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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-24 23:57 |
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Conference: Bucharest University Faculty of Physics 2004 Meeting
Section: Atomic and Molecular Physics; Astrophysics
Title:
SEELIGER`S TWO-BODY PROBLEM: COLLISION, ESCAPE, SYMMETRIES
Authors:
Michael Barbosu1, Vasile Mioc2, Mircea V. Rusu3
Affiliation:
1 SUNY Brockport, Department of Mathematics, Brockport, NY, USA
2 Astronomical Instituite of Romanian Academy, Bucharest, Romania
3 University of Bucharest, Faculty of Physics, Bucharest, Romania
E-mail
Keywords:
celestial mechanics - two-body problem - Seeliger theory of gravitation - collision - escape - symmetries
Abstract:
We offer a first insight into the two-body problem associated to the potential proposed by Hugo Seeliger at the end of 1800s. Our goals is twofold: to describe two limit situations (collision and escape), and to emphasize the symmetries of the problem. First we resort to McGehee-type transformations to blow up the collision singularity and escape (artificial) singularity, and to replace them by manifolds pasted on phase space. Then we describe the flows on these manifolds, which are useful to understand the behaviour of nearby orbits. An improtant issue is that collision solutions are regularizable, whereas escape solutions are not regularizable. Finally, we point out the symmetries that characterize the vector field in various coordinates. These symmetries form isomorphic Abelian groups endowed with an idempotent structure, owing proper subgrups isomorphic to Klein`s group.
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