Monthly notices of the Royal Astronomical Society

Vol. 472, num. 3, p. 2554

DOI: 10.1093/mnras/stx1990

Date of publication: 2017-01-01

Abstract:

After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the so-called parabolic restricted three-body problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we showthat the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.

This article has been accepted for publication in Monthly notices of the Royal Astronomical Society ©: 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.]]>

Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Special session on dynamical systems and ODE

Presentation's date: 2016-06-07

Abstract:

We consider the motion of the Parabolic restricted three body problem (PRTBP). The goal of this problem is to study the motion of a massless body attracted, under the Newton’s law of gravitation, by two masses moving in parabolic orbits all over in the same plane. The PRTBP may be regarded as a simplified model for the motion of two galaxies, taken as the primaries, and an infinitessimal mass. In order to discuss possible motions for the particle, first we consider a rotating and pulsating frame where the primaries remain at rest. For the system of ODE obtained we apply dynamical systems tools. More precisely, this system of ODE is gradient-like and has exactly ten hyperbolic equilibrium points lying on the boundary invariant manifolds corresponding to escape of the primaries in past and future time. The invariant manifolds of the equilibrium points play a key role in the dynamics and we study some trajectories described by the particle before and after a close encounter between the primaries. Finally some numerical simulations are done, paying special attention to capture and escape orbits]]>

Communications in nonlinear science and numerical simulation

Vol. 29, num. 1-3, p. 400-415

DOI: 10.1016/j.cnsns.2015.05.025

Date of publication: 2015-12-01

Abstract:

The main purpose of the paper is the study of the motion of a massless body attracted, under the Newton's law of gravitation, by two equal masses moving in parabolic orbits all over in the same plane, the planar parabolic restricted three body problem. We consider the system relative to a rotating and pulsating frame where the equal masses (primaries) remain at rest. The system is gradient like and has exactly ten hyperbolic equilibrium points lying on the boundary invariant manifolds corresponding to escape of the primaries in past and future time. The global flow of the system is described in terms of the final evolution (forwards and backwards in time) of the solutions. The invariant manifolds of the equilibrium points play a key role in the dynamics. We study the connections, restricted to the invariant boundaries, between the invariant manifolds associated to the equilibrium points. Finally we study numerically the connections in the whole phase space, paying special attention to capture and escape orbits.]]>

Celestial mechanics and dynamical astronomy

Vol. 89, num. 4, p. 319-342

DOI: 10.1023/B:CELE.0000043569.25307.ab

Date of publication: 2004-10

Abstract:

We study the planar central configurations of the 1 +n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2=n=4. Numerically, first we provide evidence that when n9 the only central configuration is the regular n-gon with the large mass in its barycenter, and second we provide also evidence of the existence of an axis of symmetry for every central configuration.

The final publication is available at Springer via http://dx.doi.org/10.1023/B:CELE.0000043569.25307.ab]]>

Tianjin International Conference on Nonlinear Analysis - Hamiltonian Systems and Celestial Mechanics

p. 6

Presentation's date: 2004-06

Abstract:

This is a joint work with J. M. Cors and M. Olle. In this talk we study the central configurations of the coorbital satellite problem, also called 1+n body problem. That is, we study the central conØgurations of a large mass and n small and equal masses, which do not have any gravitational influence on the large mass but they do among them. We deal with this problem analytically for n = 3,4 and also from a numerical point of view and we give some results for n < 16.]]>

Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada

p. 265-

Presentation's date: 2003-09

Abstract:

In this communication we study the central configurations of the coorbital satellite problem -also called 1+n body problem-, that is, we study the central configurations of a large mass and n small and equal masses, which do not have any gravitational influence on the large mass but they do among them. We deal with this problem analytically and also from a numerical point of view and we give some results for n= 15.]]>

Congreso No Lineal

p. 102

Presentation's date: 2002-06-06