Abstract
Hsiang and Straume have treated the kinematic geometry of the three-body problem in [3], using a particular set of geometric invariants for three-body motions. The corresponding reduced equations of motion were however not present, except in the special case of zero angular momentum. This article extends [3] by providing the reduced equations of motion in the general case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hildeberto E. Cabral, Journal of Differential Equations 84, 215–227 (1990).
Wu-Yi Hsiang and Eldar Straume, Kinematic Geometry of Triangles with Given Mass Distribution (Center for Pure and Applied Mathematics, University of California, Berkeley, PAM-636, 1995).
Wu-Yi Hsiang and Eldar Straume, Lobachevskii Journal of Mathematics 25(1), 9–130 (2007).
Joseph-Louis Lagrange. Prix de l’Académie royale des sciences de Paris 9, 229–331 (1772).
C. Marchal, The three-body problem (Elsevier, 1990).
Mahdi K. Salehani, Celestial Mehcanics and Dynamical Astronomy 111(4), 465–479 (2011).
G. Strang, Linear Algebra and Its Applications (Thomson Brooks/Cole Cengage learning, 2006).
Eldar Straume, Lobachevskii Journal of Mathematics 24(1), 73–134 (2006).
Lars Sydnes, Geometric Reduction and the three body problem, PhD thesis, Doctoral theses at NTNU, 2012: 211, (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted by V. V. Lychagin
Rights and permissions
About this article
Cite this article
Sydnes, L. Geometric reduction of the three-body problem. Lobachevskii J Math 34, 332–343 (2013). https://doi.org/10.1134/S1995080213040161
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080213040161