Infinity manifolds on energy levels for celestial mechanics
We consider the n-body problem of celestial mechanics. Our goal will be to describe its energy surfaces with some added asymptotic boundaries, as well as to picture the kind of orbits arising in some simple examples. Among the asymptotic boundaries, we will mainly focus on the infinity manifolds , which describe escape orbits.
KeywordsEquilibrium Point Configuration Space Celestial Mechanic Asymptotic Boundary Triple Collision
Unable to display preview. Download preview PDF.
- F. Calogero, Integrable dinamical systems and related mathematical results. These Proceedings.Google Scholar
- R. Devaney, Singularities in classical mechanical systems. In Ergodic Theory and Dynamical Systems. Vol. I. (A. Katok, ed.) pp. 211–333, Birkhauser, Basel, 1981.Google Scholar
- W. Kaplan,Topology of the two-body problem. Amer. Math. Monthly 49, 316–323 (1942).Google Scholar
- E. Lacomba, Variétés de l'infini por une énergie non nulle en mécanique célèste. C.R.A.S., Paris 1295, 503–506 (1982).Google Scholar
- R. Moeckel, Orbits of the three-body problem which pass infinitely close to triple collision. Amer. J. Math. 103, 1323–1341 (1981).Google Scholar
- H. Sperling, On the real singularities of the n-body problem. J. Reine Angew. Math. 145, 14–50 (1970).Google Scholar