Gauge transformations for higher-order lagrangians

Noether's symmetry transformations for higher-order lagrangians are studied. A characterization of these transformations is presented, which is useful to find gauge transformations for higher-order singular lagrangians. The case of second-order lagrangians is studied in detail. Some examples that illustrate our results are given; in particular, for the lagrangian of a relativistic particle with curvature, lagrangian gauge transformations are obtained, though there are no hamiltonian gauge generators for them.Comment: 22 pages, LaTe

Structural aspects of Hamilton-Jacobi theory

In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (`slicing vector fields') on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.Comment: 26 pages. Minor changes (some minor mistakes are corrected

Estimació de construccions compromeses per la presència de coves en el litoral del sud i llevant de Mallorca mitjançant l’ús de Sistemes d’Informació Geogràfica (SIGs)

[cat] S’exposen els resultats estimats de l’extensió de construccions (habitatges) i infraestructures construïdes sobre quatre cavitats càrstiques a la franja litoral del Sud i Llevant de Mallorca a partir de l’ús de Sistemes d’Informació Geogràfica (SIGs). L’estudi s’ha basat en l’anàlisi cartogràfic en el que s’ha contrastat la cartografia existent del recorregut de les coves, el mapa topogràfic digital a escala 1/5.000, diverses col·leccions de fotografies aèries i la cartografia digital del cadastre. La informació manejada es troba disponible al visor cartogràfic del Servei d’Informació Territorial de les Illes Balears S.A. i es pot visualitzar a qualsevol programa de SIG. La cartografia corresponent al recorregut de les cavitats es troba a les publicacions de la revista Endins, també disponibles a internet. Els resultat es una estimació dels metres quadrats construïts sobre les coves. D’aquesta manera s’ofereix una informació que podria esser una eina de consulta per a la presa de decisions i contribuir a la sostenibilitat de la zona costanera d’acord amb una concepció integrada de les àrees costeres i marines.[eng] This work exposes the estimated results of the built area (homes and infrastructures) above four karstic caves located at the coastal fringe in the South and East of the Mallorca Island using Geographical Information Systems (GIS). The study has been based on the analysis of the cartography of the path/extension of the caves, 1/5.000 scale topographic maps, many collections of digital aerial photography and the cartography of the cadastre. The information managed is available in the map viewer of the Geographical Information Service of the Balearic Islands and can be displayed in any GIS program. Cartography of the paths of the caves are in the issues of Endins Journal, also available in internet. The result is an estimation of the square meters built above the caves. In this way, we offer a kind of information that could be a decision support tool to contribute to the sustainability of the coastal zone according with the concept of integrity of coastal and marine areas

Mineralogical and Sedimentological Characterization of the Clay-Rich Sediments from Ases Cave (Cova Dets Ases, Mallorca, Spain): Origin and Classification

The Mallorca coastal caves present large amounts of speleothems that have been studied for decades. However, the sedimentary deposits also present in these cases have not been given the same attention. This work is the first study entirely focused on these deposits, specifically the ones found in the Ases cave. These deposits are formed by clay minerals (illitic phases, kaolinite, smectite, and chlorite), calcite and quartz, and minor proportions of dolomite, albite, orthoclase, hematite, and goethite. The grain size and the electron microscopy studies suggested the presence of different sedimentation processes (bedrock degradation, creep or saltation, and suspension) and different origins (authigenic and detrital origins) for the different sediments. Based on these differences, two types of deposits were characterized: autochthonous and allochthonous deposits. The first ones are located on the floor of chambers and corridors in subaqueous zones, indicating the stability of the mixing zone (and therefore the sea level) over time. The second ones appear filling voids on the walls and the ceiling in the terrestrial zone, evidencing the filling of the cavity in the presence of water (during a wet period). These results are very important to complete the understanding of the caves and their evolution and support the relevance of these materials in paleoenvironmental studies

Illustration, re-enactment, citizenship and heritage of contemporary conflict: the case of the Ebro (1938)

Historical illustrations give us hypothetical visual reconstructions of the past, which contribute to their interpretation, knowledge, and understanding. The progress of software for the design and production of images has optimized the possibilities of generating models of educational and understandable illustrations of spaces, facts, and concepts of the past. At the same time, promoting historical recreation activities allows us to obtain photographic and moving images of a historical nature, which can be integrated into image processing software. This paper describes the experience of the DIDPATRI group (Heritage Education, comprehensive museography and new technologies) the University of Barcelona with the Battle of the Ebro (Spanish Civil War, 1938), concerning the design of models/educational illustrations of the conflict. The developed actions show that, with well-defined criteria, support for recreation, and basic but highly educational software that is understandable and replicable, iconographic models can be obtained at a reasonable cost. The final result provides us with the possibility to understand the past in greater detail. The heritage of the conflict gives us the possibility to reflect, thereby directly affecting the formation of quality citizenship

Forgotten Pilots, Airfields and Aircraft: A Transdisciplinary Approach to the Memory of the Republican Air Force During the Spanish Civil War (1936-39)

As the adage goes, 'History is written by the winners', and the Spanish Civil War (1936-39) is a example of how difficult it is to revert this process. Franco's regime (1939-75) developed a range of narratives focused on a) the justification of the military rebellion against the democratically elected Second Republic government, b) the 'damnatio memoriae' of the Republican armed forces and c) the development of a collective guilt about the war. The transition from fascist dictatorship to democracy did not contest Francoist official discourse, and forged a 'pact of oblivion' based on the idea that Spanish society should look to the future and forget about the conflict: from personal memories to cultural heritage. One of the victims of this process of targeted forgetfulness was the Republican Air Force because it was an uncomfortable thorn in Francoist narratives. If the Republic was immersed in chaos and its army non-existent, then how did it manage to contest the skies against the most modern German and Italian aircraft? This work describes the activities developed by a long-term public archaeology project designed to rediscover the memory of the people that formed the Republican Air Force. This multifaceted initiative explored the materiality of air warfare through a combination of battlefield archaeology, educational research, museum exhibitions and community engagement. The results presented here are an example of how community based archaeology projects can promote new critical narratives and rediscover silenced voices even after decades of heavily biased official history

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems

The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered