Papers by Josep J. Masdemont
World scientific monograph series in mathematics, Feb 1, 2001
WORLD SCIENTIFIC eBooks, Feb 1, 2001
Monthly Notices of the Royal Astronomical Society, Mar 21, 2009
In this paper we present building blocks which can explain the formation and properties both of s... more In this paper we present building blocks which can explain the formation and properties both of spirals and of inner and outer rings in barred galaxies. We first briefly summarize the main results of the full theoretical description we have given elsewhere, presenting them in a more physical way, aimed to an understanding without the requirement of extended knowledge of dynamical systems or of orbital structure. We introduce in this manner the notion of manifolds, which can be thought of as tubes guiding the orbits. The dynamics of these manifolds can govern the properties of spirals and of inner and outer rings in barred galaxies. We find that the bar strength affects how unstable the L 1 and L 2 Lagrangian points are, the motion within the manifold tubes and the time necessary for particles in a manifold to make a complete turn around the galactic centre. We also show that the strength of the bar, or, to be more precise, of the non-axisymmetric forcing at and somewhat beyond the corotation region, determines the resulting morphology. Thus, less strong bars give rise to R 1 rings or pseudo-rings, while stronger bars drive R 2 , R 1 R 2 and spiral morphologies. We examine the morphology as a function of the main parameters of the bar and present descriptive two-dimensional plots to that avail. We also derive how the manifold morphologies and properties are modified if the L 1 and L 2 Lagrangian points become stable. Finally, we discuss how dissipation affects the manifold properties and compare the manifolds in gas like and in stellar cases. Comparison with observations as well as clear predictions to be tested by observations will be given in an accompanying paper.
World scientific monograph series in mathematics, 2001
Page 1. orld Scientific Monograph Series i Mathematics - Vol. 2 Mission Design Near Libration Poi... more Page 1. orld Scientific Monograph Series i Mathematics - Vol. 2 Mission Design Near Libration Points Vol. I Fundamentals: The Case of Collinear Libration Points '. Gómez . Llibre . Martínez i f~< ' . Simo World Scientific Page 2. Page 3. ...
A new approach is proposed for the systematic detection and refinement of natural connections bet... more A new approach is proposed for the systematic detection and refinement of natural connections between the libration points eml1,2 of the Earth-Moon system and sel1,2 of the Sun-Earth system. It makes use of the Quasi-Bicircular Problem, a coherent periodic four-body dynamical model of the Sun-Earth-Moon system. The dynamics about the libration points are described by high-order periodic semi-analytical expansions obtained via the parameterization method. In their domain of convergence, such series directly yield initial conditions about the departure libration point. They also allow to estimate the distance between any state along the trajectories and the set of staging orbits (center manifold) at the targeted libration point. The potential connections can then be located and refined in the parameterization space. The complete orbit-to-orbit transfer trajectories are finally transposed in a higher-fidelity ephemeris model and the accordance between both models is discussed
World scientific monograph series in mathematics, Feb 1, 2001
In this paper we consider the attitude synchronization problem for a swarm of spacecrafts flying ... more In this paper we consider the attitude synchronization problem for a swarm of spacecrafts flying in formation. Starting from previous works on consensus dynamics, we construct a distributed attitude control law and derive analytically sufficient conditions for the formation to converge asymptotically towards a synchronized, non-accelerating state (possibly defined a priori). Moreover, motivated by the results obtained on a particular consensus model, first introduced by F. Cucker and S. Smale to modellize the translational dynamics of flocks, we numerically explore the dependence of the convergence process on the dimension of the formation and the relative initial conditions of the spacecrafts. Finally, we generalize the class of weights defined by the previous authors in order to dampen the aforementioned effects, thus making our control law suitable for very large formations.
The Terrestrial Planet Finder (TPF) is one of the center pieces of NASA's Origins Program. Th... more The Terrestrial Planet Finder (TPF) is one of the center pieces of NASA's Origins Program. The goal of TPF is to identify terrestrial planets around stars nearby the Sun. For this purpose, a space-based interferometer with a baseline of approximately 100 m is required. To achieve such a large baseline, a distributed system of five spacecraft flying in formation is an efficient approach. Since the TPF instruments need a cold and stable environment, a halo orbit about 4 is ideal. First, we describe formation flight near the Lagrange point is feasible for the TPF mission. Second, we propose a novel approach for human servicing of Lagrange point missions by placing a Lunar service station in an Lunar L1 orbit. The TPF spacecraft can be transferred to a Lunar L1 orbit in a few days and requires relatively little delta-V. This efficient transfer results from the system of low energy pathways connecting the entire Solar System generated by the Lagrange points. The halo orbits are the portals of this Interplanetary . A Lunar Station at the L,portal, in addition to servicing missions from the Sun-Earth Lagrange points, may play an even more important role in the future development of space.
The aim of this paper is to study the capture of small Near Earth Objects (NEOs) into the Sun-Ear... more 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.
WORLD SCIENTIFIC eBooks, 2001
Quasi-periodic solutions near the equilateral points of the Earth-Moon system global description ... more Quasi-periodic solutions near the equilateral points of the Earth-Moon system global description of the orbits near the "L1" point of the Earth-Sun system in the RTBP quasi-periodic halo orbits transfer from the Earth to a halo orbit appendices - the JPL model, references systems and equations of motion, the model equations near the equilateral points in the Earth-Moon system, transfer between halo orbits of the RTBP.
American Astronautical Society eBooks, Jul 30, 2001
The invariant manifold structures of the collinear libration points for the spatial restricted th... more The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as a "Petit Grand Tour" of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.
WORLD SCIENTIFIC eBooks, 2001
Global stability zones around the triangular libration points the normal form around L5 in the th... more Global stability zones around the triangular libration points the normal form around L5 in the three-dimensional RTBP normal form of the bicircular model and related topics the quasi-periodic model nominal paths and stability properties transfer to orbits in a vicinity of the Lagrangian points. Appendices: global stability zones around the triangular libration points in the elliptic RTBP Fourier analysis geometrical bounds for the dynamics - codimension 1 manifolds.
We propose a theory to explain the formation of spiral arms and of all types of outer rings in ba... more We propose a theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies, extending and applying the technique used in celestial mechanics to compute transfer orbits. Thus, our theory is based on the chaotic orbital motion driven by the invariant manifolds associated to the periodic orbits around the hyperbolic equilibrium points. In particular, spiral arms and outer rings are related to the presence of heteroclinic or homoclinic orbits. Thus, R 1 rings are associated to the presence of heteroclinic orbits, while R 1 R 2 rings are associated to the presence of homoclinic orbits. Spiral arms and R 2 rings, however, appear when there exist neither heteroclinic nor homoclinic orbits. We examine the parameter space of three realistic, yet simple, barred galaxy models and discuss the formation of the different morphologies according to the properties of the galaxy model. The different morphologies arise from differences in the dynamical parameters of the galaxy.
World scientific monograph series in mathematics, Feb 1, 2001
We propose a theory to explain the formation of both spirals and rings in barred galaxies using a... more We propose a theory to explain the formation of both spirals and rings in barred galaxies using a common dynamical framework. It is based on the orbital motion driven by the unstable equilibrium points of the rotating bar potential. Thus, spirals, rings and pseudo-rings are related to the invariant manifolds associated to the periodic orbits around these equilibrium points. We examine the parameter space of three barred galaxy models and discuss the formation of the different morphological structures according to the properties of the bar model. We also study the influence of the shape of the rotation curve in the outer parts, by making families of models with rising, flat or falling rotation curves in the outer parts. The differences between spiral and ringed structures arise from differences in the dynamical parameters of the host galaxies.
WORLD SCIENTIFIC eBooks, Feb 1, 2001
Simulation of formation flight near Lagrange points for the TPF mission. G Gomez, M Lo, J Masdemo... more Simulation of formation flight near Lagrange points for the TPF mission. G Gomez, M Lo, J Masdemont, K Museth Advances in the Astronautical Sciences, 2002. The TPF Mission (Terrestrial Planet Finder) is one of the centerpieces of the NASA Origins Program. ...
Mathematics, Dec 22, 2022
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
World scientific monograph series in mathematics, 2001
Page 1. orld Scientific Monograph Series i Mathematics - Vol. 2 Mission Design Near Libration Poi... more Page 1. orld Scientific Monograph Series i Mathematics - Vol. 2 Mission Design Near Libration Points Vol. I Fundamentals: The Case of Collinear Libration Points '. Gómez . Llibre . Martínez i f~< ' . Simo World Scientific Page 2. Page 3. ...
Monthly Notices of the Royal Astronomical Society, Jan 27, 2023
We establish a dynamical mechanism to explain the origin of the asymmetry between the arms observ... more We establish a dynamical mechanism to explain the origin of the asymmetry between the arms observed in some barred disk galaxies, where one of the two arms emanating from the bar ends is very well defined, while the second one displays a ragged structure, extending between its ridge and the bar. To this purpose, we study the invariant manifolds associated to the Lyapunov periodic orbits around the unstable equilibrium points at the ends of the bar. Matter from the galaxy center is transported along these manifolds to the periphery, forming this way the spiral arms that emanate from the bar ends. If the mass distribution in the galaxy center is not homogeneous, because of an asymmetric bar with one side stronger than the other, or because of a non-centered bulge, the dynamics about the two unstable Lagrange points at the ends of the bar will not be symmetric as well. One of their invariant manifolds becomes more extended than the other, enclosing a smaller section and the escaping orbits on it are fewer and dispersed in a wider region. The result is a weaker arm, and more ragged than the one at the other end of the bar.
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Papers by Josep J. Masdemont