Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics & Space Scienc

Periodic orbits in the gravity field of a fixed homogeneous cube

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry planes of the fixed cube, periodic orbits are obtained using the method of the Poincar\'e surface of section. While in general positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes. The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics & Space Scienc

Elastografía cuantitativa en la evaluación de nódulos tiroideos

Objective To retrospectively assess the diagnostic capacity of quantitative elastography to determine the odds between benign and malignant thyroid nodules, and determine its usefulness in deciding which nodules should be subjected to fine needle aspiration puncture (FNA). Patients and methods 203 thyroid nodules from 195 patients referred by the Endocrinology Service for cytological study during the year 2018 were analyzed. All of them underwent conventional ultrasound, quantitative elastography and FNA. A statistical analysis was performed using logistic regression that relates the probability that a nodule is suspected of malignancy and the elasticity value measured in kilopascals (kPa) and the elastographic ratio. Results There is a significant and positive relationship between the cytological result of Bethesda V / VI and the kPas / elastographic ratio. FNA is recommended for those nodules with values greater than 25kPa and / or elastographic ratio greater than 1.5. Conclusion Quantitative elastography is a useful tool that, together with other ultrasound parameters, would help to predict the malignancy of a thyroid nodule and to better select for FNA. © 2021 Georg Thieme Verlag. All rights reserved

Análisis de la situación de los estudios agronómicos y forestales en Europa. Anexo III: análisis de los estudios europeos

El documento que se presenta es el resultado del análisis de la situación actual en estas ingenierías y del estudio del futuro de las mismas. Todas las propuestas que aquí se hacen se han consensuado en las sesiones del Plenario del grupo de trabajo. Por ello, es justo reconocer la aportación que este trabajo puede suponer a la futura Convergencia Europea en la Educación Superior

Computation of families of periodic orbits and bifurcations around a massive annulus

This paper studies the main features of the dynamics around a planar annular disk. It is addressed an appropriated closed expression of the gravitational potential of a massive disk, which overcomes the difficulties found in previous works in this matter concerning its numerical treatment. This allows us to define the differential equations of motion that describes the motion of a massless particle orbiting the annulus. We describe the computation methods proposed for the continuation of uni-parametric families of periodic orbits, these algorithms have been applied to analyze the dynamics around a massive annulus by means of a description of the main families of periodic orbits found, their bifurcations and linear stability

Dynamics of a particle under the gravitational potential of a massive annulus: properties and equilibrium description

This paper studies the main features of the dynamics around a massive annular disk. The first part addresses the difficulties finding an appropriated expression of the gravitational potential of a massive disk, which will be used to define the differential equations of motion of our dynamical system. The second part describes the main features of the dynamics with special attention to equilibrium of the system

Non linear stability in resonant cases: A geometrical approach.

In systems with two degrees of freedom, Arnold's theorem is used for studying nonlinear stability of the origin when the quadratic part of the Hamiltonian is a nondefinite form. In that case, a previous normalization of the higher orders is needed, which reduces the Hamiltonian to homogeneous polynomials in the actions. However, in the case of resonances, it could not be possible to bring the Hamiltonian to the normal form required by Arnold's theorem. In these cases, we determine the stability from analysis of the normalized phase flow. Normalization up to an arbitrary order by Lie-Deprit transformation is carried out using a generalization of the Lissajous variables

Preliminary results of mastitis control program in meat sheep herds of rasa aragonesa breed

5 páginas, 3 figuras.-- Trabajo presentado al XXXVII Congreso de la Sociedad Española de Ovinotecnia y Caprinotecnia (Ciudad Real, España, 19 al 21 de septiembre del 2012).[EN] From previously established data regarding the prevalence (44%) and economic importance (12-42€/affected sheep) of mastitis in Rasa Aragonesa sheep, this study shows the results of a program for the control of mastitis applied in 64 flocks of this breed specialized meat production. This program is based on the application of preventive measures in the general management of the flock (control of orphan lambs, treatment of acute mastitis, improvement of hygiene in the milking and weaning ewes, prevention of diseases, and any predisposing factor, which could affect the mammary gland) and specific management over the weaning period (mammary gland palpation and culling of those sheep showing irreversible chronic lesions, application of treatments and dried-off procedure). The results from this program are showed based on the evolution of the intramammary infections and the analysis of the economic repercussions according to the rates of lamb mortality and average daily gain until weaning (45 days). This results show the costeffectiveness of the measures established under this program.[ES]Establecidas previamente la prevalencia (44%) y repercusiones económicas de las mamitis en ovejas Rasa aragonesa (12-24€/ovejas con infección intramamaria) en este trabajo se presentan los resultados de un programa de control de mamitis en 64 rebaños de ovino de carne de esta raza. El programa de control de mamitis propuesto, se basa en la implantación de prácticas preventivas relacionadas con el manejo general (control de corderos robadores, pautas a seguir ante las mamitis agudas, mejora de la higiene de los lotes de lactación y destete, prevención de enfermedades y causas predisponentes que lesionan la mama) y prácticas de secado/destete (palpación mamaria y eliminación de ovejas con lesiones crónicas irreversibles, manejo del secado y aplicación del tratamiento). Se exponen los resultados del Programa, basados en la evolución de la infección intramamaria y el estudio de repercusiones económicas con los indicadores de la evolución de la mortalidad de los corderos y de la ganancia media diaria de los mismos desde su nacimiento hasta el destete a los 45 días, que ponen de manifiesto la eficacia y rentabilidad de las medidas integradas en el mismo.Peer reviewe