Abstract
The method of Lie series is used to construct a solution for the elliptic restricted three body problem. In a synodic pulsating coordinate system, the Lie operator for the motion of the third infinitesimal body is derived as function of coordinates, velocities and true anomaly of the primaries. The terms of the Lie series for the solution are then calculated with recurrence formulae which enable a rapid successive calculation of any desired number of terms. This procedure gives a very useful analytical form for the series and allows a quick calculation of the orbit.
Similar content being viewed by others
References
Gröbner, W.: 1967,Die Lie Reihen und ihre Anwendungen, VEB Berlin
Hanslmeier, A., Dvorak, R.: 1983, ‘Numerical Integration with Lie series’, Astron.Astrophys.132, pp. 203
Schneider, M.: 1979,Himmelsmechanik, BI Mannheim, p. 408
Stumpff, K.: 1974,Himmelsmechanik, Vol.I I I, VEB Berlin
Szebehely, V., Giacaglia, G.E.O.: 1964, Astron.J.69, 270
Author information
Authors and Affiliations
Additional information
The project is supported by the Austrian Fonds zur Förderung der wissénschaftlichen Forschung under Project No. 4471.
Rights and permissions
About this article
Cite this article
Delva, M. Integration of the elliptic restricted three-body problem with Lie series. Celestial Mechanics 34, 145–154 (1984). https://doi.org/10.1007/BF01235797
Issue Date:
DOI: https://doi.org/10.1007/BF01235797