Geodesic
Kinematic geometry of triangles and the study of the three-body problem
Lobachevskii journal of mathematics, Tome 25 (2007), pp. 9-130.

Voir la notice de l'article provenant de la source Math-Net.Ru

The classical three-body problem studies the motion of a system with three point masses under the action of the Newtonian gravitational potential. The paper concerns both the geometry and the analysis of the solutions of the above problem. 
@article{LJM_2007_25_a1,
     author = {W.-Y. Hsiang and E. Straume},
     title = {Kinematic geometry of triangles and the study of the three-body problem},
     journal = {Lobachevskii journal of mathematics},
     pages = {9--130},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_25_a1/}
}
TY  - JOUR
AU  - W.-Y. Hsiang
AU  - E. Straume
TI  - Kinematic geometry of triangles and the study of the three-body problem
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 9
EP  - 130
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_25_a1/
LA  - en
ID  - LJM_2007_25_a1
ER  - 
%0 Journal Article
%A W.-Y. Hsiang
%A E. Straume
%T Kinematic geometry of triangles and the study of the three-body problem
%J Lobachevskii journal of mathematics
%D 2007
%P 9-130
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_25_a1/
%G en
%F LJM_2007_25_a1
W.-Y. Hsiang; E. Straume. Kinematic geometry of triangles and the study of the three-body problem. Lobachevskii journal of mathematics, Tome 25 (2007), pp. 9-130. http://geodesic.mathdoc.fr/item/LJM_2007_25_a1/

[1] V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate texts in Mathematics, 60, Springer-Verlag, 1978 | MR | Zbl

[2] L. Euler, “De motu rectilineo trium corporum se mutuo attahentium”, Novi Comm. Acad. Sci. Imp. Petrop., 11 (1767), 144–151

[3] W. Y. Hsiang, Geometric Study of the Three-Body Problem, I, PAM-620, Center for Pure and Applied Mathematics, Univ. of California, Berkeley, 1994

[4] W. Y. Hsiang, E. Straume, Kinematic Geometry of Triangles with Given Mass Distribution, PAM-636, Center for Pure and Applied Mathematics, Univ. of California, Berkeley, 1995

[5] S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volume I, Interscience Publishers, 1963 | MR | Zbl

[6] C. G. J. Jacobi, Vorlesungen über Dynamik, ed. A. Clebsch, Berlin, 1866 | Zbl

[7] J. L. Lagrange, Essai sur le problème des trois corps, Ouvres, vol. 6

[8] J. Lützen, “Interactions between mechanics and differential geometry in the 19th century”, Archive for History of Exact Sciences, 49 (1995), 1–72 | DOI | MR | Zbl

[9] C. Marchal, The Three-body Problem, Elsevier, New York, 1990 | MR | Zbl

[10] H. Poincaré, “Sur les solutions périodiques et le principe de moindre action”, Comptes rendus de l'Aacadémie des Sciences, 123 (1896), 915–918 | Zbl

[11] C. L. Siegel, “Der Dreierstoss”, Ann. of Math., 42 (1941), 127–168 | DOI | MR | Zbl

[12] C. L. Siegel, Lectures on the Singularities of the Three-body Problem, Tata Institute of Fundamental Research Lectures on Mathematics, no. 42 | MR

[13] C. L. Siegel, J. K. Moser, Lectures on Celestial Mechanics, Die Grundlehren der mathematischen Wissenschaften, 187, Springer-Verlag, 1971 | MR | Zbl

[14] K. F. Sundman, “Recherches sur le problème des trois corps”, Acta Soc. Sci. Fennicae, 34:6 (1907), 144–151

[15] K. F. Sundman, “Mémoire sur le problème des trois corps”, Acta Math., 36 (1912), 105–179 | DOI | MR | Zbl