The zero angular momentum, three-body problem: All but one solution has syzygies
- 1 February 2007
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 27 (6), 1933-1946
- https://doi.org/10.1017/s0143385707000338
Abstract
A syzygy in the three-body problem is a collinear instant. We prove that, with the exception of Lagrange’s solution, every solution to the zero angular momentum, Newtonian three-body problem suffers syzygies. The proof works for all mass ratios.Keywords
This publication has 9 references indexed in Scilit:
- Collisions, Rings, and Other Newtonian 𝑁-Body ProblemsCBMS Regional Conference Series in Mathematics, 2005
- Synchronized similar triangles for three-body orbits with zero angular momentumJournal of Physics A: General Physics, 2004
- Infinitely Many SyzygiesArchive for Rational Mechanics and Analysis, 2002
- A Remarkable Periodic Solution of the Three-Body Problem in the Case of Equal MassesAnnals of Mathematics, 2000
- Fitting hyperbolic pants to a three-body problemErgodic Theory and Dynamical Systems, 1999
- TheN-body problem, the braid group, and action-minimizing periodic solutionsNonlinearity, 1998
- Chaotic dynamics near triple collisionArchive for Rational Mechanics and Analysis, 1989
- Sur la régularisation du problème des trois corpsActa Mathematica, 1920
- Mémoire sur le problème des trois corpsActa Mathematica, 1913