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We complete Mc Gehee's picture of introducing a boundary (total collision) manifold to each energy surface. 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 caseh=0,h>0 orh<0 separately. In the first case, we repeat the known result that the behavior at total escape is the same as in total collision. In particular, we explain why the situation is radically different in theh>0 case compared with the zero energy case. In the caseh<0 we have many infinity manifold components. and the general situation is not quite well understood.Finally, our results forh0 are shown to be valid for general homogeneous potentials.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.The research conducted in this paper has been partially supported by CONACYT (México), under grant PCCBNAL 790178.Partially supported by an Ajut a l'Investigacio of the University of Barcelona. 相似文献
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Celestial Mechanics and Dynamical Astronomy - On reprend ici l'étude du problème trapezoïdal des 4 corps, qui a été commencée par l'auteur dans [2]. En... 相似文献
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Ernesto A. Lacomba Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):343-355
We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case. 相似文献
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Ernesto A. Lacomba 《Celestial Mechanics and Dynamical Astronomy》1980,21(1):45-53
In this work we will describe the sets in the rigid body phase space where the energy and angular momentum are constant, and it will turn out that in nontrivial cases they will simply take the form of cartesian products of the polhodes byS
1. These sets are important for the global study of said geodesic mechanical system for being invariant under Euler's equations (energy and momentum are constant along their solutions).To motivate from something more familiar in celestial mechanics, we will begin to relate the problem to Smale's study of the planarn-body problem (Smale, 1970) and Easton's study of the planar 3-body problem (Easton, 1971), exemplifying in particular with the central force problem.In the last Sections 4 and 5, we extent our methods to give results for generalized solids on Lie groups, mentioning the further extensions to transitive mechanical systems.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.This work was partially supported by the Consejo Nacional de Ciencia y Tecnología (México) under grant PNCB-049. 相似文献
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Jesús Arturo Robles-Gutiérrez Ernesto Lacomba Zamora Jesús Martiniano Arturo Robles-Domínguez Cinna Lomnitz María Eugenia Robles-Gutiérrez 《Geofísica Internacional》2013,52(2):153-157
Experimental data in fluids suggest that nonadditive electromagnetic forces between 3 or more molecules account for the existence of critical points, triple states and phase transitions (Robles-Domínguez et al., 2007; Robles-Gutiérrez et al., 2010). Similar nonadditive forces between 3 or more molecules in the gravitational field incorporated into Newton’s universal gravitational law may also explain the existence of dark matter. 相似文献
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Ernesto A. Lacomba Ernesto Pérez-Chavela 《Celestial Mechanics and Dynamical Astronomy》1993,57(3):411-437
In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals. 相似文献
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We study a symmetric collinear restricted 3-body problem, where the equal mass primaries perform elliptic collisions, while
a third massless body moves in the line between the primaries, during the time between two consecutive elliptic collisions.
After desingularizing binary and triple collisions, we prove the existence of a transversal heteroclinic orbit beginning and
ending in triple collision. This orbit is the unique homothetic orbit that the problem possess. Finally, we describe the topology
of the compact extended phase space.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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Analysis of some degenerate quadruple collisions 总被引：1，自引：1，他引：0
We consider the trapezoidal problem of four bodies. This is a special problem where only three degrees of freedom are involved. The blow up method of McGehee can be used to deal with the quadruple collision. Two degenerate cases are studied in this paper: the rectangular and the collinear problems. They have only two degrees of freedom and the analysis of total collapse can be done in a way similar to the one used for the collinear and isosceles problems of three bodies. We fully analyze the flow on the total collision manifold, reducing the problem of finding heteroclinic connections to the study of a single ordinary differential equation. For the collinear case, from which arises a one parameter family of equations, the analysis for extreme values of the parameter is done and numerical computations fill up the gap for the intermediate values. Dynamical consequences for possible motions near total collision as well as for regularization are obtained.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.Dedicated to Prof. Szebehely on the occasion of his sixtieth birthday. 相似文献
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Manuel Falconi Ernesto A. Lacomba Jaume Llibre 《Celestial Mechanics and Dynamical Astronomy》2000,77(4):325-326
Volume Contents
Volume contents 相似文献10.
José F. Cariñena Luis A. Ibort Ernesto A. Lacomba 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):201-213
We show that time scaling transformations for Hamiltonian systems are infinitesimal canonical transformations in a suitable extended phase space constructed from geometrical considerations. We compute its infinitesimal generating function in some examples: regularization and blow up in celestial mechanics, classical mechanical systems with homogeneous potentials and Scheifele theory of satellite motion.Research partially supported by CONACYT (México), Grant PCCBBNA 022553 and CICYT (Spain). 相似文献
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