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Articles, 10 records found
Articles 10 records found  
1.
31 p, 10.1 MB Trapezoid central configurations / Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez-Chavela, Ernesto (UAM-Iztapalapa(México). Departamento de Matemáticas)
We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. [...]
2019 - 10.1016/j.amc.2018.10.066
Applied Mathematics and Computation, Vol. 346 (April 2019) , p. 127-142  
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2.
33 p, 10.7 MB Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances / Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
2018 - 10.3934/dcdsb.2018101
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 6 (Aug. 2018) , p. 2299-2337  
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3.
8 p, 285.3 KB A Four-body convex central configuration with perpendicular diagonals is necessarily a kite / Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Roberts, Gareth E. (College of the Holy Cross. Department of Mathematics and Computer Science)
We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.
2018 - 10.1007/s12346-017-0238-z
Qualitative theory of dynamical systems, Vol. 17, issue 2 (Jul. 2018) , p. 367-374  
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4.
23 p, 689.0 KB Periodic motion in perturbed elliptic oscillators revisited / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We analytically study the Hamiltonian system in R^4 with Hamiltonian H= 12 (p_x^2 p_y^2) 12 (_1^2 x^2 _2^2 y^2)- V_1(x,y) being (a) V_1(x,y)=-(xy^2 ax^3) and (b) V_1(x,y)=-(x^2y ax^3) with aR, where is a small parameter and _1 and _2 are the unperturbed frequencies of the oscillations along the x and y axis, respectively. [...]
2016 - 10.1007/s10509-016-2927-5
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 361:348 (2016) , p. 1-8  
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5.
50 p, 625.7 KB Central configurations of the 4-body problem with masses m_1=m_2>m_3=m_4=m>0 and m small / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we give a complete description of the families of central configurations of the planar 4–body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an analytical proof that this particular 4–body problem has exactly 34 different classes of central configurations. [...]
2014 - 10.1016/j.amc.2014.07.109
Applied Mathematics and Computation, Vol. 246 (2014) , p. 121-147  
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6.
24 p, 448.9 KB Spatial bi-stacked central configurations formed by two dual regular polyhedra / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez-Chavela, Ernesto (UAM-Iztapalapa(México). Departamento de Matemáticas)
In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, and the other one consisting of twenty masses at the vertices of a regular dodecahedron and twelve masses at the vertices of a regular icosahedron. [...]
2014 - 10.1016/j.jmaa.2013.12.015
Journal of Mathematical Analysis and Applications, Vol. 413 Núm. 2 (2014) , p. 648-659  
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7.
14 p, 382.5 KB Double-antiprism central configurations of the 3n-body problem / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study numerically a new type of central configurations of the 3n–body problem with equal masses which consist of three n–gons contained in three planes z = 0 and z = ±β 6= 0. The n–gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. [...]
2013 - 10.1007/s12346-012-0076-y
Qualitative Theory of Dynamical Systems, Vol. 12 (2013) , p. 11-24  
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8.
12 p, 376.4 KB On the existence of bi-pyramidal central configurations of the n 2-body problem with an n-gon base / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we prove the existence of central configurations of the n + 2–body problem where n equal masses are located at the vertices of a regular n–gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n–gon passing through its center. [...]
2013 - 10.3934/dcds.2013.33.1049
Discrete and Continuous Dynamical Systems. Series A, Vol. 33 Núm. 3 (2013) , p. 1049-1060  
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9.
22 p, 447.3 KB On the central configurations of the planar (1 3)-body problem / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Matemàtica Aplicada III) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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 different classes of central configurations depending on the mutual distances between the infinitesimals masses. [...]
2011 - 10.1007/s10569-010-9316-0
Celestial Mechanics & Dynamical Astronomy. An International Journal of Space Dynamics, Vol. 109 Núm. 1 (2011) , p. 27-43  
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10.
33 p, 6.0 MB Bifurcation of relative equilibria of the (1 3)-body problem / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Matemàtica Aplicada III) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Moeckel, Richard (University of Minnesota. School of Mathematics)
We study the relative equilibria of the limit case of the planar Newtonian 4-body problem when three masses tend to zero, the so-called (1 3)-body problem. Depending on the values of the infinitesimal masses the number of relative equilibria varies from ten to fourteen. [...]
2015
SIAM Journal on Mathematical Analysis, Vol. 47 Núm. 2 (2015) , p. 1377-1404  
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