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 Manresa School of Engineering (EPSEM)
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Generalized hiphop solutions of the N+Nbody problem
Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Celestial, Molecular, and Atomic Dynamics
Presentation's date: 201307
Presentation of work at congresses
Read the abstract View Share Reference managersHip{hop solutions of the equal{mass 2 N {body problem are periodic solutions in which the bodies lie on the vertices of a regular antiprism for all time. A regular antiprism is a polyhedron formed by two congruent regular N {gons lying on parallel planes and such that the orthogonal projection on each other is a regular 2 N {gon. In [1] and [2] it was shown that there exist families of Hip{hop solutions in the neighbourhood of planar regular 2 N {gon relative equilibria solution and of planar highly eccentric elliptic homographic solutions, the planes containing each group of bodies performing small oscillations along the line joining the centres of the N {gons. Consider now two regular N {gons, with masses equal within each group, lying on two planes perpendicular to the line joining their centres. It is easily seen that, if the initial velocities within each group are invariant under a 2 =N rotation around that line, then the bodies remain on such a conguration for all time, provided no collision occurs. A periodic solution of this type with the same mean angular velocity for each group will be called a Generalized Hip{Hop solution of the ( N + N ){body problem. We show the existence of Generalized Hip{Hop solutions in the case of almost equal mass. These solutions are close to the planar regular 2 N {gon relative equi libria solutions with small vertical oscillations described above. 
On a special cocircular central configuration
Cors Iglesias, Josep Maria; Hall, G.R.; Roberts, Gareth E.
Colloquium on Dynamical Systems Control and Applications
Presentation's date: 20130621
Presentation of work at congresses
Read the abstract View Share Reference managersFor a class of potential functions including the planar n body and n vortex problems, we investigate cocircular central configurations whose center of mass coincides with the center of the circle containing the bodies. New equations are derived that completely describe the problem. Using a topological approach, it is shown that for any choice of positive masses (or circulations), if such a central configuration exists, then it is unique. For the planar n vortex problem, it is shown that the only possible solution is the regular n gon. 
Roads of the sky
Arisa Alemany, Eloi; Cors Iglesias, Josep Maria; Ros Ferré, Rosa Maria
Date of publication: 2013
Book
Read the abstract View Share Reference managersEl libro "Caminos del cielo" es una guía práctica para empezar a reconocer las principales constelaciones y localizar algunas de las estrellas más características de nuestro cielo. Además de ser también un guía para reconocer, con la ayuda de unos prismáticos, algunos de los mares y cráteres más característicos de la Luna. 
Camiños do ceo
Arisa Alemany, Eloi; Cors Iglesias, Josep Maria; Ros Ferré, Rosa Maria
Date of publication: 20130114
Book
Read the abstract View Share Reference managersEl llibre "Camiños do ceo" és una guia pràctica per començar a reconèixer les principals constel·lacions i localitzar algunes de les estrelles més característiques del nostre cel. A més de ser també un a guia per reconèixer, amb l'ajuda d'uns prismàtics, alguns dels mars i cràters més característics de la Lluna. 
Camins del cel
Arisa Alemany, Eloi; Cors Iglesias, Josep Maria; Ros Ferré, Rosa Maria
Date of publication: 20130115
Book
Read the abstract View Share Reference managersEl llibre "Camins del cel" és una guia pràctica per començar a reconèixer les principals constel·lacions i localitzar algunes de les estrelles més característiques del nostre cel. A més de ser també un a guia per reconèixer, amb l'ajuda d'uns prismàtics, alguns dels mars i cràters més característics de la Lluna. 
Zeruko bideak
Arisa Alemany, Eloi; Cors Iglesias, Josep Maria; Ros Ferré, Rosa Maria
Date of publication: 20130114
Book
Read the abstract View Share Reference managersEl llibre "Zeruko bideak" és una guia pràctica per començar a reconèixer les principals constel·lacions i localitzar algunes de les estrelles més característiques del nostre cel. A més de ser també un a guia per reconèixer, amb l'ajuda d'uns prismàtics, alguns dels mars i cràters més característics de la Lluna. 
Numerical exploration of the limit ring problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Hall, G.R.
Qualitative theory of dynamical systems
Date of publication: 201304
Journal article
Read the abstract View Share Reference managersThe aim of this work is to provide an insight of an idealized model of a planetary ring. The model is a limit case of the planar circular restricted 1 + n body problem, where an infinitesimal particle moves under the gravitational influence of a large central body and n smaller bodies located on the vertices of a regular ngon. When considering n tending to infinity, a model depending on one parameter is obtained. We study the main important structures of the problem depending on this parameter (equilibria, Hill¿s regions, linear stability, ¿). We use Poincaré maps, for different values of the parameter, in order to predict the width of the ring and the richness of the dynamics that occur is discussed. This work is a continuation of the work presented in Barrabés by (SIAM J Appl Dyn Syst 9:634¿658, 2010). 
Fourbody cocircular central configurations
Cors Iglesias, Josep Maria; Roberts, Gareth E.
Nonlinearity
Date of publication: 201202
Journal article
Read the abstract Access to the full text Share Reference managersWe classify the set of central configurations lying on a common circle in the Newtonian fourbody problem. Using mutual distances as coordinates, we show that the set of fourbody cocircular central configurations with positive masses is a twodimensional surface, a graph over two of the exterior sidelengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a cocircular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general fourbody case, we show that if any two masses of a fourbody cocircular central configuration are equal, then the configuration has a line of symmetry.
We classify the set of central configurations lying on a common circle in the Newtonian fourbody problem. Using mutual distances as coordinates, we show that the set of fourbody cocircular central configurations with positive masses is a twodimensional surface, a graph over two of the exterior sidelengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a cocircular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general fourbody case, we show that if any two masses of a fourbody cocircular central configuration are equal, then the configuration has a line of symmetry.
Postprint (author’s final draft) 
On the central configurations of the planar 1 + 3 body problem
Corbera, M.; Cors Iglesias, Josep Maria; Llibre Saló, Jaume
Celestial mechanics and dynamical astronomy
Date of publication: 2011
Journal article
Read the abstract Access to the full text Share Reference managersWe consider the Newtonian 4 body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two diferent classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and nonsymmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.
We consider the Newtonian 4 body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two diferent classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and nonsymmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.
Postprint (author’s final draft) 
Central configurations of the planar 1+3 body problem
Cors Iglesias, Josep Maria; Corbera, M.; Llibre Saló, Jaume
Spring Eastern Sectional Meeting
Presentation's date: 20110409
Presentation of work at congresses
Read the abstract View Share Reference managersWe study congurations with one massive central mass, M , and several innitesimal co{orbital satellites (in our case, 3 satellites) describing the same circular orbit around M . A conguration that allows relative equilibria (in a rotation frame the satellites remain xed) and homographic motions (the conguration of the satellites change it size, but keep the shape) is called central conguration. We obtain two dierent classes of central congurations depending on the mutual distances between the innitesimal masses. Both classes exhibit symmetric and non{symmetric congurations. In the case when two innitesimal masses are equal we provide evidence that the number of central congurations varies from ve to seven. 
BUILDING ON THE INTERNATIONAL YEAR OF ASTRONOMY: MAKING YOUNG CHILDREN AWARE OF THE UNIVERSE
Cors Iglesias, Josep Maria; Ros Ferre, Rosa Maria; Gutierrez Cabello, Jorge Luis; Mazon Bueso, Jordi; Espona Dones, Margarida; Fabregat Fillet, Jaime
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Highly eccentric hiphop solutions of the 2Nbody problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Physica. D, Nonlinear phenomena
Date of publication: 201002
Journal article
Read the abstract Access to the full text Share Reference managersWe show the existence of families of hiphop solutions in the equalmass 2Nbody problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular nonharmonic oscillations. By introducing a parameter ¿, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ¿ ¿ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system.
We show the existence of families of hiphop solutions in the equalmass 2Nbody problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular nonharmonic oscillations. By introducing a parameter Є, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small Є ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system.
Postprint (author’s final draft) 
A limit case of the "Ring problem": the planar circular restricted 1+n body problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Hall, G.R.
SIAM journal on applied dynamical systems
Date of publication: 2010
Journal article
Read the abstract View Share Reference managersWe study the dynamics of an extremely idealized model of a planetary ring. In particular, we study the motion of an infinitesimal particle moving under the gravitational influence of a large central body and a regular ngon of smaller bodies as n tends to infinity. Our goal is to gain insight into the structure of thin, isolated rings. 
J2 efect and the collision restricted threebody problem
Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
International Symposium on Hamiltonian Systems and Celestial Mechanics
Presentation's date: 201012
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Lowcost trajectories using dynamical systems
Cors Iglesias, Josep Maria; Barrabés Vera, Esther
Jornada de Sostenibilitat i Compromís Social
Presentation's date: 20101202
Presentation of work at congresses
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The restricted planar isosceles threebody problem with nonnegative energy
Cors Iglesias, Josep Maria; Castilho, César E.; Vidal Díaz, Claudio
Celestial mechanics and dynamical astronomy
Date of publication: 200902
Journal article
Read the abstract View Share Reference managersWe consider a restricted threebody problem consisting of two positive equal masses m 1 = m 2 moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m 3 moving in the plane P perpendicular to the line joining m 1 and m 2. The plane P is assumed to pass through the center of mass of m 1 and m 2. Since the motion of m 1 and m 2 is not affected by m 3, from the symmetry of the configuration it is clear that m 3 remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles threebody problem describes the motion of m 3 when its angular momentum is different from zero and the motion of m 1 and m 2 is not periodic. Our main result is the characterization of the global flow of this problem. 
A limit case of the "Ring problem"
Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Hall, G.R.
International Meeting on Celestial Mechanics
Presentation's date: 200909
Presentation of work at congresses
Read the abstract View Share Reference managersWe study the dynamics of an idealized model of a planetary ring. We start with the n + 1 ring problem in a rotating coordinate system where an infinitesimal mass is attracted by n small masses m located in a regular n gon around a central mass m 0 . Assuming the mass ratio m 0 /m of order n 3 , we construct a limiting problem as n tends to infinity. This limit process is similar to Hill ´s problem. The central mass is pushed towards the infinity while the distances between two consecutive ring bodies is kept equal 1. We study the dynamics of the problem including equilibria, periodic orbits and stability. 
J2 effect and elliptic inclined periodic orbits in the collision threebody problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
SIAM journal on applied dynamical systems
Date of publication: 200801
Journal article
Read the abstract Access to the full text Share Reference managersThe existence of a new class of inclined periodic orbits of the collision restricted three¿body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet. Key words. Collision restricted threebody problem, periodic orbits, symmetric orbits, critical inclination, continuation method. AMS subject classifications. 70F07, 70F15, 70H09, 70H12, 70M20. 1. Introduction. The launch of the Sputnik in October 1957 opened the space age. The use of circular, elliptic, and synchronous orbits, combined with dynamical effects due to the Earths equatorial bulge gives rise to an array of orbits with specific properties to support various mission constraints. One example is the Molniya orbit: a highly elliptic 12hourperiod orbit the former USSR originally designed to observe
The existence of a new class of inclined periodic orbits of the collision restricted three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet.
Postprint (author’s final draft) 
Hiphop solutions of the 2Nbody problem with eccentricity close to 1
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Jornadas de Trabajo en Mecánica Celeste
Presentation's date: 200806
Presentation of work at congresses
Read the abstract View Share Reference managersHipHop solutions of the 2Nbody problem with equal masses are shown to exist using a topological argument. These solutions are close to a planar regular 2Ngon homographic conØguration with values of the eccentricity close to 1, plus a small vertical oscillations in which each mass. 
Highly eccentric hiphop solutions of the 2Nbody problem
Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
International Symposium on Hamiltonian Systems and Celestial Mechanics
Presentation's date: 200807
Presentation of work at congresses
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J2 effect and the collision restricted threebody problem
Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Congreso de Ecuaciones Diferenciales y Aplicaciones. Congreso de Matemática Aplicada
Presentation's date: 200709
Presentation of work at congresses
Read the abstract View Share Reference managersThe existence of a new class of inclined periodic orbits of the collision restricted threebody problem is shown. The symmetric periodic solutions found are perturba tions of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet. 
On final evolutions in the restricted planar parabolic threebody problem
Alvarez, Martha; Cors Iglesias, Josep Maria; Delgado, Joaquin
Celestial mechanics and dynamical astronomy
Date of publication: 200609
Journal article
Read the abstract View Share Reference managersIn this paper, we prove the existence of special type of motions in the restricted planar parabolic threebody problem, of the type exchange, emission¿capture, and emission¿escape with close passages to collinear and equilateral triangle configuration, among others. The proof is based on a gradientlike property of the Jacobian function when equations of motion are written in a rotatingpulsating reference frame, and the extended phase space is compactified in the time direction. Thus a phase space diffeomorphic to [p/2, p/2] × Cµ1,µ2 × C coordinates (¿, ¿, ¿') is obtained with the boundary manifolds ¿ = ±p/2 corresponding to escapes of the binaries when time tends to±8. It is shown there exists exactly five critical points on each boundary, corresponding to classic homographic solutions. The connections of the invariant manifolds associated to the collinear configurations, and stable/unstable sets associated to binary collision on the boundary manifolds, are obtained for arbitrary masses of the primaries. For equal masses extra connections are obtained, which include equilateral configurations. Based on the gradientlike property, a geometric criterion for capture is proposed and is compared with a criterion introduced by Merman (1953b) in the fifties, and an example studied numerically by Kocina (1954). 
Hiphop solutions of the 2Nbody problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Celestial mechanics and dynamical astronomy
Date of publication: 200609
Journal article
Read the abstract Access to the full text Share Reference managersHiphop solutions of the 2Nbody problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2Ngon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are threedimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.
Hip{Hop solutions of the 2 N {body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2 N {gon relative equilibria with small vertical oscillations. For Øxed N , an inØnity of these solutions are three{dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.
Postprint (author’s final draft) 
Solutions forming an antiprism in the 2N body problem of equal masses
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
International Meeting on Celestial Mechanics
Presentation's date: 20050912
Presentation of work at congresses
Read the abstract View Share Reference managersWe consider the problem of 2N bodies of equal masses moving under their mutual gravitational attraction. With a suitable choice of the initial conditions, there exist solutions with all bodies on the vertices of an antiprism at all time. Using the symmetries of this configuration, the problem can be reduced to a problem with 3 degrees of freedom. In this context, the existence of families of symmetric solutions can be proved using analytic continuation. 
Soluciones periódicas y simétricas del problema de 6 cuerpos con masas iguales
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Jornadas de Trabajo en Mecánica Celeste
Presentation's date: 20050627
Presentation of work at congresses
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On final evolutions in the restricted planar parabolic threebody problem
Alvarez, Martha; Cors Iglesias, Josep Maria; Delgado, Joaquín
International Meeting on Celestial Mechanics
Presentation's date: 200509
Presentation of work at congresses
Read the abstract View Share Reference managersIn this paper, we prove the existence of special type of motions in the restricted planar parabolic threebody problem, of the type exchange, emission¿capture, and emission¿escape with close passages to collinear and equilateral triangle configuration, among others. The proof is based on a gradientlike property of the Jacobian function when equations of motion are written in a rotatingpulsating reference frame, and the extended phase space is compactified in the time direction. Thus a phase space diffeomorphic to [p/2, p/2] × Cµ1,µ2 × C coordinates (¿, ¿, ¿') is obtained with the boundary manifolds ¿ = ±p/2 corresponding to escapes of the binaries when time tends to±8. It is shown there exists exactly five critical points on each boundary, corresponding to classic homographic solutions. The connections of the invariant manifolds associated to the collinear configurations, and stable/unstable sets associated to binary collision on the boundary manifolds, are obtained for arbitrary masses of the primaries. For equal masses extra connections are obtained, which include equilateral configurations. Based on the gradientlike property, a geometric criterion for capture is proposed and is compared with a criterion introduced by Merman (1953b) in the fifties, and an example studied numerically by Kocina (1954). 
Hiphop solutions of the 2Nbody problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
International Meeting on Celestial Mechanics
Presentation's date: 200509
Presentation of work at congresses
Read the abstract View Share Reference managersHiphop solutions of the 2Nbody problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2Ngon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are threedimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame. 
Coorbital periodic orbits in the three body problem
Cors Iglesias, Josep Maria; Hall, G.R.
Meeting on Celestial Mechanics
Presentation's date: 20050915
Presentation of work at congresses
Read the abstract View Share Reference managersWe consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. These moons avoid collision because they switch orbits during each close encounter. We approach the problem as a perturbation of decoupled Kepler problems. The perturbation is large but only in a small region in the phase space. We discuss the relationship required among the small quantities (radial separation, mass, and minimum angular separation) that admits coorbital motion like that observed for the moons of Saturn, Janus and Epimetheus. Persistence of the orbits is also given. 
Analytic continuation in the case of nonregular dependency on a small parameter with an application to celestial mechanics
Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Journal of differential equations
Date of publication: 200512
Journal article
Read the abstract View Share Reference managersWe consider a nonautonomous system of ordinary differential equations. Assume that the time dependence is periodic with a very high frequency 1/¿, where ¿ is a small parameter and differentiability with respect to the parameter is lost when ¿ equals zero. We derive from Arenstorf's implicit function theorem a set of conditions to show the existence of periodic solutions. These conditions look formally like the standard analytic continuation method, namely, checking that a certain minor does not vanish. We apply this result to show the existence of a new class of periodic orbits of very large radii in the threedimensional elliptic restricted threebody problem for arbitrary values of the masses of the primaries. 
The global flow of the parabolic restricted threebody problem
Cors Iglesias, Josep Maria; Llibre Saló, Jaume
Celestial mechanics and dynamical astronomy
Date of publication: 200409
Journal article
Read the abstract View Share Reference managersWe have two mass points of equal masses m 1=m 2 > 0 moving under Newton¿s law of attraction in a noncollision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m 3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m 3=0, the motion of m 1 and m 2 is not affected by the third and from the symmetry of the motion it is clear that m 3 will remain on the line L. The parabolic restricted threebody problem describes the motion of m 3. Our main result is the characterization of the global flow of this problem. 
Central configurations of the planar coorbial satellite problem
Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Olle Torner, Maria Mercedes
Celestial mechanics and dynamical astronomy
Date of publication: 200410
Journal article
Read the abstract View Share Reference managersWe 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 ngon 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. 
On the central configurations of the coorbital satellite problem
Llibre Saló, Jaume; Cors Iglesias, Josep Maria; Olle Torner, Maria Mercedes
Tianjin International Conference on Nonlinear Analysis  Hamiltonian Systems and Celestial Mechanics
Presentation's date: 200406
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Read the abstract View Share Reference managersThis 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. 
Coorbital periodic orbits in the three body problem
Cors Iglesias, Josep Maria; Hall, G.R.
SIAM journal on applied mathematics
Date of publication: 200305
Journal article
Read the abstract Access to the full text Share Reference managersWe consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. These moons avoid collision because they switch orbits during each close encounter. We approach the problem as a perturbation of decoupled Kepler problems as in Poincaré's periodic orbits of the first kind. The perturbation is large but only in a small region in the phase space. We discuss the relationship required among the small quantities (radial separation, mass, and minimum angular separation). Persistence of the orbits is discussed.
We consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. These moons avoid collision because they switch orbits during each close encounter. We approach the problem as a perturbation of decoupled Kepler problems as in Poincar ́ e’s periodic orbits of the first kind. The perturbation is large but only in a small region in the phase space. We discuss the relationship required among the small quantities (radial separation, mass, and minimum angular separation). Persistence of the orbits is discussed. 
Problemes de mètodes estadístics de l'enginyeria: curs 20062007
Cors Iglesias, Josep Maria; Freixas Bosch, Josep; Rossell Garriga, Josep Maria
Date of publication: 200310
Book
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The planar restricted parabolic 3body problem
Cors Iglesias, Josep Maria; Alvarez, Martha; Delgado, Joaquín
International Conference of Differential Equations
Presentation's date: 20030722
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On the central configurations of the coorbital satellite problem
Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Olle Torner, Maria Mercedes
Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada
Presentation's date: 200309
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Configuraciones centrales del problema de 1+4 cuerpos
Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Olle Torner, Maria Mercedes
Congreso No Lineal
Presentation's date: 20020606
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Exchange and capture orbits in the planar restricted parabolic 3body problem
Alvarez, Martha; Delgado, Joaquín; Cors Iglesias, Josep Maria
International Symposium on Hamiltonian Systems and Celestial Mechanics
Presentation's date: 200104
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Read the abstract View Share Reference managersTwo attracting bodies m 1,m 2 move in parabolic orbits and a third massless body mo = 0 moves in the plane under the attraction of the primaries. We obtain the equations of motion of the massless particle in a rotatingpulsating coordinate system where the primaries remain fixed. Introducing an appropriate time scaling we obtain two invariant subsystems corresponding to final evolutions as time goes to±8. We show that the set of initial conditions leading to parabolic escape of the infinitesimal mass is the union of invariant manifolds of dimension 3 and 4 and tend asymptotically to a central configuration. We also give a new criterion based in the Jacobi function analogous to the circular case, to guarantee elliptic capture. This criterion seems to be distinct from criteria introduced by Merman [1954] for the hyperbolic and parabolic restricted problems. We review Kocina¿s example of exchange where the infinitesimal mass mo comes from infinity forming a bounded binary with m2 and escapes forming a bounded binary with m 1, and obtain new classes of orbits of symmetric exchange. 
Innovate control tehnologies for vibration sensitive civil engineering structures
Cors Iglesias, Josep Maria; Rodellar Benede, Jose Julian
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Periodic solutions in the spatial elliptic restricted threebody problem
Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
Physica. D, Nonlinear phenomena
Date of publication: 200106
Journal article
Read the abstract View Share Reference managersWe show the existence of a new class of periodic orbits in the threedimensional elliptic restricted threebody problem in the case of equal masses of the primaries. The doubly symmetric periodic solutions found are perturbations of very large circular Keplerian orbits lying in a plane perpendicular to that of the primaries. They exist for a discrete sequence of values of the mean motion, irrespective of the values of the eccentricity of the primaries orbit. 
Sistemas de control robusto para la reducción de vibraciones en sistemas sometidos a excitaciones desconocidas. Diseño y verifiación experimental
Cors Iglesias, Josep Maria; Rodellar Benede, Jose Julian
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Anàlisi, disseny i control de sistemes no lineals amb aplicacions als sistemes mecànics dissipatius. UPCPR9908
Cors Iglesias, Josep Maria; Rossell Garriga, Josep Maria; Pérez Mañosas, Antonio
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Periodic solution in the spatial elliptic restricted threebody problem
Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
International Conference on Differential Equations
Presentation's date: 19990803
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Slow chads in the system of coorbiting saturn satelites
Cors Iglesias, Josep Maria; Hall, G.R.; Koiller, J.
Date: 199904
Report
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Saturn's coorbiting satelites
Cors Iglesias, Josep Maria; Hall, G.R.
International Symposium on Hamiltonian Systems and Celestial Mechanics
Presentation's date: 19981207
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An approach to the problem of saturn's coorbiting satelites
Cors Iglesias, Josep Maria; Hall, G.R.
Date: 199809
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Qualitative theory of dinamical systems with focus on periodic orbits
Cors Iglesias, Josep Maria; Llibre Saló, Jaume
Participation in a competitive project
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Continuació analítica d'òrbites periòdiques
Cors Iglesias, Josep Maria
Fòrum R+D Manresa
Presentation's date: 19970626
Presentation of work at congresses
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Qualitative study of the hyperbolic colliston restricted threebody problem
Cors Iglesias, Josep Maria; Llibre Saló, Jaume
Nonlinearity
Date of publication: 199612
Journal article
Read the abstract View Share Reference managersWe have two mass points of equal masses moving under Newton's law of gravitational attraction in a collision hyperbolic orbit while their centre of mass is at rest. We consider a third mass point, of mass , moving on the straight line L perpendicular to the line of motion of the first two mass points and passing through their centre of mass. Since , the motion of the masses and is not affected by the third mass and from the symmetry of the motion it is clear that will remain on the line L. The hyperbolic collision rectricted threebody problem consists in describing the motion of . Our main result is the characterization of the global flow of this problem.
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