Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry

By Alain Chenciner. 2003

141 citations recorded by the source corpus.

An action minimizing path between two given configurations, spatial or planar, of the $n$-body problem is always a true -- collision-free -- solution. Based on a remarkable idea of Christian Marchal, this theorem implies the existence of new "simple" symmetric periodic solutions, among which the Eight for 3 bodies, the Hip-Hop for 4 bodies and their generalizations.

Subfields: Aerospace Engineering, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/26f5467c5dfc73b8b3403c20f5f696767e2329dc

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In Aerospace Engineering

1. S. Terracini
2. D. Ferrario
3. Xijun Hu
4. Shanzhong Sun

In Astronomy and Astrophysics

1. S. Terracini
2. D. Ferrario
3. Xijun Hu
4. Shanzhong Sun

Citations in the corpus

• On the existence of collisionless equivariant minimizers for the classical n-body problem (2003, background): “M ore precisely,we give a fairly generalcondition on sym m etry groups G oftheloop space forthen-body problem (with potentialofhom ogeneous degree ,with > 0)which ensuresthatthe restriction ofthe Lagrangian action A to thespace G ofG -equivariantloopsiscoerciveand itsm inim izers are…”