Open Access
Chaos in the libration motion of an asymmetric non-rigid spacecraft
(2004) Iñarrea, Manuel; Lanchares, Víctor; Palacián Subiela, Jesús Francisco; Pascual, Ana Isabel; Salas, José Pablo; Yanguas Sayas, Patricia; Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Matemáticas; Gobierno de Navarra / Nafarroako Gobernua
We study the libration motion dynamics of an asymmetric spacecraft in circular orbit under the influence of a gravity gradient torque
Open Access
Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
(Springer, 2018) Carrasco, Dante; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática
We study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.
Open Access
Bright fireballs recorded along February 2021 in the framework of the Southwestern Europe Meteor Network
(MeteorNews, 2021) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
This work focuses on the analysis of some of the brightest bolides recorded along February 2021 by the meteorobserving stations operating in the framework of the Southwestern Europe Meteor Network (SWEMN). Some of them were produced by meteoroids belonging to recently discovered and poorly-known streams. The absolute magnitude of these fireballs, which were observed over the Iberian Peninsula, ranged between ±7 and ±10. The emission spectra produced by some of these events are also presented and discussed.
Open Access
Extension of Delaunay normalisation for arbitrary powers of the radial distance
(Elsevier, 2025-01-01) Lanchares Sánchez, Ernesto; Palacián Subiela, Jesús Francisco; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
In the framework of perturbed Keplerian systems we deal with the Delaunay normalisation of a wide class of perturbations such that the radial distance is raised to an arbitrary real number ϒ. The averaged function is expressed in terms of the Gauss hypergeometric function 2F1 whereas the associated generating function is the so called Appell hypergeometric function F1. The Gauss hypergeometric function related to the average depends on the eccentricity, e, whereas the Appell function depends additionally on the eccentric anomaly, E, and both special functions are properly defined and evaluated for all e Є [0,1) and E Є [-ꙥ ꙥ]. We analyse when the functions we determine can be extended to e=1. When the exponent of the radial distance is an integer, the usual values of the averaged and generating functions are recovered.
Open Access
Analysis of remarkable bolides observed between June and July 2022 in the framework of the Southwestern EuropeMeteor Network
(MeteorNews, 2022) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Tosar, Borja; Gómez-Hernández, A.; Gómez-Martínez, Juan; García, A.; Aimee, A. I.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
Some of the bright bolides spotted in the framework of the Southwestern Europe Meteor Network from June to July 2022 are discussed here. These were observed from Spain. Their absolute magnitude ranges from –6 to –11. Fireballs included in this work were generated by different sources: the sporadic background, major meteoroid streams, and poorly known streams.
Open Access
Invariant tori of rectilinear type in the spatial three-body problem
(Elsevier, 2024) Palacián Subiela, Jesús Francisco; Sayas Bordonaba, Flora; Yanguas Sayas, Patricia; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
In the context of the spatial three-body problem and KAM theory, specifically in the regime where the Hamiltonian function is split as the sum of two Keplerian terms plus a small perturbation, we deal with quasi-periodic motions of the three bodies such that two of the three particles (the so-called inner bodies) describe near-collision orbits. More precisely the inner bodies never collide, but they follow orbits that are bounded straight lines or close to straight lines. The motion of the inner bodies occurs either near the axis that is perpendicular to the invariable plane (i.e. the fixed plane orthogonal to the angular momentum vector that passes through the centre of mass of the system) or near the invariable plane. The outer particle’s trajectory has an eccentricity varying between zero and a value that is upper bounded by eM 2 < 1 and lies near the invariable plane. The three bodies’ orbits fill in invariant 5-tori and when the inner particles move in an axis perpendicular to the invariable plane, they correspond to new solutions of the three-body problem. Our approach consists in a combination of a regularisation procedure with the construction of various reduced spaces and the explicit determination of sets of symplectic coordinates. The various reduced spaces we build depend on what symmetries are taken into consideration for the reduction. Moreover we apply an iso-energetic theorem by Han, Li and Yi on the persistence of quasi-periodic solutions for Hamiltonian systems with high-order proper degeneracy. All these elements allow us to calculate explicitly the torsions for the possible combinations that the three particles’ motions can achieve
Open Access
On the nonlinear stability of the triangular points in the circular spatial restricted three-body problem
(Pleiades Publishing, 2020) Cárcamo Díaz, Daniela Jacqueline; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
The well-known problem of the nonlinear stability of L4 and L5 in the circular spatial restricted three-body problem is revisited. Some new results in the light of the concept of Lie (formal) stability are presented. In particular, we provide stability and asymptotic estimates for three specific values of the mass ratio that remained uncovered. Moreover, in many cases we improve the estimates found in the literature.
Open Access
On co-orbital quasi-periodic motion in the three-body problem
(Society for Industrial and Applied Mathematics (SIAM), 2019) Cors, Josep Maria; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 4-tori related to the co-orbital motion of two small moons about a large planet where the moons move in nearly circular orbits with almost equal radii. The approach is based on a combination of normal form and symplectic reduction theories and the application of a KAM theorem for high-order degenerate systems. To accomplish our results we need to expand the Hamiltonian of the three-body problem as a perturbation of two uncoupled Kepler problems. This approximation is valid in the region of phase space where co-orbital solutions occur.
Open Access
Magnetic confinement of a neutral atom in a double-wire waveguide: a nonlinear dynamics approach
(Elsevier, 2021) Salas, José Pablo; Iñarrea, Manuel; Lanchares, Víctor; Palacián Subiela, Jesús Francisco; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Estadística, Informática y Matemáticas
In this paper we focus on the classical dynamics of a neutral atom trapped in a doublewire waveguide in the presence of two uniform bias fields. Because the trapping region takes place in a plane perpendicular to the (parallel) wires, the dynamics is governed by a two-degrees of freedom Hamiltonian where, besides the energy, the two bias fields are the relevant system’s parameters. An exhaustive study of the critical points of the potential energy surface, their stability and bifurcations is carried out, so that, two different trapping regions are characterized. The dynamics in each of these regions is studied by applying classical perturbation theory, which provides an integrable approximation of the original Hamiltonian. The dynamics arising from this normalized Hamiltonian (stability of the equilibrium points, their bifurcations and the phase flow evolution) is then analyzed in a convenient set of phase variables. Poincaré surfaces of section to describe the structure and evolution of the phase space governed by the full Hamiltonian are also used. A complete agreement between the descriptions of the dynamics provided by the perturbation theory and the numerical studies is obtained.
Open Access
Analysis of bright bolides recorded between October and November 2022 by the Southwestern Europe Meteor Network
(MeteorNews, 2023) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Tosar, Borja; Gómez-Hernández, A.; Gómez-Martínez, Juan; García, Antonio; Aimee, A. I.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
We present in this work the analysis of some of the bright fireballs spotted in the framework of the Southwestern Europe Meteor Network (SWEMN) between October and November 2022. They have been observed from the Iberian Peninsula and had a maximum brightness ranging from mag. –7 to mag. –15. Most meteors included in this report were linked to the sporadic background and also to the Southern Taurids.