Unified formalism for the generalized kth-order Hamilton-Jacobi problem

The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.Comment: 9pp. Revised version: Minor corrections done. Second part of our previous work arXiv:1309.2166. arXiv admin note: substantial text overlap with arXiv:1309.216

Comparison of Brans Promethee multicriteria decision method and Promethee modified by authors for the optimization of an erosion control integral plan in Chaco area in Salta province (Argentine)

Chaco area is situated in the Province of Salta at North West of Argentine. The desertification is a big problem. In order to mitigate the problem it is necessary to take into account not only pedologic criteria but the economical, environmental, cultural and sociological criteria. Six sub zones have been established following previous studies. Eight criteria and six alternatives have been introduced in the model. Following the results of the study carried out by a collaborative project between UPM and UCS financed by AECID (1) were established several initial matrix. Brans Promethee multicriteria decision method (MCDM) was applied and the authors modified that method introducing weights like in Electre metho

Contact Lagrangian systems subject to impulsive constraints

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily surface and a rolling sphere on a non-uniform surface, both with dissipation.Comment: 23 page

An Hardware-in-the-Loop Tool for the Design of Complex Mechanical Systems Controllers

In this paper we propose an Hardware-In-the-Loop (HIL) system for industrial drives. The system allows the user to optimize the design of control strategies by emulating complex mechanical applications. In fact, with this approach it is possible to simulate the behavior of the real mechanical system, and therefore to verify a priori the effectiveness of a control strategy and to achieve a rapid prototyping of the mechatronic system. The structure of the system consists of a couple of brushless motor which are connected by a mechanical joint. In one drive the control functions related to a specific application are implemented while the other one is used to replicate the mechanical system model of the application. A modular approach has been selected in order to allow a rapid development of a given application. In particular, a library of components has been implemented both in Simulink and in an IEC61131-3 language

Contact formalism for dissipative mechanical systems on Lie algebroids

In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and Hamiltonian settings through a convenient notion of Legendre transformation. We also discuss the Hamilton-Jacobi problem in this framework and introduce the notion of a Legendrian Lie subalgebroid of a contact Lie algebroid.Comment: 36 pages. arXiv admin note: text overlap with arXiv:2204.11537 by other author

Jacobi structure for dissipative mechanical systems on Lie Algebroids

We extend the Jacobi structure from $TQ\times \mathbb{R}$ and $T^{*}Q \times \mathbb{R}$ to $A\times \mathbb{R}$ and $A^{*}\times \mathbb{R}$, respectively, where $A$ is a Lie algebroid and $A^{*}$ carries the associated Poisson structure. We see that $A^*\times \mathbb{R}$ possesses a natural Jacobi structure from where we are able to model dissipative mechanical systems, generalizing previous models on $TQ\times \mathbb{R}$ and $\mathfrak{g}\times \mathbb{R}$.Comment: 16 page

Geometric Hamilton-Jacobi theory for higher-order autonomous systems

The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Peer ReviewedPreprin

Hybrid Routhian reduction for simple hybrid forced Lagrangian systems

This paper discusses Routh reduction for simple hybrid forced mechanical systems. We give general conditions on whether it is possible to perform symmetry reduction for a simple hybrid Lagrangian system subject to non-conservative external forces, emphasizing the case of case of cyclic coordinates. We illustrate the applicability of the symmetry reduction procedure with an example and numerical simulations.Comment: Submitted. arXiv admin note: substantial text overlap with arXiv:2112.02573, arXiv:2003.07484, arXiv:2001.0894

Airborne PAHs and PCBs along a coastal, urban-industrial gradient in Rio de la Plata Estuary, Argentina

Atmospheric transport is the principal route of transference of Semivolatile Organic Compounds (SVOCs) from local to global distances. Airborne SVOCs such as Polycyclic aromatic hydrocarbons (PAHs) and Polychlorinated Biphenyls (PCBs) are included in the POP protocol under the Convention on Long-Range Transboundary Air Pollution (LRTAP) and the Stockholm Convention due to their toxicity and environmental persistence. Owing to their practicality (autonomous, easy handled and affordable), in the last decades, polyurethane foam passive air samplers (PUF-PAS) have been widely used to evaluate spatial and temporal patterns of SVOCs allowing a higher temporal resolution than active air samplers. La Plata city, capital of Buenos Aires state, is located 15 km away from the Rio de la Plata Estuary coast, in a highly industrialized (major oil refinery of the country and associated industries [4], an important shipyard and container port) and densely populated region of the country (about 1,000,000 inhabitants). In this study, we report the patterns of airborne PAHs and PCBs along a transitional gradient from the coast to urban-suburban area of La Plata City in order to evaluate their sources, composition and spatial variability.Facultad de Ciencias Naturales y Muse

Sobrecarga sentida por la figura del cuidador principal en una cohorte de pacientes pluripatológicos

ObjetivoConocer el perfil del cuidador principal (CP) y los factores relacionados con la sobrecarga sentida, en una cohorte multicéntrica de pacientes pluripatológicos (PP).DiseñoEstudio transversal, multicéntrico.EmplazamientoCuatro zonas básicas de salud del área sanitaria de los Hospitales Universitarios Virgen del Rocío, Sevilla.ParticipantesLa cohorte de PP se generó prospectivamente mediante el censado de todos los pacientes que cumplían los criterios de PP de la Consejería de Salud (2002): aquellos que tienen enfermedades crónicas de dos o más de las 7 categorías clínicas definidas.Mediciones principalesEl perfil del cuidador se determinó a todos los PP. El cansancio del CP se determinó mediante el índice de esfuerzo del cuidador (IEC). Los factores predictores se analizaron mediante los tests de la t de Student, ANOVA y Pearson.Posteriormente se realizó una regresión lineal multivariable paso a paso hacia delante.ResultadosAccedieron a la entrevista 461 (69% de los 662 elegibles) PP; 293 (63,6%) pacientes tenían CP, que en el 88% eran familiares de primer grado (146 [49,7%] de ellos, el cónyuge), de 62±15 años de edad, y el 80%, mujeres. El IEC fue > 7 puntos en el 41,5% y en general fue 5,35±3,5, mayor en los que cuidaban de PP con enfermedades neurológicas (7±3,2 frente a 4,5±3,3; p<0,0001). El IEC se correlacionó directamente con la vulnerabilidad clínica del PP (R=0,37; p<0,001), con el deterioro cognitivo por escala de Pfeiffer (R=0,4; p<0,0001), e inversamente con la situación funcional por índice de Barthel (R=−0,67; p<0,0001). La edad del paciente (p=0,03), su vulnerabilidad clínica (p=0,016) y el deterioro funcional (p<0,0001) y cognitivo (p=0,019) predijeron de forma independiente el IEC.ConclusionesEl perfil del CP de los PP se correspondió con mujeres familiares en primer grado de unos 60 años. Más de la tercera parte estaban sobrecargadas; los factores predictores fueron la edad, la vulnerabilidad clínica y el deterioro funcional y cognitivo del PP.ObjectiveTo determine the profile of the main caregiver (MC) and the factors associated with her/his care burden, in a multi-centre cohort of patients with multiple pathologies (PMP).DesignMulti-centre cross-sectional study.SettingFour health districts in the Virgen del Rocío University Hospitals Health Area, Seville, Spain.ParticipantsThe PMP cohort was created by checking all the patients who satisfied the health department criteria for PMP (2002): patients suffering from chronic diseases in 2 or more of the 7 clinical categories defined.Main measurementsThe profile of PMP caregiver was determined for all patients. The caregiver strain index (CSI) was determined by the index of care stress (ICS). Predictive factors were analysed by the Student t, ANOVA, and Pearson's tests. Multivariate analysis was performed by a forward stepwise linear regression model.ResultsThe interview was attended by 461 (69%) out of 662 eligible PMP. Of these, 293 (63.6%) had an MC whose mean age was 62 (15) years; 80% of them were women. First-degree relatives made up 88% of caregivers, with spouses 49.7% of them (n=146). In 41.5%, the CSI was >7points (mean CSI was 5.35 [3.5]). This was higher in those caring for PMP with neurological illnesses (7 [3.2 vs 4.5 [3.3]; P=.0001).The CSI was compared directly with the medical vulnerability of the PMP (R=0.37; P=.001), cognitive deterioration on the Pfeiffer scale (PS) (R=0.4; P=.0001), and inversely with functional status on Barthel's scale (BS) (R=-0.67; P=.0001). Patient's age (P=.03), his/her medical vulnerability (P=.016) and functional (P<.0001) and cognitive (P=.019) deterioration were independently associated with the CSI.ConclusionsThe profile of the MC of the PMP cohort corresponded mainly to first-degree female relatives around sixty years old. The burden of care was high in more than a third of them. Predictive factors were age, medical vulnerability, and the functional and cognitive deterioration of the PMP