On the n-body problem

Some solutions

• A homographic solution with 5 bodies

Solutions described in the papers Rotating Eights (2005) and The flow of the equal mass three-body problem (2008)

• The Figure-Eight solution of Chenciner-Montgomery
• The P_{12 family}

Solutions described in Unchained polygons (2009)

• The Hip-Hop solution of the 4-body problem
• The 4-loop chain of the 5-body problem
• The family of the 4-loop chain of the 5-body problem, and its Lyapunov surface
• A symmetric, 2-frequency quasiperiodic solution (periodic in a rotating frame) of the 5-body problem, and the same solution in a rotating frame

Other

• An exchange solution with 3 bodies, and another one

Documents

• Sur le problème des deux corps, ou la merveilleuse démonstration que Lagrange faisait de la première loi de Kepler (texte de niveau L2)
• Alain Chenciner (2007) The three-body problem. Scholarpedia, 2(10):2111
• Some choreographies of the planar 3-body problem, computed by Carles Simó