  The ideal Penning trap consists of a uniform magnetic field and an
electrostatic quadrupole potential. In the classical low-energy limit, the
three characteristic eigenfrequencies of a charged particle trapped in this
configuration do not depend on the amplitudes of the three eigenmotions. No
matter how accurate the experimental realization of the ideal Penning trap, its
harmonicity is ultimately compromised by special relativity. Using a classical
formalism of first-order perturbation theory, we calculate the relativistic
frequency-shifts associated with the motional degrees of freedom for a spinless
particle stored in an ideal Penning trap, and we compare the results with the
simple but surprisingly accurate model of relativistic mass-increase.
