The Stark problem in the Weierstrassian formalism

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 formulae 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 characterization of the equilibrium points.