Geodesic
Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses
Kuo-Chang Chen1
1 Department of Mathematics<br/>National Tsing Hua University<br/>Hsinchu 300<br/>Taiwan
Annals of mathematics, Tome 167 (2008) no. 2, pp. 325-348.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Poincaré made the first attempt in 1896 on applying variational calculus to the three-body problem and observed that collision orbits do not necessarily have higher values of action than classical solutions. Little progress had been made on resolving this difficulty until a recent breakthrough by Chenciner and Montgomery. Afterward, variational methods were successfully applied to the $N$-body problem to construct new classes of solutions. In order to avoid collisions, the problem is confined to symmetric path spaces and all new planar solutions were constructed under the assumption that some masses are equal. A question for the variational approach on planar problems naturally arises: Are minimizing methods useful only when some masses are identical?
DOI : 10.4007/annals.2008.167.325

Kuo-Chang Chen 1

1 Department of Mathematics<br/>National Tsing Hua University<br/>Hsinchu 300<br/>Taiwan 
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Kuo-Chang Chen. Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses. Annals of mathematics, Tome 167 (2008) no. 2, pp. 325-348. doi : 10.4007/annals.2008.167.325. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.325/

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