The dynamics of charged particles in the Penning–Malmberg–Surco trap with a rotating electric field [1–3] (the Charlton trap) is investigated. Two different algorithms for determining Lyapunov characteristic exponents for solutions of a nonstationary system describing the dynamics of particles in a trap are constructed and realized. This allows us to construct approximate analytical solutions and analyze the behavior of the envelope of the particle beam, and not only of individual trajectories. The asymptotic stability of motions of charged particles is checked for a different choice of the system parameters and their relations.