second time transformation in the solution.

These advantages are critical in providing new insights in the dynamics of the Stark problem. On the other hand, the use of the Weierstrassian formalism presents a few additional difficulties with respect to the approach described in @lantoine_complete_2011, the most notable of which is probably the necessity of operating in the complex domain. Throughout the paper, we will highlight these difficulties and address them from the point of view of the actual implementation of the formulæ describing our solution to the Stark problem.

In this paper, we will focus our attention specifically on the full three-dimensional Stark problem, where the motion of the test particle is not confined to a plane, and we will only hint occasionally at the bidimensional case (where instead the motion is constrained to a plane).

Problem formulation
===================

From a dynamical point of view, the Stark problem is equivalent to a one-body gravitational problem with an additional force field which is constant both in magnitude and direction. The corresponding Lagrangian in cartesian coordinates $\boldsymbol{r} = \left(x,y,z\right)$ and velocities $\boldsymbol{v} = \left(\dot{x},\dot{y},\dot{z}\right)$ is then $$L\left(\boldsymbol{v};\boldsymbol{r}\right)=\frac{1}{2}v^{2}+\frac{\mu}{r}+\varepsilon z,
\label{eq:orig_lagr}$$ where the inertial coordinate system has been centred on the central body, $v 