Cors Iglesias, Josep Maria
Total activity: 58
Department
Department of Applied Mathematics III
School
Manresa School of Engineering (EPSEM)
E-mail
josep.m.corsupc.edu
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1 to 50 of 58 results
  • Generalized hip-hop solutions of the N+N-body problem

     Cors Iglesias, Josep Maria; Barrabés Vera, Esther; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    Celestial, Molecular, and Atomic Dynamics
    Presentation's date: 2013-07
    Presentation of work at congresses

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    Hip{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 co-circular central configuration

     Cors Iglesias, Josep Maria; Hall, G.R.; Roberts, Gareth E.
    Colloquium on Dynamical Systems Control and Applications
    Presentation's date: 2013-06-21
    Presentation of work at congresses

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    For a class of potential functions including the planar n -body and n -vortex problems, we investigate co-circular 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

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    El 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: 2013-01-14
    Book

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    El 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: 2013-01-15
    Book

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    El 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: 2013-01-14
    Book

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    El 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: 2013-04
    Journal article

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    The 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 n-gon. 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).

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    Four-body co-circular central configurations  Open access

     Cors Iglesias, Josep Maria; Roberts, Gareth E.
    Nonlinearity
    Date of publication: 2012-02
    Journal article

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    We classify the set of central configurations lying on a common circle in the Newtonian four-body problem. Using mutual distances as coordinates, we show that the set of four-body co-circular central configurations with positive masses is a two-dimensional surface, a graph over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a co-circular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general four-body case, we show that if any two masses of a four-body co-circular 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 four-body problem. Using mutual distances as coordinates, we show that the set of four-body co-circular central configurations with positive masses is a two-dimensional surface, a graph over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a co-circular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general four-body case, we show that if any two masses of a four-body co-circular central configuration are equal, then the configuration has a line of symmetry.

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    On the central configurations of the planar 1 + 3 body problem  Open access

     Corbera, M.; Cors Iglesias, Josep Maria; Llibre Saló, Jaume
    Celestial mechanics and dynamical astronomy
    Date of publication: 2011
    Journal article

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    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 non-symmetric 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 non-symmetric 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: 2011-04-09
    Presentation of work at congresses

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    We 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.

  • EU-UNAWE

     Fabregat Fillet, Jaime; Mazon Bueso, Jordi; Gutierrez Cabello, Jorge Luis; Cors Iglesias, Josep Maria
    Participation in a competitive project

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  • 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
    Participation in a competitive project

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    Highly eccentric hip-hop solutions of the 2N-body problem  Open access

     Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    Physica. D, Nonlinear phenomena
    Date of publication: 2010-02
    Journal article

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    We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic 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 hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic 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

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    We 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 n-gon 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 three-body 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: 2010-12
    Presentation of work at congresses

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  • Low-cost trajectories using dynamical systems  Open access

     Cors Iglesias, Josep Maria; Barrabés Vera, Esther
    Jornada de Sostenibilitat i Compromís Social
    Presentation's date: 2010-12-02
    Presentation of work at congresses

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  • The restricted planar isosceles three-body problem with non-negative energy

     Cors Iglesias, Josep Maria; Castilho, César E.; Vidal Díaz, Claudio
    Celestial mechanics and dynamical astronomy
    Date of publication: 2009-02
    Journal article

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    We consider a restricted three-body 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 three-body 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: 2009-09
    Presentation of work at congresses

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    We 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.

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    J2 effect and elliptic inclined periodic orbits in the collision three-body problem  Open access

     Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    SIAM journal on applied dynamical systems
    Date of publication: 2008-01
    Journal article

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    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. Key words. Collision restricted three-body 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 12-hour-period 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.

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  • Hip-hop solutions of the 2-N-body 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: 2008-06
    Presentation of work at congresses

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    Hip-Hop solutions of the 2N-body problem with equal masses are shown to exist using a topological argument. These solutions are close to a planar regular 2N-gon homographic conØguration with values of the eccentricity close to 1, plus a small vertical oscillations in which each mass.

  • Highly eccentric hip-hop solutions of the 2N-body 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: 2008-07
    Presentation of work at congresses

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  • J2 effect and the collision restricted three-body 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: 2007-09
    Presentation of work at congresses

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    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 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 three-body problem

     Alvarez, Martha; Cors Iglesias, Josep Maria; Delgado, Joaquin
    Celestial mechanics and dynamical astronomy
    Date of publication: 2006-09
    Journal article

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    In this paper, we prove the existence of special type of motions in the restricted planar parabolic three-body 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 gradient-like property of the Jacobian function when equations of motion are written in a rotating-pulsating reference frame, and the extended phase space is compactified in the time direction. Thus a phase space diffeomorphic to [-p/2, p/2] × C-µ1,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 gradient-like 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).

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    Hip-hop solutions of the 2N-body problem  Open access

     Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    Celestial mechanics and dynamical astronomy
    Date of publication: 2006-09
    Journal article

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    Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional 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: 2005-09-12
    Presentation of work at congresses

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    We 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: 2005-06-27
    Presentation of work at congresses

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  • On final evolutions in the restricted planar parabolic three-body problem

     Alvarez, Martha; Cors Iglesias, Josep Maria; Delgado, Joaquín
    International Meeting on Celestial Mechanics
    Presentation's date: 2005-09
    Presentation of work at congresses

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    In this paper, we prove the existence of special type of motions in the restricted planar parabolic three-body 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 gradient-like property of the Jacobian function when equations of motion are written in a rotating-pulsating reference frame, and the extended phase space is compactified in the time direction. Thus a phase space diffeomorphic to [-p/2, p/2] × C-µ1,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 gradient-like 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).

  • Hip-hop solutions of the 2N-body problem

     Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    International Meeting on Celestial Mechanics
    Presentation's date: 2005-09
    Presentation of work at congresses

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    Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional 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: 2005-09-15
    Presentation of work at congresses

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    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. 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 non-regular 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: 2005-12
    Journal article

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    We consider a non-autonomous 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 three-dimensional elliptic restricted three-body problem for arbitrary values of the masses of the primaries.

  • The global flow of the parabolic restricted three-body problem

     Cors Iglesias, Josep Maria; Llibre Saló, Jaume
    Celestial mechanics and dynamical astronomy
    Date of publication: 2004-09
    Journal article

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    We have two mass points of equal masses m 1=m 2 > 0 moving under Newton¿s law of attraction in a non-collision 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 three-body 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: 2004-10
    Journal article

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    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.

  • 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: 2004-06
    Presentation of work at congresses

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    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.

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    Coorbital periodic orbits in the three body problem  Open access

     Cors Iglesias, Josep Maria; Hall, G.R.
    SIAM journal on applied mathematics
    Date of publication: 2003-05
    Journal article

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    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 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 2006-2007

     Cors Iglesias, Josep Maria; Freixas Bosch, Josep; Rossell Garriga, Josep Maria
    Date of publication: 2003-10
    Book

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  • The planar restricted parabolic 3-body problem

     Cors Iglesias, Josep Maria; Alvarez, Martha; Delgado, Joaquín
    International Conference of Differential Equations
    Presentation's date: 2003-07-22
    Presentation of work at congresses

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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: 2003-09
    Presentation of work at congresses

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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: 2002-06-06
    Presentation of work at congresses

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  • Exchange and capture orbits in the planar restricted parabolic 3-body problem

     Alvarez, Martha; Delgado, Joaquín; Cors Iglesias, Josep Maria
    International Symposium on Hamiltonian Systems and Celestial Mechanics
    Presentation's date: 2001-04
    Presentation of work at congresses

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    Two 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 rotating-pulsating 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
    Participation in a competitive project

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  • Periodic solutions in the spatial elliptic restricted three-body problem

     Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    Physica. D, Nonlinear phenomena
    Date of publication: 2001-06
    Journal article

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    We show the existence of a new class of periodic orbits in the three-dimensional elliptic restricted three-body 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.

  • Anàlisi, disseny i control de sistemes no lineals amb aplicacions als sistemes mecànics dissipatius. UPC-PR99-08

     Cors Iglesias, Josep Maria; Rossell Garriga, Josep Maria; Pérez Mañosas, Antonio
    Participation in a competitive project

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  • Periodic solution in the spatial elliptic restricted three-body problem

     Cors Iglesias, Josep Maria; Pinyol Pérez, Conxita; Soler Villanueva, Jaume
    International Conference on Differential Equations
    Presentation's date: 1999-08-03
    Presentation of work at congresses

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  • Slow chads in the system of co-orbiting saturn satelites

     Cors Iglesias, Josep Maria; Hall, G.R.; Koiller, J.
    Date: 1999-04
    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: 1998-12-07
    Presentation of work at congresses

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  • An approach to the problem of saturn's coorbiting satelites

     Cors Iglesias, Josep Maria; Hall, G.R.
    Date: 1998-09
    Report

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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: 1997-06-26
    Presentation of work at congresses

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  • Qualitative study of the hyperbolic colliston restricted three-body problem

     Cors Iglesias, Josep Maria; Llibre Saló, Jaume
    Nonlinearity
    Date of publication: 1996-12
    Journal article

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    We 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 three-body problem consists in describing the motion of . Our main result is the characterization of the global flow of this problem.