Search results for "Three-body problem"
showing 10 items of 32 documents
Ejection and collision orbits of the spatial restricted three-body problem
1985
We begin by describing the global flow of the spatial two body rotating problem, μ=0. The remainder of the work is devoted to study the ejection and collision orbits when μ>-0. We make use of the ‘blow up’ techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.
Limits to the fixed center approximation to Faddeev equations: The case of theϕ(2170)
2011
The fixed center approximation to the Faddeev equations has been used lately with success in the study of bound systems of three hadrons. It is also important to set the limits of the approach in those problems to prevent proliferation of inaccurate predictions. In this paper, we study the case of the $\ensuremath{\phi}(2170)$, which has been described by means of Faddeev equations as a resonant state of $\ensuremath{\phi}$ and $K\overline{K}$, and show the problems derived from the use of the fixed center approximation in its study. At the same time, we also expose the limitations of an alternative approach recently proposed.
Periodic Orbits in the Isosceles Three-Body Problem
1991
The Saturn’s satellites Janus and Epimetheus are the first known bodies in the Solar System that has horseshoe orbits in a frame that rotates with uniform angular velocity. Both satellites have similar masses and orbital elements when they are far from one another. Moreover, their orbits are nearly symmetric. In fact, in the past, they have been identify as a unique satellite and afterwards, some mathematical theories about their orbits has been necessaries to understand why they do not collide. In particular, the interest in planar three-body problem with two small masses has increased6. We assume that the two small masses have similar symmetric initial conditions. The aim of this paper is…
Causality, non-locality and three-body Casimir–Polder energy between three ground-state atoms
2006
The problem of relativistic causality in the time-dependent three-body Casimir–Polder interaction energy between three atoms, initially in their bare ground-state, is discussed. It is shown that the non-locality of the spatial correlations of the electromagnetic field emitted by the atoms during their dynamical self-dressing may become manifest in the dynamical three-body Casimir–Polder interaction energy between the three atoms.
Three-body approach to proton-hydrogen charge exchange and elastic scattering
1999
The impact-parameter Faddeev approach to atomic three-body collisions which has been developed for, and successfully applied to, ion-atom scattering processes, has now been developed further by including, instead of the Coulomb potentials, the full two-particle off-shell Coulomb {ital T} matrices in all {open_quotes}triangle{close_quotes} contributions to the effective potentials. Results of calculations of proton-hydrogen collisions with only the ground states of the hydrogen retained in both the direct and the rearrangement channels are presented. Total and differential electron transfer, as well as differential elastic scattering cross sections, are obtained simultaneously in very good a…
Numerical studies to detect chaotic motion in the full planar averaged three-body problem
2023
AbstractIn this paper, the author deals with a well-known problem of Celestial Mechanics, namely the three-body problem. A numerical analysis has been done in order to prove existence of chaotic motions of the full-averaged problem in particular configurations. Full because all the three bodies have non-negligible masses and averaged because the Hamiltonian describing the system has been averaged with respect to a fast angle. A reduction of degrees of freedom and of the phase-space is performed in order to apply the notion of covering relations and symbolic dynamics.
Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941)
2005
International audience; Tullio Levi-Civita was one of the most important Italian mathematicians in the early part of the 20th century, contributing significantly to a number of research fields in mathematics and physics. In addition, he was involved in the social and political life of his time and suffered severe political and racial persecution during the period of Fascism. He tried repeatedly and in several cases successfully to help colleagues and students who were victims of anti-Semitism in Italy and Germany. His scientific and private life is well documented in the letters and documents contained in his Archive. The authors' aim is to illustrate the events of his life by means of his …
Symbolic dynamics in a binary asteroid system
2020
We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem.
Invariant rotational curves in Sitnikov's Problem
1993
The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.
Quark-model based study of the triton binding energy
2001
The three-nucleon bound state problem is studied employing a nucleon-nucleon potential obtained from a basic quark-quark interaction in a five-channel Faddeev calculation. The obtained triton binding energy is comparable to those predicted by conventional models of the $NN$ force.