Diseño de una metodología CASE de desarrollo de software

En la actualidad existe una gran expectación ante la introducción de nuevas herramientas y métodos para el desarrollo de productos software, que permitirán en un futuro próximo un planteamiento de ingeniería del proceso de producción software. Las nuevas metodologías que empiezan a esbozarse suponen un enfoque integral del problema abarcando todas las fases del esquema productivo. Sin embargo el grado de automatización conseguido en el proceso de construcción de sistemas es muy bajo y éste está centrado en las últimas fases del ciclo de vida del software, consiguiéndose así una reducción poco significativa de sus costes y, lo que es aún más importante, sin garantizar la calidad de los productos software obtenidos. Esta tesis define una metodología de desarrollo software estructurada que se puede automatizar, es decir una metodología CASE. La metodología que se presenta se ajusta al modelo de ciclo de desarrollo CASE, que consta de las fases de análisis, diseño y pruebas; siendo su ámbito de aplicación los sistemas de información. Se establecen inicialmente los principios básicos sobre los que la metodología CASE se asienta. Posteriormente, y puesto que la metodología se inicia con la fijación de los objetivos de la empresa que demanda un sistema informático, se emplean técnicas que sirvan de recogida y validación de la información, que proporcionan a la vez un lenguaje de comunicación fácil entre usuarios finales e informáticos. Además, estas mismas técnicas detallarán de una manera completa, consistente y sin ambigüedad todos los requisitos del sistema. Asimismo, se presentan un conjunto de técnicas y algoritmos para conseguir que desde la especificación de requisitos del sistema se logre una automatización tanto del diseño lógico del Modelo de Procesos como del Modelo de Datos, validados ambos conforme a la especificación de requisitos previa. Por último se definen unos procedimientos formales que indican el conjunto de actividades a realizar en el proceso de construcción y cómo llevarlas a cabo, consiguiendo de esta manera una integridad en las distintas etapas del proceso de desarrollo.---ABSTRACT---Nowdays there is a great expectation with regard to the introduction of new tools and methods for the software products development that, in the very near future will allow, an engineering approach in the software development process. New methodologies, just emerging, imply an integral approach to the problem, including all the productive scheme stages. However, the automatization degree obtained in the systems construction process is very low and focused on the last phases of the software lifecycle, which means that the costs reduction obtained is irrelevant and, which is more important, the quality of the software products is not guaranteed. This thesis defines an structured software development methodology that can be automated, that is a CASE methodology. Such a methodology is adapted to the CASE development cycle-model, which consists in analysis, design and testing phases, being the information systems its field of application. Firstly, we present the basic principies on which CASE methodology is based. Secondly, since the methodology starts from fixing the objectives of the company demanding the automatization system, we use some techniques that are useful for gathering and validating the information, being at the same time an easy communication language between end-users and developers. Indeed, these same techniques will detail completely, consistently and non ambiguously all the system requirements. Likewise, a set of techniques and algorithms are shown in order to obtain, from the system requirements specification, an automatization of the Process Model logical design, and of the Data Model logical design. Those two models are validated according to the previous requirement specification. Finally, we define several formal procedures that suggest which set of activities to be accomplished in the construction process, and how to carry them out, getting in this way integrity and completness for the different stages of the development process.

Método para el análisis independiente de problemas

habilidades de comprensión y resolución de problemas. Tanto es así que se puede afirmar con rotundidad que no existe el método perfecto para cada una de las etapas de desarrollo y tampoco existe el modelo de ciclo de vida perfecto: cada nuevo problema que se plantea es diferente a los anteriores en algún aspecto y esto hace que técnicas que funcionaron en proyectos anteriores fracasen en los proyectos nuevos. Por ello actualmente se realiza un planteamiento integrador que pretende utilizar en cada caso las técnicas, métodos y herramientas más acordes con las características del problema planteado al ingeniero. Bajo este punto de vista se plantean nuevos problemas. En primer lugar está la selección de enfoques de desarrollo. Si no existe el mejor enfoque, ¿cómo se hace para elegir el más adecuado de entre el conjunto de los existentes? Un segundo problema estriba en la relación entre las etapas de análisis y diseño. En este sentido existen dos grandes riesgos. Por un lado, se puede hacer un análisis del problema demasiado superficial, con lo que se produce una excesiva distancia entre el análisis y el diseño que muchas veces imposibilita el paso de uno a otro. Por otro lado, se puede optar por un análisis en términos del diseño que provoca que no cumpla su objetivo de centrarse en el problema, sino que se convierte en una primera versión de la solución, lo que se conoce como diseño preliminar. Como consecuencia de lo anterior surge el dilema del análisis, que puede plantearse como sigue: para cada problema planteado hay que elegir las técnicas más adecuadas, lo que requiere que se conozcan las características del problema. Para ello, a su vez, se debe analizar el problema, eligiendo una técnica antes de conocerlo. Si la técnica utiliza términos de diseño entonces se ha precondicionado el paradigma de solución y es posible que no sea el más adecuado para resolver el problema. En último lugar están las barreras pragmáticas que frenan la expansión del uso de métodos con base formal, dificultando su aplicación en la práctica cotidiana. Teniendo en cuenta todos los problemas planteados, se requieren métodos de análisis del problema que cumplan una serie de objetivos, el primero de los cuales es la necesidad de una base formal, con el fin de evitar la ambigüedad y permitir verificar la corrección de los modelos generados. Un segundo objetivo es la independencia de diseño: se deben utilizar términos que no tengan reflejo directo en el diseño, para que permitan centrarse en las características del problema. Además los métodos deben permitir analizar problemas de cualquier tipo: algorítmicos, de soporte a la decisión o basados en el conocimiento, entre otros. En siguiente lugar están los objetivos relacionados con aspectos pragmáticos. Por un lado deben incorporar una notación textual formal pero no matemática, de forma que se facilite su validación y comprensión por personas sin conocimientos matemáticos profundos pero al mismo tiempo sea lo suficientemente rigurosa para facilitar su verificación. Por otro lado, se requiere una notación gráfica complementaria para representar los modelos, de forma que puedan ser comprendidos y validados cómodamente por parte de los clientes y usuarios. Esta tesis doctoral presenta SETCM, un método de análisis que cumple estos objetivos. Para ello se han definido todos los elementos que forman los modelos de análisis usando una terminología independiente de paradigmas de diseño y se han formalizado dichas definiciones usando los elementos fundamentales de la teoría de conjuntos: elementos, conjuntos y relaciones entre conjuntos. Por otro lado se ha definido un lenguaje formal para representar los elementos de los modelos de análisis – evitando en lo posible el uso de notaciones matemáticas – complementado con una notación gráfica que permite representar de forma visual las partes más relevantes de los modelos. El método propuesto ha sido sometido a una intensa fase de experimentación, durante la que fue aplicado a 13 casos de estudio, todos ellos proyectos reales que han concluido en productos transferidos a entidades públicas o privadas. Durante la experimentación se ha evaluado la adecuación de SETCM para el análisis de problemas de distinto tamaño y en sistemas cuyo diseño final usaba paradigmas diferentes e incluso paradigmas mixtos. También se ha evaluado su uso por analistas con distinto nivel de experiencia – noveles, intermedios o expertos – analizando en todos los casos la curva de aprendizaje, con el fin de averiguar si es fácil de aprender su uso, independientemente de si se conoce o no alguna otra técnica de análisis. Por otro lado se ha estudiado la capacidad de ampliación de modelos generados con SETCM, para comprobar si permite abordar proyectos realizados en varias fases, en los que el análisis de una fase consista en ampliar el análisis de la fase anterior. En resumidas cuentas, se ha tratado de evaluar la capacidad de integración de SETCM en una organización como la técnica de análisis preferida para el desarrollo de software. Los resultados obtenidos tras esta experimentación han sido muy positivos, habiéndose alcanzado un alto grado de cumplimiento de todos los objetivos planteados al definir el método.---ABSTRACT---Software development is an inherently complex activity, which requires specific abilities of problem comprehension and solving. It is so difficult that it can even be said that there is no perfect method for each of the development stages and that there is no perfect life cycle model: each new problem is different to the precedent ones in some respect and the techniques that worked in other problems can fail in the new ones. Given that situation, the current trend is to integrate different methods, tools and techniques, using the best suited for each situation. This trend, however, raises some new problems. The first one is the selection of development approaches. If there is no a manifestly single best approach, how does one go about choosing an approach from the array of available options? The second problem has to do with the relationship between the analysis and design phases. This relation can lead to two major risks. On one hand, the analysis could be too shallow and far away from the design, making it very difficult to perform the transition between them. On the other hand, the analysis could be expressed using design terminology, thus becoming more a kind of preliminary design than a model of the problem to be solved. In third place there is the analysis dilemma, which can be expressed as follows. The developer has to choose the most adequate techniques for each problem, and to make this decision it is necessary to know the most relevant properties of the problem. This implies that the developer has to analyse the problem, choosing an analysis method before really knowing the problem. If the chosen technique uses design terminology then the solution paradigm has been preconditioned and it is possible that, once the problem is well known, that paradigm wouldn’t be the chosen one. The last problem consists of some pragmatic barriers that limit the applicability of formal based methods, making it difficult to use them in current practice. In order to solve these problems there is a need for analysis methods that fulfil several goals. The first one is the need of a formal base, which prevents ambiguity and allows the verification of the analysis models. The second goal is design-independence: the analysis should use a terminology different from the design, to facilitate a real comprehension of the problem under study. In third place the analysis method should allow the developer to study different kinds of problems: algorithmic, decision-support, knowledge based, etc. Next there are two goals related to pragmatic aspects. Firstly, the methods should have a non mathematical but formal textual notation. This notation will allow people without deep mathematical knowledge to understand and validate the resulting models, without losing the needed rigour for verification. Secondly, the methods should have a complementary graphical notation to make more natural the understanding and validation of the relevant parts of the analysis. This Thesis proposes such a method, called SETCM. The elements conforming the analysis models have been defined using a terminology that is independent from design paradigms. Those terms have been then formalised using the main concepts of the set theory: elements, sets and correspondences between sets. In addition, a formal language has been created, which avoids the use of mathematical notations. Finally, a graphical notation has been defined, which can visually represent the most relevant elements of the models. The proposed method has been thoroughly tested during the experimentation phase. It has been used to perform the analysis of 13 actual projects, all of them resulting in transferred products. This experimentation allowed evaluating the adequacy of SETCM for the analysis of problems of varying size, whose final design used different paradigms and even mixed ones. The use of the method by people with different levels of expertise was also evaluated, along with the corresponding learning curve, in order to assess if the method is easy to learn, independently of previous knowledge on other analysis techniques. In addition, the expandability of the analysis models was evaluated, assessing if the technique was adequate for projects organised in incremental steps, in which the analysis of one step grows from the precedent models. The final goal was to assess if SETCM can be used inside an organisation as the preferred analysis method for software development. The obtained results have been very positive, as SETCM has obtained a high degree of fulfilment of the goals stated for the method.

Discussion of "Simplified Model of Low Cycle Fatigue for RC Frames"

To model strength degradation due to low cycle fatigue, at least three different approaches can be considered. One possibility is based on the formulation of a new free energy function and damage energy release rate, as was proposed by Ju(1989). The second approach uses the notion of bounding surface introduced in cyclic plasticity by Dafalias and Popov (1975). From this concept, some models have been proposed to quantify damage in concrete or RC (Suaris et al. 1990). The model proposed by the author to include fatigue effects is based essentially in Marigo (1985) and can be included in this approach.

Numerical Model of a Variable-Combined-Cycle Engine for Dual Subsonic and Supersonic Cruise

Efficient high speed propulsion requires exploiting the cooling capability of the cryogenic fuel in the propulsion cycle. This paper presents the numerical model of a combined cycle engine while in air turbo-rocket configuration. Specific models of the various heat exchanger modules and the turbomachinery elements were developed to represent the physical behavior at off-design operation. The dynamic nature of the model allows the introduction of the engine control logic that limits the operation of certain subcomponents and extends the overall engine operational envelope. The specific impulse and uninstalled thrust are detailed while flying a determined trajectory between Mach 2.5 and 5 for varying throttling levels throughout the operational envelope.

A simplified energy consumption model for fiber-based Next Generation Access Networks

ICTs account nowadays for 2% of total carbon emissions. However, in a time when strict measures to reduce energyconsumption in all the industrial and services sectors are required, the ICT sector faces an increase in services and bandwidth demand. The deployment of NextGenerationNetworks (NGN) will be the answer to this new demand and specifically, the NextGenerationAccessNetworks (NGANs) will provide higher bandwidth access to users. Several policy and cost analysis are being carried out to understand the risks and opportunities of new deployments, though the question of which is the role of energyconsumption in NGANs seems off the table. Thus, this paper proposes amodel to analyze the energyconsumption of the main fiber-based NGAN architectures, i.e. Fiber To The House (FTTH) in both Passive Optical Network (PON) and Point-to-Point (PtP) variations, and FTTx/VDSL. The aim of this analysis is to provide deeper insight on the impact of new deployments on the energyconsumption of the ICT sector and the effects of energyconsumption on the life-cycle cost of NGANs. The paper presents also an energyconsumption comparison of the presented architectures, particularized in the specific geographic and demographic distribution of users of Spain, but easily extendable to other countries.

Semantic technologies in idea management systems: a model for interoperability, linking and filtering

Abstract Idea Management Systems are web applications that implement the notion of open innovation though crowdsourcing. Typically, organizations use those kind of systems to connect to large communities in order to gather ideas for improvement of products or services. Originating from simple suggestion boxes, Idea Management Systems advanced beyond collecting ideas and aspire to be a knowledge management solution capable to select best ideas via collaborative as well as expert assessment methods. In practice, however, the contemporary systems still face a number of problems usually related to information overflow and recognizing questionable quality of submissions with reasonable time and effort allocation. This thesis focuses on idea assessment problem area and contributes a number of solutions that allow to filter, compare and evaluate ideas submitted into an Idea Management System. With respect to Idea Management System interoperability the thesis proposes theoretical model of Idea Life Cycle and formalizes it as the Gi2MO ontology which enables to go beyond the boundaries of a single system to compare and assess innovation in an organization wide or market wide context. Furthermore, based on the ontology, the thesis builds a number of solutions for improving idea assessment via: community opinion analysis (MARL), annotation of idea characteristics (Gi2MO Types) and study of idea relationships (Gi2MO Links). The main achievements of the thesis are: application of theoretical innovation models for practice of Idea Management to successfully recognize the differentiation between communities, opinion metrics and their recognition as a new tool for idea assessment, discovery of new relationship types between ideas and their impact on idea clustering. Finally, the thesis outcome is establishment of Gi2MO Project that serves as an incubator for Idea Management solutions and mature open-source software alternatives for the widely available commercial suites. From the academic point of view the project delivers resources to undertake experiments in the Idea Management Systems area and managed to become a forum that gathered a number of academic and industrial partners. Resumen Los Sistemas de Gestión de Ideas son aplicaciones Web que implementan el concepto de innovación abierta con técnicas de crowdsourcing. Típicamente, las organizaciones utilizan ese tipo de sistemas para conectar con comunidades grandes y así recoger ideas sobre cómo mejorar productos o servicios. Los Sistemas de Gestión de Ideas lian avanzado más allá de recoger simplemente ideas de buzones de sugerencias y ahora aspiran ser una solución de gestión de conocimiento capaz de seleccionar las mejores ideas por medio de técnicas colaborativas, así como métodos de evaluación llevados a cabo por expertos. Sin embargo, en la práctica, los sistemas contemporáneos todavía se enfrentan a una serie de problemas, que, por lo general, están relacionados con la sobrecarga de información y el reconocimiento de las ideas de dudosa calidad con la asignación de un tiempo y un esfuerzo razonables. Esta tesis se centra en el área de la evaluación de ideas y aporta una serie de soluciones que permiten filtrar, comparar y evaluar las ideas publicadas en un Sistema de Gestión de Ideas. Con respecto a la interoperabilidad de los Sistemas de Gestión de Ideas, la tesis propone un modelo teórico del Ciclo de Vida de la Idea y lo formaliza como la ontología Gi2MO que permite ir más allá de los límites de un sistema único para comparar y evaluar la innovación en un contexto amplio dentro de cualquier organización o mercado. Por otra parte, basado en la ontología, la tesis desarrolla una serie de soluciones para mejorar la evaluación de las ideas a través de: análisis de las opiniones de la comunidad (MARL), la anotación de las características de las ideas (Gi2MO Types) y el estudio de las relaciones de las ideas (Gi2MO Links). Los logros principales de la tesis son: la aplicación de los modelos teóricos de innovación para la práctica de Sistemas de Gestión de Ideas para reconocer las diferenciasentre comu¬nidades, métricas de opiniones de comunidad y su reconocimiento como una nueva herramienta para la evaluación de ideas, el descubrimiento de nuevos tipos de relaciones entre ideas y su impacto en la agrupación de estas. Por último, el resultado de tesis es el establecimiento de proyecto Gi2MO que sirve como incubadora de soluciones para Gestión de Ideas y herramientas de código abierto ya maduras como alternativas a otros sistemas comerciales. Desde el punto de vista académico, el proyecto ha provisto de recursos a ciertos experimentos en el área de Sistemas de Gestión de Ideas y logró convertirse en un foro que reunión para un número de socios tanto académicos como industriales.

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

A Simplified Energy Consumption Model for Fibre-Based Next Generation Access Networks

Presentación realizada en el PhD Seminar del ITS 2011 en Budapest. ICTs (Information and Communication Technologies) currently account for 2% of total carbon emissions. However, although modern standards require strict measures to reduce energy consumption across all industrial and services sectors, the ICT sector also faces an increase in services and bandwidth demand. The deployment of Next Generation Networks (NGN) will be the answer to this new demand; more specifically, Next Generation Access Networks (NGANs) will provide higher bandwidth access to users. Several policy and cost analyses are being carried out to understand the risks and opportunities of new deployments, but the question of what role energy consumption plays in NGANs seems off the table. Thus, this paper proposes a model to analyse the energy consumption of the main fibre-based NGAN architectures: Fibre To The House (FTTH), in both Passive Optical Network (PON) and Point-to-Point (PtP) variations, and FTTx/VDSL. The aim of this analysis is to provide deeper insight on the impact of new deployments on the energy consumption of the ICT sector and the effects of energy consumption on the life-cycle cost of NGANs. The paper also presents an energy consumption comparison of the presented architectures, particularised to the specific geographic and demographic distribution of users of Spain but easily extendable to other countries.

A damage model for seismic retrofitting of structures

Numerous damage models have been developed in order to analyse the seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of Continuum Damage Mechanics are more consistent with the definition of damage like a phenomenon with mechanical consequences as they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, many of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Flórez is made in order to include the low cycle fatigue. Such model employs in its formulation irreversible thermodynamics and internal state variable theory.

Quantity of CO2 Emissions in the Life Cycle of a Highway Infrastructure.

The complexity of climate change and its evolution during the last few years has a positive impact on new developments and approaches to reduce the emissions of CO2. Looking for a methodology to evaluate the sustainability of a roadway, a tool has been developed. Life Cycle Assessment (LCA) is being accepted by the road industry to measure and evaluate the environmental impacts of an infrastructure, as the energy consumption and carbon footprint. This paper describes the methodology to calculate the CO2 emissions associated with the energy embodied on a roadway along its life cycle, including construction, operations and demolition. It will assist to find solutions to improve the energy footprint and reduce the amount of CO2 emissions. Details are provided of both, the methodology and the data acquisition. This paper is an application of the methodology to the Spanish highways, using a local database. Two case studies and a practical example are studied to show the model as a decision support for sustainable construction in the road industry.

A management model for closed-loop supply chains of reusable articles

This PhD dissertation is framed in the emergent fields of Reverse Logistics and ClosedLoop Supply Chain (CLSC) management. This subarea of supply chain management has gained researchers and practitioners' attention over the last 15 years to become a fully recognized subdiscipline of the Operations Management field. More specifically, among all the activities that are included within the CLSC area, the focus of this dissertation is centered in direct reuse aspects. The main contribution of this dissertation to current knowledge is twofold. First, a framework for the so-called reuse CLSC is developed. This conceptual model is grounded in a set of six case studies conducted by the author in real industrial settings. The model has also been contrasted with existing literature and with academic and professional experts on the topic as well. The framework encompasses four building blocks. In the first block, a typology for reusable articles is put forward, distinguishing between Returnable Transport Items (RTI), Reusable Packaging Materials (RPM), and Reusable Products (RP). In the second block, the common characteristics that render reuse CLSC difficult to manage from a logistical standpoint are identified, namely: fleet shrinkage, significant investment and limited visibility. In the third block, the main problems arising in the management of reuse CLSC are analyzed, such as: (1) define fleet size dimension, (2) control cycle time and promote articles rotation, (3) control return rate and prevent shrinkage, (4) define purchase policies for new articles, (5) plan and control reconditioning activities, and (6) balance inventory between depots. Finally, in the fourth block some solutions to those issues are developed. Firstly, problems (2) and (3) are addressed through the comparative analysis of alternative strategies for controlling cycle time and return rate. Secondly, a methodology for calculating the required fleet size is elaborated (problem (1)). This methodology is valid for different configurations of the physical flows in the reuse CLSC. Likewise, some directions are pointed out for further development of a similar method for defining purchase policies for new articles (problem (4)). The second main contribution of this dissertation is embedded in the solutions part (block 4) of the conceptual framework and comprises a two-level decision problem integrating two mixed integer linear programming (MILP) models that have been formulated and solved to optimality using AIMMS as modeling language, CPLEX as solver and Excel spreadsheet for data introduction and output presentation. The results obtained are analyzed in order to measure in a client-supplier system the economic impact of two alternative control strategies (recovery policies) in the context of reuse. In addition, the models support decision-making regarding the selection of the appropriate recovery policy against the characteristics of demand pattern and the structure of the relevant costs in the system. The triangulation of methods used in this thesis has enabled to address the same research topic with different approaches and thus, the robustness of the results obtained is strengthened.

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.