  We consider the stability of systems subjected to periodic parametric driving
such that their equations of motion are ordinary differential equations with
periodic coefficients and carry out a detailed analysis of important aspects of
such systems in the context of the confinement of ions by oscillating electric
fields. We show how they can be understood in terms of a pseudopotential
approximation and resonances arising from the parametric excitation and
investigate the properties of a novel linear Paul trap configuration operating
with two radio-frequencies to simultaneously confine two species with extremely
different charge-to-mass ratios. The theoretical calculations have been
verified by molecular dynamics simulations and normal modes analysis.
