Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations.

EDROMO: An accurate propagator for elliptical orbits in the perturbed two-body problem

EDROMO is a special perturbation method for the propagation of elliptical orbits in the perturbed two-body problem. The state vector consists of a time-element and seven spatial elements, and the independent variable is a generalized eccentric anomaly introduced through a Sundman time transformation. The key role in the derivation of the method is played by an intermediate reference frame which enjoys the property of remaining fixed in space as long as perturbations are absent. Three elements of EDROMO characterize the dynamics in the orbital frame and its orientation with respect to the intermediate frame, and the Euler parameters associated to the intermediate frame represent the other four spatial elements. The performance of EDromo has been analyzed by considering some typical problems in astrodynamics. In almost all our tests the method is the best among other popular formulations based on elements.

Asymptotic Solution for the Two Body Problem with Radial Perturbing Acceleration

In this article, an approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. The results reveal that the physics of the problem evolve in two fundamental scales of the true anomaly. The first one drives the oscillations of the orbital parameters along each orbit. The second one is responsible of the long-term variations in the amplitude and mean values of these oscillations. A good agreement is found with high precision numerical solutions.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje

DROMO formulation for planar motions: Solution to the Tsien Problem

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen?s ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo?Stiefel methods.

Gravitational actions upon a tether in a non-uniform gravity field with arbitrary number of zonal harmonics

We develop general closed-form expressions for the mutual gravitational potential, resultant and torque acting upon a rigid tethered system moving in a non-uniform gravity field produced by an attracting body with revolution symmetry, such that an arbitrary number of zonal harmonics is considered. The final expressions are series expansion in two small parameters related to the reference radius of the primary and the length of the tether, respectively, each of which are scaled by the mutual distance between their centers of mass. A few numerical experiments are performed to study the convergence behavior of the final expressions, and conclude that for high precision applications it might be necessary to take into account additional perturbation terms, which come from the mutual Two-Body interaction.

El Problema de Lambert en el Contexto de Optimización de Trayectorias Espaciales

Esta tesis se basa en el estudio de la trayectoria que pasa por dos puntos en el problema de los dos cuerpos, inicialmente desarrollado por Lambert, del que toma su nombre. En el pasado, el Problema de Lambert se ha utilizado para la determinación de órbitas a partir de observaciones astronómicas de los cuerpos celestes. Actualmente, se utiliza continuamente en determinación de órbitas, misiones planetaria e interplanetarias, encuentro espacial e interceptación, o incluso en corrección de orbitas. Dada su gran importancia, se decide investigar especialmente sobre su solución y las aplicaciones en las misiones espaciales actuales. El campo de investigación abierto, es muy amplio, así que, es necesario determinar unos objetivos específicos realistas, en el contexto de ejecución de una Tesis, pero que sirvan para mostrar con suficiente claridad el potencial de los resultados aportados en este trabajo, e incluso poder extenderlos a otros campos de aplicación. Como resultado de este análisis, el objetivo principal de la Tesis se enfoca en el desarrollo de algoritmos para resolver el Problema de Lambert, que puedan ser aplicados de forma muy eficiente en las misiones reales donde aparece. En todos los desarrollos, se ha considerado especialmente la eficiencia del cálculo computacional necesario en comparación con los métodos existentes en la actualidad, destacando la forma de evitar la pérdida de precisión inherente a este tipo de algoritmos y la posibilidad de aplicar cualquier método iterativo que implique el uso de derivadas de cualquier orden. En busca de estos objetivos, se desarrollan varias soluciones para resolver el Problema de Lambert, todas ellas basadas en la resolución de ecuaciones transcendentes, con las cuales, se alcanzan las siguientes aportaciones principales de este trabajo: • Una forma genérica completamente diferente de obtener las diversas ecuaciones para resolver el Problema de Lambert, mediante desarrollo analítico, desde cero, a partir de las ecuaciones elementales conocidas de las cónicas (geométricas y temporal), proporcionando en todas ellas fórmulas para el cálculo de derivadas de cualquier orden. • Proporcionar una visión unificada de las ecuaciones más relevantes existentes, mostrando la equivalencia con variantes de las ecuaciones aquí desarrolladas. • Deducción de una nueva variante de ecuación, el mayor logro de esta Tesis, que destaca en eficiencia sobre todas las demás (tanto en coste como en precisión). • Estudio de la sensibilidad de la solución ante variación de los datos iniciales, y como aplicar los resultados a casos reales de optimización de trayectorias. • También, a partir de los resultados, es posible deducir muchas propiedades utilizadas en la literatura para simplificar el problema, en particular la propiedad de invariancia, que conduce al Problema Transformado Simplificado. ABSTRACT This thesis is based on the study of the two-body, two-point boundary-value problem, initially developed by Lambert, from who it takes its name. Since the past, Lambert's Problem has been used for orbit determination from astronomical observations of celestial bodies. Currently, it is continuously used in orbit determinations, for planetary and interplanetary missions, space rendezvous, and interception, or even in orbit corrections. Given its great importance, it is decided to investigate their solution and applications in the current space missions. The open research field is very wide, it is necessary to determine specific and realistic objectives in the execution context of a Thesis, but that these serve to show clearly enough the potential of the results provided in this work, and even to extended them to other areas of application. As a result of this analysis, the main aim of the thesis focuses on the development of algorithms to solve the Lambert’s Problem which can be applied very efficiently in real missions where it appears. In all these developments, it has been specially considered the efficiency of the required computational calculation compared to currently existing methods, highlighting how to avoid the loss of precision inherent in such algorithms and the possibility to apply any iterative method involving the use of derivatives of any order. Looking to meet these objectives, a number of solutions to solve the Lambert’s Problem are developed, all based on the resolution of transcendental equations, with which the following main contributions of this work are reached: • A completely different generic way to get the various equations to solve the Lambert’s Problem by analytical development, from scratch, from the known elementary conic equations (geometrics and temporal), by providing, in all cases, the calculation of derivatives of any order. • Provide a unified view of most existing relevant equations, showing the equivalence with variants of the equations developed here. • Deduction of a new variant of equation, the goal of this Thesis, which emphasizes efficiency (both computational cost and accuracy) over all other. • Estudio de la sensibilidad de la solución ante la variación de las condiciones iniciales, mostrando cómo aprovechar los resultados a casos reales de optimización de trayectorias. • Study of the sensitivity of the solution to the variation of the initial data, and how to use the results to real cases of trajectories’ optimization. • Additionally, from results, it is possible to deduce many properties used in literature to simplify the problem, in particular the invariance property, which leads to a simplified transformed problem.

Nutritional intake and body composition of adolescent soccer player of two different levels of performance: a comparative study

Soccer participation worldwide is increasing and every club try to discover new talents. It is well know that there is an important correlation between body composition (BC) and talent detection (TD) and when coaches and selectors choose players, they tend to choose them with optimum BC.

Determinant factors to discriminate the body weight loss in overweight people

Introduction. Most studies have described how the weight loss is when different treatments are compared (1-3), while others have also compared the weight loss by sex (4), or have taken into account psychosocial (5) and lifestyle (6, 7) variables. However, no studies have examined the interaction of different variables and the importance of them in the weight loss. Objective. Create a model to discriminate the range of weight loss, determining the importance of each variable. Methods. 89 overweight people (BMI: 25-29.9 kg?m-2), aged from 18 to 50 years, participated in the study. Four types of treatments were randomly assigned: strength training (S), endurance training (E), strength and endurance training (SE), and control group (C). All participants followed a 25% calorie restriction diet. Two multivariate discriminant models including the variables age, sex, height, daily energy expenditure (EE), type of treatment (T), caloric restriction (CR), initial body weight (BW), initial fat mass (FM), initial muscle mass (MM) and initial bone mineral density (BMD) were performed having into account two groups: the first and fourth quartile of the % of weight loss in the first model; the groups above and below the mean of the % of weight loss in the second model. The discriminant models were built using the inclusion method in SPSS allowing us to find a function that could predict the body weight loss range that an overweight person could achieve in a 6 months weight loss intervention.Results. The first discriminant analysis predicted that a combination of the studied variables would discriminate between the two ranges of body weight loss with 81.4% of correct classification. The discriminant function obtained was (Wilks? Lambda=0.475, p=0.003): Discriminant score=-18.266-(0.060xage)- (1.282xsex[0=female;1=male])+(14.701xheight)+(0.002xEE)- (0.006xT[1=S;2=E;3=SE;4=C])-(0.047xCR)- (0.558xBW)+(0.475xFM)+(0.398xMM)+(3.499xBMD) The second discriminant model obtained would discriminate between the two groups of body weight loss with 74.4% of correct classification. The discriminant function obtained was (Wilks? Lambda=0.725, p=0.005): Discriminant score=-5.021-(0.052xage)- (0.543xsex[0=female;1=male])+(3.530xheight)+(0.001xEE)- (0.493xT[1=S;2=E;3=SE;4=C])+(0.003xCR)- (0.365xBW)+(0.368xFM)+(0.296xMM)+(4.034xBMD) Conclusion. The first developed model could predict the percentage of weight loss in the following way: if the discriminant score is close to 1.051, the range of weight loss will be from 7.44 to -4.64% and if it is close to - 1.003, the range will be from -11.03 to -25,00% of the initial body weight. With the second model if the discriminant score is close to 0.623 the body weight loss will be above -7.93% and if it is close to -0.595 will be below - 7.93% of the initial body weight. References. 1. Brochu M, et al. Resistance training does not contribute to improving the metabolic profile after a 6-month weight loss program in overweight and obese postmenopausal women. J Clin Endocrinol Metab. 2009 Sep;94(9):3226-33. 2. Del Corral P, et al. Effect of dietary adherence with or without exercise on weight loss: a mechanistic approach to a global problem. J Clin Endocrinol Metab. 2009 May;94(5):1602-7. 3. Larson-Meyer DE, et al. Caloric Restriction with or without Exercise: The Fitness vs. Fatness Debate. Med Sci Sports Exerc. 2010;42(1):152-9. 4. Hagan RD, et al. The effects of aerobic conditioning and/or caloric restriction in overweight men and women. Medicine & Science in Sports & Exercise. 1986;18(1):87-94. 5. Teixeira PJ, et al. Mediators of weight loss and weight loss maintenance in middle-aged women. Obesity (Silver Spring). 2010 Apr;18(4):725-35. 6. Bautista-Castano I, et al. Variables predictive of adherence to diet and physical activity recommendations in the treatment of obesity and overweight, in a group of Spanish subjects. Int J Obes Relat Metab Disord. 2004 May;28(5):697-705.

In situ conversion of protochlorophyllide b to protochlorophyllide a in barley. Evidence for a novel role of 7-formyl reductase in the prolamellar body of etioplasts

We recently put forth a model of a protochlorophyllide (Pchlide) light-harvesting complex operative during angiosperm seedling de-etiolation (Reinbothe, C., Lebedev, N., and Reinbothe, S. (1999) Nature 397, 80–84). This model, which was based on in vitro reconstitution experiments with zinc analogs of Pchlide a and Pchlide b and the two NADPH:protochlorophyllide oxidoreductases (PORs), PORA and PORB, of barley, predicted a 5-fold excess of Pchlide b, relative to Pchlide a, in the prolamellar body of etioplasts. Recent work (Scheumann, V., Klement, H., Helfrich, M., Oster, U., Schoch, S., and Rüdiger, W. (1999) FEBS Lett. 445, 445–448), however, contradicted this model and reported that Pchlide b would not be present in etiolated plants. Here we demonstrate that Pchlide b is an abundant pigment in barley etioplasts but is rather metabolically unstable. It is rapidly converted to Pchlide a by virtue of 7-formyl reductase activity, an enzyme that had previously been implicated in the chlorophyll (Chl) b to Chl a reaction cycle. Our findings suggest that etiolated plants make use of 7-formyl reductase to fine tune the levels of Pchlide b and Pchlidea and thereby may regulate the steady-state level of light-harvesting POR-Pchlide comple

Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model.

The vertical dynamic actions transmitted by railway vehicles to the ballasted track infrastructure is evaluated taking into account models with different degree of detail. In particular, we have studied this matter from a two-dimensional (2D) finite element model to a fully coupled three-dimensional (3D) multi-body finite element model. The vehicle and track are coupled via a non-linear Hertz contact mechanism. The method of Lagrange multipliers is used for the contact constraint enforcement between wheel and rail. Distributed elevation irregularities are generated based on power spectral density (PSD) distributions which are taken into account for the interaction. The numerical simulations are performed in the time domain, using a direct integration method for solving the transient problem due to the contact nonlinearities. The results obtained include contact forces, forces transmitted to the infrastructure (sleeper) by railpads and envelopes of relevant results for several track irregularities and speed ranges. The main contribution of this work is to identify and discuss coincidences and differences between discrete 2D models and continuum 3D models, as wheel as assessing the validity of evaluating the dynamic loading on the track with simplified 2D models

Validation of a Dumbbell Body Sway Test in Olympic Air Pistol Shooting

We present and validate a test able to provide reliable body sway measurements in air pistol shooting, without the use of a gun. 46 senior male pistol shooters who participated in Spanish air pistol championships participated in the study. Body sway data of two static bipodal balance tests have been compared: during the first test, shooting was simulated by use of a dumbbell, while during the second test the shooters own pistol was used. Both tests were performed the day previous to the competition, during the official training time and at the training stands to simulate competition conditions. The participants performance was determined as the total score of 60 shots at competition. Apart from the commonly used variables that refer to movements of the shooters centre of pressure (COP), such as COP displacements on the X and Y axes, maximum and average COP velocities and total COP area, the present analysis also included variables that provide information regarding the axes of the COP ellipse (length and angle in respect to X). A strong statistically significant correlation between the two tests was found (with an interclass correlation varying between 0.59 and 0.92). A statistically significant inverse linear correlation was also found between performance and COP movements. The study concludes that dumbbell tests are perfectly valid for measuring body sway by simulating pistol shooting.

El fitness como factor determinante en el riesgo de discapacidad, su relación con la composición corporal y el estado cognitivo en población mayor institucionalizada y de vida independiente = Fitness as a determinant factor in the risk of disability, and its relationship to body composition and cognitive status in institutionalized elderly population and independent living

La condición física, o como mejor se la conoce hoy en día el “fitness”, es una variable que está cobrando gran protagonismo, especialmente desde la perspectiva de la salud. La mejora de la calidad de vida que se ha experimentado en los últimos años en las sociedades desarrolladas, conlleva un aumento de la esperanza de vida, lo que hace que cada vez más personas vivan más años. Este rápido crecimiento de la población mayor de 60 años hace que, un grupo poblacional prácticamente olvidado desde el punto de vista de la investigación científica en el campo de la actividad física y del deporte, cobre gran relevancia, con el fin de poder ayudar a alcanzar el dicho “no se trata de aportar años a la vida sino vida a lo años”. La presente memoria de Tesis Doctoral tiene como principal objetivo valorar los niveles de fitness en población mayor española, además de analizar la relación existente entre el fitness, sus condicionantes y otros aspectos de la salud, tales como la composición corporal y el estado cognitivo. Entendemos que para poder establecer futuras políticas de salud pública en relación a la actividad física y el envejecimiento activo es necesario conocer cuáles son los niveles de partida de la población mayor en España y sus condicionantes. El trabajo está basado en los datos del estudio multicéntrico EXERNET (Estudio Multi-céntrico para la Evaluación de los Niveles de Condición Física y su relación con Estilos de Vida Saludables en población mayor española no institucionalizada), así como en los datos de dos estudios, llevados a cabo en población mayor institucionalizada. Se han analizado un total de 3136 mayores de vida independiente, procedentes de 6 comunidades autónomas, y 153 mayores institucionalizados en residencias de la Comunidad de Madrid. Los principales resultados de esta tesis son los siguientes: a) Fueron establecidos los valores de referencia, así como las curvas de percentiles, para cada uno de los test de fitness, de acuerdo a la edad y al sexo, en población mayor española de vida independiente y no institucionalizada. b) Los varones obtuvieron mejores niveles de fitness que las mujeres, excepto en los test de flexibilidad; existe una tendencia a disminuir la condición física en ambos sexos a medida que la edad aumenta. c) Niveles bajos de fitness funcional fueron asociados con un aumento en la percepción de problemas. d) El nivel mínimo de fitness funcional a partir del cual los mayores perciben problemas en sus actividades de la vida diaria (AVD) es similar en ambos sexos. e) Niveles elevados de fitness fueron asociados con un menor riesgo de sufrir obesidad sarcopénica y con una mejor salud percibida en los mayores. f) Las personas mayores con obesidad sarcopénica tienen menor capacidad funcional que las personas mayores sanas. g) Niveles elevados de fuerza fueron asociados con un mejor estado cognitivo siendo el estado cognitivo la variable que más influye en el deterioro de la fuerza, incluso más que el sexo y la edad. ABSTRACT Fitness is a variable that is gaining in prominence, especially from the health perspective. Improvement of life quality that has been experienced in the last few years in developed countries, leads to an expanded life expectancy, increasing the numbers of people living longer. This population consisting of people of over 60 years, an almost forgotten population group from the point of view of scientific research in the field of physical activity and sport, is becoming increasingly important, with the main aim of helping to achieve the saying “do not only add years to life, but also add life to years”. The principal aim of the current thesis was to assess physical fitness levels in Spanish elderly people, of over 65 years, analyzing relationship between physical fitness, its determinants, and other aspects of health such as body composition and cognitive status. In order to establish further public health policies in relation to physical activity and active ageing it is necessary to identify the starting physical fitness levels of the Spanish population and their determinants. The work is based on data from the EXERNET multi-center study ("Multi-center Study for the Evaluation of Fitness levels and their relationship to Healthy Lifestyles in noninstitutionalized Spanish elderly"), and on data from two studies conducted in institutionalized elderly people: a total of 3136 non-institutionalized elderly, from 6 Regions of Spain, and 153 institutionalized elderly in nursing homes of Madrid. The main outcomes of this thesis are: a) sex- and age-specific physical fitness normative values and percentile curves for independent and non-institutionalized Spanish elderly were established. b) Greater physical fitness was present in the elderly men than in women, except for the flexibility test, and a trend toward decreased physical fitness in both sexes as their age increased. c) Lower levels of functional fitness were associated with increased perceived problems. d) The minimum functional fitness level at which older adults perceive problems in their ADLs, is similar for both sexes e) Higher levels of physical fitness were associated with a reduced risk of suffering sarcopenic obesity and better perceived health among the elderly. f) The elderly with sarcopenic obesity have lower physical functioning than healthy counterparts. g) Higher strength values were associated with better cognitive status with cognitive status being the most influencing variable in strength deterioration even more than sex and age.

Associations between macronutrient intake and serum lipid profile depend on body fat in European adolescents: the Healthy Lifestyle in Europe by Nutrition in Adolescence (HELENA) study

The present study aimed to investigate the relationships between macronutrient intake and serum lipid profile in adolescents from eight European cities participating in the HELENA (Healthy Lifestyle in Europe by Nutrition in Adolescence) cross-sectional study (2006–7), and to assess the role of body fat-related variables in these associations. Weight, height, waist circumference, skinfold thicknesses, total choles- terol, HDL-cholesterol (HDL-C), LDL-cholesterol, TAG, apoB and apoA1 were measured in 454 adolescents (44 % boys) aged 12·5–17·5 years. Macronutrient intake (g/4180 kJ per d (1000 kcal per d)) was assessed using two non-consecutive 24 h dietary recalls. Associations were evaluated by multi-level analysis and adjusted for sex, age, maternal education, centre, sum of four skinfolds, moderate-to-vigorous.