Implantació d’Anglès Tècnic en Cicles Formatius de Grau Mig de la Família d’Instal·lació i Manteniment.

Donada la creixent necessitat d’un mercat laboral integrat a la Unió Europea (UE), la llengua anglesa esdevé fonamental per als alumnes dels cicles formatius, tant de grau mig com de grau superior. És important, per tant, l’adaptació dels currículums del cicles per tal d’integrar en els citats mòduls formatius la llengua anglesa. A partir del proper curs 2012-2013, tots els cicles formatius de grau mig tant d’Instal·lacions de Producció de Calor, com d’Instal·lacions Frigorífiques i de Climatització, han d’incorporar l’anglès tècnic com a mòdul professional. Per tant, sorgeix la necessitat d’establir la programació d’aquest nou mòdul professional dintre del cicle: Anglès Tècnic

The potential of discs from a "mean Green function"

By using various properties of the complete elliptic integrals, we have derived an alternative expression for the gravitational potential of axially symmetric bodies, which is free of singular kernel in contrast with the classical form. This is mainly a radial integral of the local surface density weighted by a regular "mean Green function" which depends explicitly on the body's vertical thickness. Rigorously, this result stands for a wide variety of configurations, as soon as the density structure is vertically homogeneous. Nevertheless, the sensitivity to vertical stratification | the Gaussian profile has been considered | appears weak provided that the surface density is conserved. For bodies with small aspect ratio (i.e. geometrically thin discs), a first-order Taylor expansion furnishes an excellent approximation for this mean Green function, the absolute error being of the fourth order in the aspect ratio. This formula is therefore well suited to studying the structure of self-gravitating discs and rings in the spirit of the "standard model of thin discs" where the vertical structure is often ignored, but it remains accurate for discs and tori of finite thickness. This approximation which perfectly saves the properties of Newton's law everywhere (in particular at large separations), is also very useful for dynamical studies where the body is just a source of gravity acting on external test particles.Comment: Accepted for publication in MNRAS, 11 page

The First Festschrift Dedicated to Jules Verne

Sometimes chance leads us down paths that we did not intend to travel, or perhaps we did without realizing it. If, during the Second World War, a good protestant minister had not welcomed Bernard Frank, if later he had not invited him to give a lecture on Jules Verne in a Swiss village where Jean-Michel Margot lived, if Jean-Michel had not attended, perhaps he would not have bought a biography of Jules Verne and asked its author, Bernard Frank, to sign it for him. And what's next? Probably Jean-Michel would not have been so attracted to Verne and would not have started his incredible collection..

n-Dimensional congruent lattices using necklaces

This work introduces the n-dimensional congruent lattices using necklaces, a general methodology to generate uniform distributions in multidimensional modular spaces. The formulation presented in this manuscript constitutes the mathematical foundation of the most used satellite constellation designs, including Walker Constellations, and Lattice and Necklace Flower Constellations. These constellation design models are based on Number Theory and allow to obtain distributions that have some interesting properties of uniformity and large number of symmetries. This work includes the complete formulation of the methodology, proofs for existence and uniqueness of the distribution definitions, and several theorems that focus on the counting possibilities of design for the most common cases of study

Station-keeping for lattice-preserving Flower Constellations

2D-Lattice Flower Constellations present interesting dynamical features that al- low us to explore a wide range of potential applications. Their particular initial distribution (lattice) and their symmetries disappear when some perturbations are considered, such as the J2 effect. The new lattice-preserving Flower Constella- tions maintain over long periods of time the initial distribution and its symmetries under the J2 perturbation, which is known as relative station-keeping. This paper deals with the study of the required velocity change that must be applied to the satellites of the constellation to have an absolute station-keeping

Time distributions in satellite constellation design

The aim of the time distribution methodology presented in this paper is to generate constellations whose satellites share a set of relative trajectories in a given time, and maintain that property over time without orbit corrections. The model takes into account a series of orbital perturbations such as the gravitational potential of the Earth, the atmospheric drag, the Sun and the Moon as disturbing third bodies and the solar radiation pressure. These perturbations are included in the design process of the constellation. Moreover, the whole methodology allows to design constellations with multiple relative trajectories that can be distributed in a minimum number of inertial orbits

4D Lattice Flower Constellations

4D Lattice Flower Constellations is a new constellation design framework, based on the previous 2D and 3D Lattice theories of Flower Constellations, that focus on the generation of constellations whose satellites can have different semi-major axis and still present a constellation structure that is maintained during the dynamic of the system. This situation can arise when dealing with satellites with very different instruments, or when it is of interest to coordinate two different constellations. In that sense, 4D Lattice Flower Constellations constitutes the most general representation of the Flower Constellation formulation. In addition, the effects of the J2 perturbation are taken into account in order to generate distributions that maintain their initial design configuration under this perturbation for longer periods of time with a low fuel budget. Finally, examples of application are presented, showing the possibilities in satellite constellation design of this new approach

2D Necklace Flower Constellations

The 2D Necklace Flower Constellation theory is a new design framework based on the 2D Lattice Flower Constellations that allows to expand the possibilities of design while maintaining the number of satellites in the configuration. The methodology presented is a generalization of the 2D Lattice design, where the concept of necklace is introduced in the formulation. This allows to assess the problem of building a constellation in orbit, or the study of the reconfiguration possibilities in a constellation. Moreover, this work includes three counting theorems that allow to know beforehand the number of possible configurations that the theory can provide. This new formulation is especially suited for design and optimization techniques

Orbital analysis in the gravitational potential of elongated asteroids

This work studies the motion around irregular elongated asteroids through two approaches. Firstly, it revisits the dipole-segment model, identifying families of periodic orbits for asymmetric mass distribution. Additionally, a new model incorporating variable density for elongated asteroids is introduced and compared to the dipole-segment model. Several families of periodic orbits have been found through continuation of planar orbits and out-of-plane bifurcation processes, obtaining results in agreement with previous studies about the dynamics around irregular asteroids. This highlights the relevance of simple mathematical models in studying asteroid dynamics and the importance of accounting for density and geometric properties. Although the families of periodic orbits studied in this work are not comprehensively sampled, they constitute an example of the variety of orbits that can be followed by a particle orbiting the asteroid, helping us to better understand the dynamics around these elongated bodies

Corrections on repeating ground-track orbits and their applications in satellite constellation design

The aim of the constellation design model shown in this paper is to generate constellations whose satellites share the same ground-track in a given time, making all the satellites pass over the same points of the Earth surface. The model takes into account a series of orbital perturbations such as the gravitational potential of the Earth, the atmospheric drag, the Sun and the Moon as disturbing third bodies or the solar radiation pressure. It also includes a new numerical method that improves the repeating ground-track property of any given satellite subjected to these perturbations. Moreover, the whole model allows to design constellations with multiple tracks that can be distributed in a minimum number of inertial orbits