  In the relativistic description of atomic systems in external fields the
total momentum and the external electric field couple to the angular momentum
of the individual particles. Therefore, the motional state of an ion in a
particle trap influences measurements of internal observables like energy
levels or the g-factor. We calculate the resulting relativistic shift of the
Larmor frequency and the corresponding g-factor correction for a bound electron
in a hydrogen-like ion in the 1S state due to the ion moving in a Penning trap
and show that it is negligible at the current precision of measurements. We
also show that the analogous energy shift for measurements with an ion in the
ground state of a Paul trap vanishes in leading order.
