caa a22 4500 445863099 CHVBK 20180317145449.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10569-010-9331-1 doi (NATIONALLICENCE)springer-10.1007/s10569-010-9331-1 Complete closed-form solutions of the Stark problem [Elektronische Daten] [Gregory Lantoine, Ryan Russell] Perturbed two-body problems play a special role in Celestial Mechanics as they capture the dominant dynamics for a broad range of natural and artificial satellites. In this paper, we investigate the classic Stark problem, corresponding to motion in a Newtonian gravitational field subjected to an additional uniform force of constant magnitude and direction. For both the two-dimensional and three-dimensional cases, the integrals of motion are determined, and the resulting quadratures are analytically integrated. A complete list of exact, closed-form solutions is deduced in terms of elliptic functions. It is found that all expressions rely on only seven fundamental solution forms. Particular attention is given to ensure that the expressions are well-behaved for very small perturbations. A comprehensive study of the phase space is also made using a boundary diagram to describe the domains of the general types of possible motion. Numerical examples are presented to validate the solutions. Springer Science+Business Media B.V., 2011 Stark problem nationallicence Kepler problem nationallicence Perturbation nationallicence Integrability nationallicence Analytical solution nationallicence Low-thrust nationallicence Lantoine Gregory School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA aut Russell Ryan School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/4(2011-04-01), 333-366 0923-2958 109:4<333 2011 109 10569 https://doi.org/10.1007/s10569-010-9331-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-010-9331-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lantoine Gregory School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Russell Ryan School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/4(2011-04-01), 333-366 0923-2958 109:4<333 2011 109 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer