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The global flow of the Manev problem (1996)

Delgado, Joaquín ; Diacu, Florin N. ; Lacomba, Ernesto A. ; [weitere]

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 37 (1996), S. 2748-2761

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: The Manev problem (a two-body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinates and topological methods, and offer the physical interpretation of all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero-measure set of initial data, for which they are ellipses. For zero energy, the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial data leading to collisions has positive measure. © 1996 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.531539

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Digitale Medien

The Schwarzschild Problem in Astrophysics (1997)

Stoica, Cristina ; Mioc, Vasile

Springer

Astrophysics and space science 249 (1997), S. 161-173

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ISSN: 1572-946X

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold λ (a torus)pasted on the phase space. The flow on λ is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel.