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  • 1
    Electronic Resource
    Electronic Resource
    The global flow of the Manev problem (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2748-2761 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531539
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  • 2
    Electronic Resource
    Electronic Resource
    The Schwarzschild Problem in Astrophysics (1997)
    Springer
    Astrophysics and space science 249 (1997), S. 161-173 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1000347014891
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  • 3
    Electronic Resource
    Electronic Resource
    Periodic motions around pulsating stars (1993)
    Springer
    Astrophysics and space science 202 (1993), S. 11-19 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The periodic motion of a test particle (dust, grain, or a larger body) around a pulsating star with a luminosity oscillation of small amplitude (featured by a small parameterB) is being studied. The perturbations of all orbital elements are determined to first order inB, by using Delaunay-type canonical variables and a method whose bases were put forth by von Zeipel. According to the value of the ratio oscillation frequency/dynamic frequency, three possible situations are pointed out: nonresonant (NR), quasi-resonant (QR), and resonant (R). The solution of motion equations shows that only in the (QR) and (R) cases there are orbital parameters (argument of periastron and mean anomaly) affected by secular perturbations. These solutions (which indicate a secularly stable motion in a first approximation) are valid over prediction times of orderB −1 in the (NR) case andB −1/2 in the (QR) and (R) cases. The theory may be applied to various astronomical situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00626911
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  • 4
    Electronic Resource
    Electronic Resource
    Infinitesimal librations with variable primary masses (1976)
    Springer
    Celestial mechanics and dynamical astronomy 13 (1976), S. 421-427 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The motion around the libration points is studied with Charlier's first order theory assuming the isotropic mass variation of the primaries does not exceed the order of the small primary and the derivatives of the masses with respect to time are negligible second order quantities. The results are analogous to those obtained with constant primary masses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229095
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