known under multiple denominations. Historically, this system was first studied in detail in the context of particle physics (where it is known as *Stark problem* [@stark_beobachtungen_1914]) in connection with the shifting and splitting of spectral lines of atoms and molecules in the presence of an external static electric field.

In astrophysics and dynamical astronomy, the Stark problem is sometimes known as the *accelerated Kepler problem*, and it is studied in several contexts. Models based on the accelerated Kepler problem have been used to study the excitation of planetary orbits by stellar jets in protoplanetary disks and to explain the origin of the eccentricities of extrasolar planets [@namouni_origin_2005; @namouni_accelerated_2007; @namouni_excitation_2013]. The Stark problem has also been used in the study of the dynamics of dust grains in the Solar System [@belyaev_dynamics_2010; @pastor_influence_2012].

In astrodynamics, the Stark problem is relevant in connection to the *continuous-thrust problem*, describing the dynamics of spacecrafts equipped with ion thrusters. In such a context, the trajectory of the spacecraft is often considered as a series of non-Keplerian arcs resulting from the simultaneous action of the gravitational acceleration and the constant thrust provided by the engine [@sims_preliminary_1999].

From a purely mathematical perspective, the importance of the Stark problem 