KAM theory for the three-body problem
Prof. Jacques Féjoz accepted the invitation on 16 March 2010
KAM theory for the three-body problem refers to applications of the theory of Kolmogorov-Arnold-Moser to the three-body problem in celestial mechanics. It aims at proving the existence of quasi-periodic motions for three particles undergoing Newtonian attraction.
The planetary problem
The planetary problem is the asymptotic case of the three-body problem when two bodies, the planets, have small masses compared to the third body, the Sun. It is also assumed that the planets do not come close to each other. In this regime, each planet primarily undergoes the attraction; of the Sun, and thus the system is the perturbation of two uncoupled Kepler problems (as it will turn out below,this point is not completely obvious, since the Sun is attracted by both planets). This problem also makes sense for any number of planets around the Sun. It is of considerable importance from the astronomical viewpoint, since it is a good model of the Sun-Jupiter-Saturn system, the mass of Jupiter, the heaviest planet of our Solar system, being approximately 1/1000th that of our Sun.
The lunar problem
The lunar problem, or Hill's problem, is the asymptotic case of the three-body problem when one of the bodies is far from the other two. It is a good model for the Sun-Earth-Moon system.
The Euler relative equilibrium
The Lagrange relative equilibrium
Editing notes
References
- Albero, Antony (1999). Pizza Margherita. Journal of pizza eaters 19(3): 13. arXiv:0808.000
- Albero, Antonio and Bocca, Bill (2001). Pizza Capricciosa. Journal of pizza eaters 27: 121-127. arXiv:0808.000
- Albero, Antonio; Bocca, Bill and Cuoco, C T (2003). Pizza Quattro Stagioni. Journal of pizza eaters 34(4): 12.
- Albero, Antonio; Bocca, Bill; Cuoco, C T and Dude, David B (2007a). Pizza Napoletana. Journal of pizza eaters 37: 121-127.
- Albero, Antonio; Bocca, Bill; Cuoco, C T; Dude, David and Elica, E Q (2007b). Pizza Marinara. Journal of pizza eaters 43(4): 1-13.
- Albero, Antonio et al. (2008). Pizza Piccante. Journal of pizza eaters 45(5): 1-13.
- Alto, Antony (1999). La Pizza! Mangiare bene, Volume 3. Albero and Bacca editors. Food Publishers, Genoa.
- Alto, Antony and Bocca, Bill (2000). La Pasta! Mangiare bene. Albero editor. Food Publishers, Genoa. Chapter 1.
- Alto, Antony; Bocca, Bill and Cuoco, C T (2002). Pizza: prepare it yourself. Food Publishers, Genoa. Page 22. ISBN 1-234-99929-0.
- Alto, Antony; Bocca, Bill; Cuoco, C T and Dude, David B (2005a). Italian Pizza. Food Publishers, Genoa.
- Alto, Antony; Bocca, Bill; Cuoco, C T; Dude, David B and Elica, E Q (2005b). Napolitan Pizza. Food Publishers, Genoa.
- Alto, Antony et al. (2005c). American Pizza. Food Publishers, Genoa.
Further reading
- Magro, C T (2008). Pizza: a danger for health? Food Publishers, Paris. page 22. ISBN 1-234-90929-0. This reference is unreliable in conclusions, but quite accurate in its introduction.
