---
abstract: 'We present a new general, complete closed-form solution of the three-dimensional Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the external force field, and it is expressed via unique formulæ valid for all initial conditions and parameters of the system. The simple form of the solution allows us to perform a thorough investigation of the properties of the dynamical system, including the identification of quasi-periodic and periodic orbits, the formulation of a simple analytical criterion to determine the boundness of the trajectory, and the characterisation of the equilibrium points.'
author:
- |
    Francesco Biscani$^1$[^1] and Dario Izzo$^2$\
    $^{1}$Castle Mews 27, St. Thomas Street,\
    $\hphantom{^{2}}$Oxford, Oxfordshire, OX1 1JR, United Kingdom\
    $^{2}$ESA – Advanced Concepts Team, European Space Research Technology Centre (ESTEC),\
    $\hphantom{^{2}}$Keplerlaan 1, Postbus 299, 2200 AG Noordwijk The Netherlands
bibliography:
- 'biblio.bib'
title:  The Stark problem in the Weierstrassian formalism 
---

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Celestial mechanics - Gravitation - Stark problem

Introduction
============

The dynamical system consisting of a test particle subject simultaneously to an inverse-square central field and to a force field constant both in magnitude and direction is 