Mathematics
Scientific paper
Oct 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28...37l&link_type=abstract
(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani
Mathematics
8
Boundary Value Problems, Celestial Mechanics, Energy Methods, Manifolds (Mathematics), Asymptotic Methods, Collisions, Escape Velocity, Euler-Lagrange Equation, Orbits
Scientific paper
McGehee's (1974) picture of introducing a boundary (total collision) manifold to each energy surface is completed. This is done by constructing the missing components of its boundary as other submanifolds, representing now the asymptotic behavior at infinity. It is necessary to treat each case h equals 0, h greater than 0 or h less than 0 separately. In the first case, the known result that the behavior at total escape is the same as in total collision is repeated. In particular, why the situation is radically different in the h greater than 0 case compared with the zero energy case is explained. In the case h less than 0 there are many infinity manifold components, and the general situation is not quite well understood. Finally, our results for h greater than or equal to 0 are shown to be valid for general homogeneous potentials.
Lacomba Ernesto A.
Simó Carles
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