In a recent work, Cortés and Poza (2015 Eur. J. Phys. 36
[http://dx.doi.org/10.1088/0143-0807/36/5/055009] 055009 ) analysed, in full, the dynamics of a
charged particle in the field of a magnetic dipole restricted to a spherical surface with the dipole
at its centre. This model can be considered as the classical non-relativistic Störmer problem on a
sphere. Here, we started from a Lagrangian approach: we derived the Hamilton equations of motion and
observed that in this restricted case the equations can be reduced to quadratures, and they were
integrated numerically. From the Hamiltonian function we found, for the polar angle, an equivalent
one-dimensional system of a particle in the presence of an effective potential. In the present work
we start from a change of variable to the cosine of the polar angle. In terms of this variable we
obtain an equation that turns out to be the same as the one of a particle in a quartic potential.
Then, we can actually…