse (or a circle) for the case of the two central forces namely the Coulomb and the Hooke-law-force, which are the only two central forces known to permit closed orbits.

The nutation accompanying the well-known Larmor precession discussed with respect to an inertial frame in an earlier paper is now considered in the rotating Larmor frame where the precession is absent and the nutation is therefore fully emphasized. It is shown that, in this frame, the nutating vector generates, in general, what may be called interpenetrating partial cones, the two parts of which merge into a single cone traced twice over, when the orbit of the charged particle changes to a circle — giving an immediate explanation of the discontinuous jump in the nutation frequency to twice its value as the orbit changes continuously from an ellipse to a circle.