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  • Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites 2013

     Prado, Antonio F. Bertachini A.; Masdemont Soler, Josep Joaquim; Zanardi, Maria Cecilia; Winter, Silvia Maria Giuliatti; Yokoyama, Tadashi; Gomes, Vivian Martins
    Mathematical problems in engineering
    Date of publication: 2013
    Journal article

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  • The zero, minimum and maximum relative radial accelerations along a family of periodic orbits around L4 and L5 in the Earth-Moon system

     Tipan Salazar, Francisco Javier; Masdemont Soler, Josep Joaquim; Gomez Muntaner, Gerard; Macau, E.E.N.
    International Workshop on Satellite Constellations and Formation Flight
    Presentation's date: 2013-03
    Presentation of work at congresses

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  • Jet Transport propagation of uncertainties for orbits around the Earth

     Pérez, Daniel; Masdemont Soler, Josep Joaquim; Gómez Muntané, Gerard
    International Astronautical Congress
    Presentation's date: 2013-09
    Presentation of work at congresses

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    In this paper we present a tool to study the non-linear propagation of uncertainties for orbits around the Earth. The tool we introduce is known as Jet Transport and allows to propagate full neighborhoods of initial states instead of a single initial state by means of usual numerical integrators. The description of the transported neighborhood is obtained in a semi-analytical way by means of polynomials in 6 variables. These variables correspond to displacements in the phase space from the reference point selected in an orbit as initial condition. The basis of the procedure is a standard numerical integrator of ordinary differential equations (such as a Runge-Kutta or a Taylor method) where the usual arithmetic is replaced by a polynomial arithmetic. In this way, the solution of the variational equations is also obtained up to high order. This methodology is applied to the propagation of satellite trajectories and to the computation of images of uncertainty ellipsoids including high order nonlinear descriptions. The procedure can be specially adapted to the determination of collision probabilities with catalogued space debris or for the end of life analysis of spacecraft in Medium Earth Orbits

  • A note on the dynamics around the Lagrange points of the Earth-Moon system in a complete Solar System model

     Lian, Yijun; Gómez Muntané, Gerard; Masdemont Soler, Josep Joaquim; Tang, Guojian
    International Astronautical Congress
    Presentation's date: 2013-09
    Presentation of work at congresses

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    This paper studies the dynamics of a massless particle around the libration points of the Earth-Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the equilibrium points. For the analysis and computation of the quasi-periodic orbits, a novel iterative algorithm is introduced which is a combination of the multiple shooting method and a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in a complete Solar System model for large time-spans covering most of the relevant Sun-Earth-Moon periods. For the collinear points, the developed approach works well and reveals the strong relevance of the phase space around the equilibrium points in both models. For the triangular points, difficulties appear and an intermediate model (bicircular model, BCM) is introduced to aid the refinement

  • On the cucker-smale flocking model applied to a formation moving in a central force field around the Earth

     Paita, Fabrizio; Gomez Muntaner, Gerard; Masdemont Soler, Josep Joaquim
    International Astronautical Congress
    Presentation's date: 2013-09
    Presentation of work at congresses

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    The Cucker ¿ Smale (CS) flocking model is an interacting particles control system where every particle adjusts its dynamics according to a weighted average between its velocity and those of the other elements of the flock. Under this model, a rigid body configuration can be achieved exponentially fast for suitable initial configurations. Furthermore, as shown by J. Shen, if the dynamics of the formation is driven by the presence of a free willed leader then similar asymptotic results can be obtained. In the present paper we extend the CS control law in the context of a multi ¿ spacecraft system moving around a central body. Some new analytical results are given, as well as the results of the numerical explorations that have been done to evaluate the performances of the control law, with particular attention to its interaction with a central gravitational field. These performances have been evaluated mainly through the use of two indicators: the evolution of the relative spacecrafts distances and the total fuel expended to maintain the formation.

  • Methodology and estimation costs for proximity maneuvering spacecraft formations

     García-Taberner, Laura; Masdemont Soler, Josep Joaquim
    International Workshop on Satellite Constellations and Formation Flight
    Presentation's date: 2013-03
    Presentation of work at congresses

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  • End-of-life disposal of libration point orbit spacecraft

     Olikara, Zubin; Gómez Muntané, Gerard; Masdemont Soler, Josep Joaquim
    International Astronautical Congress
    Presentation's date: 2013-09
    Presentation of work at congresses

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    In this work we investigate end-of-life trajectories for spacecraft in orbit about the Sun-Earth L1 and L2 libration points. A plan for decommission is often re- quired during the mission design process. We study the spacecraft's natural dynamics in both a high- delity model and the circular restricted three-body problem. In particular, we consider the role of the unstable manifold and forbidden regions in determin- ing disposal outcomes. A simple maneuver scheme to prevent returns to the Earth vicinity is also an- alyzed. We include discussion on potential collision orbit schemes.

  • Jet transport propagation of unvertainties for orbits around the Earth

     Pérez-Palau, Daniel; Masdemont Soler, Josep Joaquim; Gómez Muntané, Gerard
    International Meeting on Celestial Mechanics
    Presentation's date: 2013-09
    Presentation of work at congresses

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    In this paper we present a new tool to study the non-linear pro pagation of un- certainties for orbits around the Earth. The tool we introdu ce is known as Jet Transport and allows to numerically propagate full neighbo urhoods of initial states instead of a single initial state with usual integrat ors. The description of the image neighbourhood is obtained in a semi-analytical way by means of polynomials in 6 variables. These variables correspond to d isplacements in the phase space from the reference point selected in an orbit as i nitial condition. The basis of the procedure is a standard numerical integrato r of ordinary differ- ential equations (such as a Runge-Kutta or a Taylor method) w here the usual arithmetic is replaced by a polynomial arithmetic, in this w ay, the solution of the variational equations is obtained up to high order. The m ethod is applied to the propagation of satellite trajectories and to obtain t he images, and high order nonlinear descriptions, of uncertainty ellipsoids. The procedure can be specially adapted to the determination of collision probab ilities with catalogued space debris or for the end of life analysis of spacecraft in M edium Earth Orbits. Joint work with G. G ´omez and J.J. Masdemont

  • Review of the paper: Lagrange-Pizzetti theorem for the quasihomogeneous N-body problem

     Masdemont Soler, Josep Joaquim
    MathSciNet
    Date of publication: 2013
    Journal article

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  • Review of the paper: Instability of the periodic hip-hop orbit in the 2N-body problem with equal masses

     Masdemont Soler, Josep Joaquim
    MathSciNet
    Date of publication: 2013
    Journal article

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  • A note on the dynamics around the Lagrange collinear points of the Earth-Moon system in a complete Solar System model

     Lian, Yijun; Gómez Muntané, Gerard; Masdemont Soler, Josep Joaquim; Tang, Guojian
    Celestial mechanics and dynamical astronomy
    Date of publication: 2013-02
    Journal article

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    In this paper we study the dynamics of a massless particle around the L 1,2 libration points of the Earth¿Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the two collinear equilibrium points. For the analysis and computation of the quasi-periodic orbits, a new iterative algorithm is introduced which is a combination of a multiple shooting method with a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds for the algorithm the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in the Solar System force-field model for large time-spans, that cover most of the relevant Sun¿Earth¿Moon periods.

  • ASTEROID RETRIEVAL MISSIONS ENABLED BY INVARIANT MANIFOLD DYNAMICS

     Masdemont Soler, Josep Joaquim
    Participation in a competitive project

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    Capturing small asteroids into Sun-Earth Lagrangian points for mining purposes  Open access

     Lladó, Neus; Ren, Yuan; Masdemont Soler, Josep Joaquim; Gomez Muntaner, Gerard
    International Astronautical Congress
    Presentation's date: 2012-10-04
    Presentation of work at congresses

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    The aim of this paper is to study the capture of small Near Earth Objects (NEOs) into the Sun-Earth L2 using low-thrust propulsion for mining or science purposes. As it is well known, the vicinity of these points is inside a net of dynamical channels suitable for the transport in the Earth-Moon neighborhood, so different final destinations from here could be easily considered. Asteroids with very small mass and not representing a potential hazard are analyzed. An initial pruning of asteroids is made, considering NEOs with stellar magnitude bigger than 28, which are the smallest available, and NEOs close to the Earth orbit with semi-major axis between 0.85-1.15. Due to the difficult determination of their physical properties, two methods to estimate the asteroid masses are conducted. A procedure to find the low-thrust optimization trajectories has been implemented. The initial seed is obtained integrating forward the equations of motion plus its conjugated equations expressed in cartesian coordinates and applying the Pontryagins maximum principle to obtain the optimal control with a switching function for the thrust. To refine the trajectory a 4 order Runge-Kutta shooting method has been used. The objective function in this study is the fuel consumption. Finally, the capable asteroids to get captured by a low-thrust engine have been listed indicating the main parameters.

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    Detecting invariant manifolds using Lagrangian coherent structures  Open access

     Pérez, Daniel; Gómez Muntané, Gerard; Masdemont Soler, Josep Joaquim
    IAA Conference on Dynamics and Control of Space Systems
    Presentation's date: 2012-03-20
    Presentation of work at congresses

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    Using as reference test model the Planar Circular Restricted Three Body Problem, this paper explores its Lagrangian Coherent Structures, as well as its Hyperbolic Lagrangian Coherent Structures. The purpose is to identify stable and unstable manifolds acting as separatrices between orbits with different qualitative behaviour and, therefore, relevant to the dynamics of the problem. Particular attention is given to the manifolds associated to the collinear libration points and to the practical stability regions around the triangular equilibrium points

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    A note on the dynamics around the L1,2 Lagrange points of the Earth-Moon system in a complete solar system model  Open access

     Tang, Guojian; Gomez Muntaner, Gerard; Masdemont Soler, Josep Joaquim; Yijun, L.
    IAA Conference on Dynamics and Control of Space Systems
    Presentation's date: 2012-03-20
    Presentation of work at congresses

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    The purpose of this paper is the study of the phase space around the collinear libration points L1 and L2 of the Earth–Moon system when the gravitational effects of the remaining bodies of the Solar System are taken into account. In the simplified model defined by the Circular Restricted Three Body Problem (CR3BP), the description of the phase space around these two points has already been done in the past, either using semi-analytical techniques1 or numerical ones.2 When using more realistic models of motion, the refinement of the different kinds of libration point orbits around both points (see G´omez et al.3) has some problems when the time interval used is large. These problems are more evident for the Earth–Moon L2 point due to a 1:2 resonance between the natural frequency of some halo orbits (!h) and the external frequency due to the perturbation of the Sun (!s); in fact !h ' 2!s for some orbits of the halo family of periodic orbits around this point. To analyse more closely this fact, Andreu4 introduced an intermediate model between the CR3BP and the restricted n-body problem, which is the so called Quasi-Bicircular Problem. It is a restricted four body problem in which the three primaries move following a “true” solution of the three body problem along orbits close to circular (the Earth and the Moon around their barycenter, and the Earth-Moon barycenter around the Sun). The description of the different types of orbits in the neighbourhood of L2 is also done in Reference 4 by means of the reduction of the Hamiltonian of the problem to the central manifold. The reduced Hamiltonian is then studied by means of Poincar´e maps at different energy levels.

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    Methodology and estimation costs for proximity maneuvering spacecraft formations in the vicinity of libration points  Open access

     Garcia Taberner, Laura; Masdemont Soler, Josep Joaquim
    International Astronautical Congress
    Presentation's date: 2012-10-04
    Presentation of work at congresses

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    The aim of this paper is to study and provide estimations of the cost of reconfiguration maneuvers in the neighbor- hood of L1 and L2 libration points of the Sun-Earth system. The problem is considered as a function of the parameters of the formation (baseline length, security distances, orientation, reconfiguration time) and simple formulae to evaluate the costs are given.

  • The zero, minimum and maximum relative radial accelerations along a family of periodic orbits around L4 in the Earth-Moon system

     Tipan Salazar, Francisco Javier; Masdemont Soler, Josep Joaquim; Gómez Muntané, Gerard; Macau, E.E.N.; Winter, O.C.
    Workshop de Computaçao Aplicada
    Presentation's date: 2012-11-06
    Presentation of work at congresses

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    Assume a constellations of satellites flighting close a given nominal trajectory around L4 or L5 in the Earth-Moon system in such a way that there is freedom in the selection of the geometry of the constellation. We are interested in to avoid large variations of the mutual distance between the spacecrafts. In this case, the possible existence of regions of zero relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. The goal of this paper is the study of theses regions.

    Constellations of satellites, Zero relative radial acceleration, Earth-Moon.

  • Review of the paper: Preserving multiple first integrals by discrete gradients. Authors: Dahlby, M.; Owren, B.; Yaguchi, T.

     Masdemont Soler, Josep Joaquim
    Zentralblatt MATH
    Date of publication: 2012-11-11
    Journal article

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  • Special section on celestial mechanics and applications 3rd Conference on Nonlinear Science and Complexity 2010 ¿ NSC10

     Gidea, Marian; Masdemont Soler, Josep Joaquim
    Communications in nonlinear science and numerical simulation
    Date of publication: 2012-12
    Journal article

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  • Review of the paper: Polygonal homographic orbits of the curved n-body problem. Author: Diacu, F.

     Masdemont Soler, Josep Joaquim
    MathSciNet
    Date of publication: 2012-12
    Journal article

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  • Computation of analytical solutions of the relative motion about a Keplerian elliptic orbit

     Ren, Yuan; Masdemont Soler, Josep Joaquim; Marcote, Manuel; Gómez, Gerard
    Acta astronautica
    Date of publication: 2012-01
    Journal article

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  • Review of the paper: Lie-Poisson integrators for a rigid satellite on a circular orbit. Authors: Aydin, A.

     Masdemont Soler, Josep Joaquim
    Zentralblatt MATH
    Date of publication: 2012
    Journal article

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  • Two mechanisms of natural transport in the Solar System

     Ren, Yuan; Gomez Muntaner, Gerard; Masdemont Soler, Josep Joaquim; Fantino, Elena
    Communications in nonlinear science and numerical simulation
    Date of publication: 2012-02
    Journal article

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    In this paper, two natural transport mechanisms in Solar System are considered. The first is a short-time transport, and is based on the existence of ‘‘pseudo-heteroclinic’’ connections between libration point orbits of pairs of Sun–planet planar circular restricted three-body problems (PCR3BP). The stable and unstable manifolds associated with the libration point orbits of different Sun–planet PCR3BP systems are computed. Then the intersections between the inner and the outer manifolds of all the consecutive planets in the Solar System are explored. The second mechanism, which is common and qualitatively well understood in two-degrees of freedom Hamiltonian systems, corresponds to a long-time transport, and is the result of the strongly chaotic motion of the minor body in the PCR3BP. In this contribution, we present an analysis of the natural transport in the Solar System based on these two mechanisms. In particular, we discuss the key properties of the natural transport, such as the possibility of transfering between two specified celestial bodies, the type of transport and the time of flight. The final objective is to provide a deeper dynamical insight into the exchange mechanisms of natural material in the Solar System.

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    An adaptive remeshing procedure for proximity maneuvering spacecraft formations  Open access

     Garcia Taberner, Laura; Masdemont Soler, Josep Joaquim
    Mathematical problems in engineering
    Date of publication: 2012
    Journal article

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    We consider a methodology to optimally obtain reconfigurations of spacecraft formations. It is based on the discretization of the time interval in subintervals (called the mesh) and the obtainment of local solutions on them as a result of a variational method. Applied to a libration point orbit scenario, in this work we focus on how to find optimal meshes using an adaptive remeshing procedure and on the determination of the parameter that governs it.

  • Further advances on low-energy lunar impact dynamics

     Alessi, Elisa Maria; Gómez, Gerard; Masdemont Soler, Josep Joaquim
    Communications in nonlinear science and numerical simulation
    Date of publication: 2012-02
    Journal article

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    We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three- Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L2 equilibrium point in the Earth–Moon system. Then we move to the Bicircular Restricted Four- Body Problem to study the effect of the Sun on the distribution of impacts on the Moon’s surface

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    Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites  Open access

     Bertachini A. Prado, Antonio F.; Zanardi, Maria Cecilia; Yokoyama, Tadashi; Giuliatti Winter, Silvia Maria; Masdemont Soler, Josep Joaquim
    Mathematical problems in engineering
    Date of publication: 2012
    Journal article

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  • Modern methodologies in celestial mechanics and mission design

     Masdemont Soler, Josep Joaquim
    Colloquium CRM: Mathematics and Space Sciences
    Presentation's date: 2011-12-14
    Presentation of work at congresses

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  • AstroNet

     Masdemont Soler, Josep Joaquim; Gómez Muntané, Gerard
    Acte de celebració del 15è aniversari de l'Institut d'Estudis Espacials de Catalunya
    Presentation's date: 2011-11-28
    Presentation of work at congresses

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  • Rings, spirals and manifolds

     Athanassoula, Evangelie; Romero Gómez, Mercè; Masdemont Soler, Josep Joaquim
    Memorie della Societá Astronomica Italiana
    Date of publication: 2011
    Journal article

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  • Haar wavelets based approach for quantifying credit portfolio loses

     Masdemont Soler, Josep Joaquim; Ortiz-Gracia, Luís
    Quantitative finance
    Date of publication: 2011
    Journal article

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    This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is particularly suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing the estimation of the VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

  • Review of the paper: orbit determination with the two-body integrals. Authors: Gronchi, G. F.; Dimare, L.; Milani, A.

     Masdemont Soler, Josep Joaquim
    Mathematical reviews
    Date of publication: 2011
    Journal article

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  • Haar Wavelets-Based Methods for Credit Risk Portfolio Modeling

     Ortiz Gracia, Luis
    Defense's date: 2011-11-24
    Department of Applied Mathematics I, Universitat Politècnica de Catalunya
    Theses

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  • Proximity maneuvering of libration point orbit formations using adapted finite element methods  Open access

     Garcia Taberner, Laura
    Defense's date: 2010-02-04
    Universitat Politècnica de Catalunya
    Theses

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    This doctoral dissertation is structured in four chapters as follows. The first chapter contains a summary of formation flying projects that have been taken into consideration since few years ago. We specially focus on the missions that have been planned to be located in a libration point regime. For completeness, this chapter also contains a general state of the art about the main reconfiguration techniques for satellite formations. The main new contributions of the thesis are contained in chapters 2, 3 and 4. Chapter 2 introduces the general methodology that will be considered in all the dissertation. It is based on a discretization in time by means of a finite element approximation, and at the same time, is suitable to incorporate optimal control problems. In this chapter we study the reconfigurations using linearized equations about a nominal Halo orbit minimizing the functional given by the sum of the square of the magnitude of the maneuvers. This functional is not directly related to the fuel consumption, but has good properties concerning minimization and regularity. In chapter 3 we are still working with the linearized model about the nonlinear orbit, but the functional that we optimize, given by the sum of the modulus of the maneuvers, is directly related to fuel consumption. As a consequence, the methodology can be tuned in such a way that, if possible, the user can choose to converge to bang-bang optimal controls (when possible) or to low thrust trajectories in general situations. In this chapter, our objective is not only to study how the reconfigurations can be accomplished. We also consider the problem of obtaining good meshes for our finite element discretization, and up to a certain extent, to decide which is the best mesh for each kind of problem. Finally, in chapter 4, we deal with non-linear and perturbed problems. In a first step we consider reconfigurations in the Restricted Three Body Problem and in a second one with JPL ephemeris. This fact slightly changes the trajectories of the spacecraft with respect to the ones obtained in the previous chapters. To correct for such deviations we design and implement a methodology based on adding small corrective maneuvers on top of the nominal ones. We also study the magnitude of corrective maneuvers that will need to be applied in case of errors in the execution of the nominal ones. Finally, this chapter ends with some other applications that can be performed using the methodology we have developed.

    Aquesta tesi doctoral està estructurada en quatre capítols. El primer capítol comprèn un resum dels projectes de vol en formació que s'han tingut en consideració els últims anys, especialment els que estan planejats de situar-se al voltant dels punts de libració. En aquest capítol també fem un estat de l'art de les principals tècniques de reconfiguració de formacions de satèl•lits. Les principals contribucions noves d'aquesta tesi es troben als capítols 2, 3 i 4. En el capítol 2 introduïm la metodologia general que s'utilitzarà en tota la dissertació. Aquesta metodologia està basada en una discretització del temps usant una aproximació en elements finits, que al mateix temps la fa factible d'incorporar en problemes d'optimització. En aquest capítol es consideren les equacions linealitzades al voltant d'una òrbita Halo. El problema d'optimització minimitza el funcional obtingut per la suma dels quadrats de les maniobres. Encara que aquest funcional no estigui directament relacionat amb el consum de combustible, es comporta bé a l'hora de minimitzar. En el capítol 3 es segueixen utilitzant les equacions linealitzades al voltant de l'òrbita Halo, però ara el funcional que es minimitza és la suma dels mòduls de les maniobres, que està directament relacionat amb el consum de combustible. Com a conseqüència, la metodologia permet que es pugui convergir a controls bang-bang en el cas que sigui possible, o a avanç continu en les altres situacions. En aquest capítol, el nostre objectiu no consisteix només en estudiar com fer les reconfiguracions, sinó que també considerem el problema d'obtenir una bona discretització per al nostre problema d'elements finits, i decidir quina és la millor malla per cada tipus de problema. Finalment, al capítol 4 considerem problemes no lineals i incloem perturbacions. Comencem considerant les reconfiguracions en el problema restringit de tres cossos, per després veure com es comporta usant les efemèrides JPL. Aquests nous models canvien una mica les trajectòries dels satèl•lits respecte les que havíem obtingut en els capítols anteriors. Per corregir aquestes desviacions implementem una metodologia basada en afegir petites correccions a les maniobres que estan donades. També estudiem la magnitud de les maniobres que cal aplicar quan es produeixen errors d'execució en les maniobres nominals. Finalment, aquest capítol acaba amb altres aplicacions que es poden dur a terme usant la metodologia que hem desenvolupat.

     Esta tesis doctoral está estructurada en cuatro capítulos. El primer capítulo contiene un resumen de los proyectos de vuelo en formación que se han tenido en consideración en los últimos años, especialmente aquellos que están planeados de situarse alrededor de los puntos de libración. En este capítulo también se hace un estado del arte de las principales técnicas de reconfiguración de formaciones de satélites.Las principales contribuciones nuevas de esta tesis se encuentran en los capítulos 2, 3 y 4. En el capítulo 2 introducimos la metodología general que se usará en toda la disertación. Esta metodología está basada en una discretización del tiempo usando una aproximación en elementos finitos, que al mismo tiempo la hace factible de incorporar en problemas de optimización. En este capítulo, se consideran las ecuaciones linealizadas alrededor de una órbita Halo. El problema de optimización minimiza el funcional obtenido como la suma de los cuadrados de las maniobras. Aunque este funcional no está directamente relacionado con el consumo de combustible, tiene un buen comportamiento en la minimización.En el capítulo 3 se siguen usando las ecuaciones linealizadas alrededor de la órbita Halo, pero ahora el funcional al minimizar es la suma de los módulos de las maniobras, que está directamente relacionado con el consumo de combustible. Como consecuencia, la metodología permite que se pueda convergir a controles bang-bang en el caso de que sea posible, o a avance continuo en las otras situaciones.En este capítulo, nuestro objetivo no consiste únicamente en estudiar cómo hacer las reconfiguraciones, sino que consideramos el problema de obtener una buena malla para el problema de los elementos finitos, y decidir cuál es la mejor malla para cada tipo de problema.Finalmente, en el capítulo 4 se consideran problemas no lineales y se incluyen perturbaciones. Empezamos considerando las reconfiguraciones en el problema restringido de 3 cuerpos, y luego observamos qué pasa cuando usamos las efemérides JPL. Estos nuevos modelos cambian un poco las trayectorias de los satélites respecto las obtenidas en los capítulos anteriores. Para corregir estas desviaciones, se implementa una metodología basada en añadir pequeñas correcciones a las maniobras dadas. También estudiamos la magnitud de las maniobras que hace falta aplicar cuando se producen errores de ejecución en las maniobras nominales. Para finalizar, este capítulo acaba con otras aplicaciones que se pueden llevar a término con la metodología desarrollada.

  • Modeling rings and spirals in barred galaxies using manifolds: morphology and kinematics

     Masdemont Soler, Josep Joaquim; Athanassoula, Evangelie; Romero Gómez, Mercè; Bosma, A.
    Dynamics and Evolution of Disk Galaxies
    Presentation's date: 2010-06-02
    Presentation of work at congresses

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  • Low-energy impact dynamics in the Earth ¿ Moon system

     Masdemont Soler, Josep Joaquim; Gómez Muntané, Gerard; Alessi, Elisa Maria
    Conference on Nonlinear Science and Complexity
    Presentation's date: 2010-07
    Presentation of work at congresses

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  • Access to the full text
    Spacecraft formations reconfiguration using finite element methodology with adaptive remeshing  Open access

     Masdemont Soler, Josep Joaquim; Garcia Taberner, Laura
    Conference on Nonlinear Science and Complexity
    Presentation's date: 2010-07
    Presentation of work at congresses

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    We present a methodology to compute trajectories for formation °ying recon¯g- uration problems using a methodology based on ¯nite elements: FEFF (Finite Elements for Formation Flying). In this paper we center ourselves on the obtention of optimal meshes using adaptive remeshing. As an application we show how adaptive remeshing is applied to two kinds of recon¯gurations: a class where is known that a bang-bang control is the optimal solution and another class where bang-bang would end up in collision. In the ¯rst case the methodology tends to the optimal bang-bang, while in the second one, tends to a low thrust control. Finally, we update the trajectories obtained with FEFF and adaptive remeshing to the JPL-ephemeris model to test the reliability of the methodology.

  • Review of the paper: Stability and chaos in celestial mechanics. Author: Celletti, Alessandra

     Masdemont Soler, Josep Joaquim
    Zentralblatt MATH
    Date of publication: 2010
    Journal article

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  • A note on libration point orbits, temporary capture and low-energy transfers

     Fantino, Elena; Gómez, Gerard; Masdemont Soler, Josep Joaquim; Ren, Yuan
    Acta astronautica
    Date of publication: 2010-11
    Journal article

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