lies mainly in fact that it belongs to the very restrictive class of Liouville-integrable dynamical systems of classical mechanics [@arnold_mathematical_1989]. Action-angle variables for the Stark problem can be introduced in a perturbative fashion, as explained in @born_mechanics_1927 and @berglund_averaged_2001.

Different types of solutions to the Stark problem are available in the literature. If the constant acceleration field is much smaller than the Keplerian attraction along the orbit of the test particle, the problem can be treated in a perturbative fashion, and the (approximate) solution is expressed as the variation in time of the Keplerian (or Delaunay) orbital elements of the osculating orbit [@vinti_effects_1966; @berglund_averaged_2001; @namouni_accelerated_2007; @belyaev_dynamics_2010; @pastor_influence_2012]. A different approach is based on regularisation procedures such as the Levi-Civita and Kustaanheimo-Stiefel transformations [@kustaanheimo_perturbation_1965; @saha_interpreting_2009], which yield exact solutions in a set of variables related to the cartesian ones through a rather complex nonlinear transformation [@kirchgraber_problem_1971; @rufer_trajectory_1976; @poleshchikov_one_2004]. A third way exploits the formulation of the Stark problem in parabolic coordinates to yield an exact solution in terms of Jacobi elliptic functions and integrals [@lantoine_complete_2011].

The aim of this paper is to introduce and examine a new solution to the Stark problem that employs the Weierstrassian elliptic and related functions. The 