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.

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.

Analysis of large-scale digital optical neural networks by Feynman diagrams

A new method to study large scale neural networks is presented in this paper. The basis is the use of Feynman- like diagrams. These diagrams allow the analysis of collective and cooperative phenomena with a similar methodology to the employed in the Many Body Problem. The proposed method is applied to a very simple structure composed by an string of neurons with interaction among them. It is shown that a new behavior appears at the end of the row. This behavior is different to the initial dynamics of a single cell. When a feedback is present, as in the case of the hippocampus, this situation becomes more complex with a whole set of new frequencies, different from the proper frequencies of the individual neurons. Application to an optical neural network is reported.

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

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.

Intensive use of aluminium in car body construction

The developments in materials over the last decade have been considerable within the automotive industry, being one of the leaders in innovative product applications. Sustainable product development of an automotive structure requires a balanced approach towards technological, economical and ecological aspects. The introduction of new materials and processes is dependent on satisfying different factors. Competitive and legislative pressures, creating the need for change, affect these factors considerably. The process, direction and speed of change are often reactive. Current paper shows the application of aluminium alloys, for the use in the bottom structure of a car to face the problem for the weight of the entire bottom structure under static load conditions, including stiffness, strength and buckling constraints. In addition to minimized mass and materials' price, the assessment of an environmental impact of materials-candidates during the entire life cycle of the structure is considered.

Aerodynamic external pressure loads on a semi-circular bluff body under wind gusts

This brief communication concerns the unsteady aerodynamic external pressure loads acting on a semi-circular bluff body lying on a floor under wind gusts and describes the theoretical model, experimental setup, and experimental results obtained. The experimental setup is based on an open circuit, closed test section, low speed wind tunnel, which includes a sinusoidal gust generating mechanism, designed and built at the Instituto de Microgravedad “Ignacio Da Riva” of the Universidad Politécnica de Madrid (IDR/UPM). Based on the potential flow theory, a theoretical model has been proposed to analyse the problem, and experimental tests have been performed to study the unsteady aerodynamic loads on a semi-circular bluff body. By fitting the theoretical model predictions with the experimental results, influencing parameters of the unsteady aerodynamic loads are ascertained. The values of these parameters can help in clarifying the phenomenon of the external pressure loads on semi-circular bluff body under various gust frequencies. The theoretical model proposed allows the pressure variation to be split into two contributions, a quasi-steady term and an unsteady term with a simple physical meaning