Abstract
The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar problem with three nonzero masses with the help of some computational algebra and geometry.
Original language | English (US) |
---|---|
Pages (from-to) | 3105-3117 |
Number of pages | 13 |
Journal | Transactions of the American Mathematical Society |
Volume | 357 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2005 |
Keywords
- Celestial mechanics
- Computational algebra
- Three-body problem