Os modelos simplificados de veículos são importantes em fases iniciais do projeto de um veículo, quando muitas características geométricas ainda não estão definidas. No caso de ônibus com sistema de suspensão a ar, os modelos encontrados na literatura não levam em conta efeitos da válvula niveladora de altura. Dois modelos de um ônibus foram desenvolvidos: um modelo não linear de veículo com três graus de liberdade e um modelo em sistema multicorpos com 109 graus de liberdade. Os dois modelos possuem sistema de suspensão a ar com a modelagem termodinâmica do bolsão com a válvula niveladora de altura. As equações do modelo não linear de três graus de liberdade foram construídas utilizando o conceito de derivativos de estabilidade. Para a validação dos modelos, foram realizados ensaios experimentais com o veículo e as seguintes grandezas foram medidas: aceleração lateral, velocidade em guinada, velocidade lateral, ângulo de escorregamento do veículo e ângulo de rolamento. Os resultados obtidos com os modelos foram validados experimentalmente. O comportamento do ângulo de rolamento do veículo devido ao sistema de suspensão a ar foi reproduzido nos dois modelos. Foi desenvolvida uma interface gráfica dentro do ambiente ADAMS para a geração automática de modelos simplificados. Os dados do veículo são inseridos através de uma interface gráfica com caixas de diálogo. Modelos simplificados de veículos são utilizados no controle da dinâmica do veículo. Neste tipo de aplicação, as equações do modelo não linear de três graus de liberdade são resolvidas em tempo real e podem servir como um modelo de referência para sistemas adaptativos de controle. / Simplified vehicle models are very important at the initial stages of vehicle development when all geometric data are not yet available. In the case of a bus with an air suspension system, the models you find in the literature does not taken into account the control leveling valve effects. Two bus models were developed: a nonlinear three degrees of freedom model and a multibody model with 109 degrees of freedom. Both models have thermodynamic air suspension system model with control leveling valve. The three degrees of freedom equations were built using the stability derivative concept. In order to validate the models, experimental tests were carried out and the following variables were measured: lateral acceleration, yaw velocity, sideslip angle and roll angle. The model results were validated against actual data. The roll angle behavior due to air suspension system was reproduced in both models. A graphic user interface for developing simplified vehicle model, based on the nonlinear three degrees of freedom model equations, was built using the ADAMS interface. All the data necessary for the model are introduced via dialog boxes. Simplified vehicle models can be used in vehicle dynamics control. In this kind of application, the three degrees of freedom equations can be solved in real time simulation and can be used as a reference model in adaptive control system, for instance.

Este trabalho realiza uma investigação sobre técnicas experimentais para a determinação de Funções de Resposta em Freqüência (FRFs) angulares com aplicações em estruturas do tipo viga. Estas FRFs são definidas considerando-se como variável de saída o movimento angular (deslocamento, velocidade ou aceleração) exibido pela estrutura sob estudo quando a mesma é excitada por uma força linear ou um momento puro. Dada a grande dificuldade em se aplicar um momento puro à estrutura sob estudo, este trabalho utiliza como forma de excitação apenas esforços lineares que podem ser aplicados através de técnicas usuais de excitação em análise modal, tais como o excitador eletrodinâmico e o martelo impulsivo. Portanto as FRFs obtidas descrevem relações de saída e entrada do tipo Angular/Linear. Uma das técnicas utilizadas na determinação das FRFs angulares consiste na excitação de uma estrutura com um excitador eletrodinâmico e utilização de um corpo rígido na forma de um bloco T que é montado sobre a estrutura sob estudo. Dois acelerômetros lineares devem ser montados sobre o bloco T e a partir das duas acelerações lineares medidas buscam-se estimar um sinal proporcional à aceleração angular da estrutura no ponto de conexão. Outra técnica utiliza uma formulação via diferenças finitas, onde dois ou três acelerômetros (de acordo com a formulação de diferenças finitas utilizada) igualmente espaçados são montados diretamente sobre a estrutura sob estudo e são usados para se derivar à aceleração angular. Os resultados obtidos a partir destas técnicas são comparados com resultados obtidos a partir da utilização de um acelerômetro angular piezelétrico recentemente disponível no mercado. Também foram desenvolvidos modelos analíticos e computacionais via método dos elementos finitos a fim de se gerar subsídios adicionais para a análise dos resultados. Foram feitas várias constatações e dentre elas destacam-se resultados onde as FRFs angulares/lineares resultantes podem sofrer alterações significativas dependendo de como os dados experimentais são processados. / The present work aims to perform an investigation on experimental techniques for the determination of angular Frequency Response Functions (FRFs) in Modal Testing. Angular FRFs are those where the output variable is given by angular displacement, velocity or acceleration, whereas the input is given in terms of linear or angular quantities (a pure moment). Since the application of a pure moment as an excitation source still remains as a challenge, this work is focused in studying techniques to estimate angular/linear types of angular FRFs. One of these techniques consists of exciting the structure with a shaker and using a rigid T-block to measure the linear accelerations and then calculating the angular FRFs from these linear accelerations. Another technique employs finite differences formulations to get the angular motions. This technique uses the closely spaced accelerometers mounted directly to the structure under test, where at least two (according to the finite difference formula employed) accelerometers are used. The translational measurements are gathered and finite difference formulas are used to derive the necessary angular quantities. Additional tests are performed with an angular piezoelectric accelerometer recently available in the market in order to provide a comparison basis for the results obtained using the two techniques. The results are also compared whit theoretical models developed using analytical and Finite Element Formulations. Among all results obtained, it was understood that depending on the level of angular vibrations exhibited by the structure, and how the signals are processed, the resulting angular FRFs can suffer some significant changes

O desbalanceamento de dados em experimentos está muitas vezes presente em diversas pesquisas nas mais variadas áreas do conhecimento. Embora existam muitas maneiras de análise de tais dados, além de diversos recursos computacionais já implementados em diversos softwares estatísticos, ainda perdura dúvidas entre os pesquisadores a respeito da opção de análise mais eficiente. A literatura fornece ao pesquisador direção na escolha da metodologia de análise a obter maior eficácia nos resultados de sua pesquisa, mas o número elevado de opções pode tornar a escolha difícil. Em se tratando de testes estatísticos, algumas das opções para se trabalhar com dados desbalanceados são os testes t e Wald-F, mas ainda resta ao pesquisador decidir entre as várias opções disponíveis nos pacotes, pois nem sempre as opções padrões são as mais indicadas. No presente trabalho foram realizadas simulações com diferentes cenários experimentais, utilizando-se o delineamento casualizado em blocos com um fator de tratamento em uma situação e o esquema de tratamentos em parcelas subdividas em outra, sendo comparados quatro métodos de cálculo do número aproximado de graus de liberdade (Containment, Residual, Satterthwaite e Kenward-Roger). Verificou-se que o método de Kenward-Roger controla de maneira mais eficiente a taxa de erro tipo I e não é inferior aos outros métodos com respeito ao poder do teste Wald-F. / The data imbalance in experiments is often present in several researches in various fields of knowledge. While there are many ways to analyze these data in addition to various computer resources already implemented in many statistical software, doubt still lingers among researchers about the most efficient analysis option. The literature provides the researcher direction in choosing the analysis methodology to get better in your search results, but the large number of options can make the difficult choice. When it comes to statistical tests, some of the options for working with unbalanced data are the tests t and Wald-F, but there is still the researcher to decide between the various options available in the packages because the defaults are not always the most suitable. This experiment was carried out simulations with different experimental scenarios, using the randomized block design with one factor in a situation treatment and treatment regimen subdivided parcels in another, and compared four methods of calculating the approximate number of degrees of freedom (Containment, Residual, Satterthwaite and Kenward-Roger). It has been found that the method of Kenward-Roger controls more efficiently the type I error rate and is not inferior to other methods with respect to the power of the test Wald-F.

Les travaux de cette thèse s'inscrivent dans une collaboration avec l'entreprise Berger-Levrault, acteur majeur du développement de logiciels de gestion administrative pour les services publics. Ces travaux s'appuient sur deux constats. D'une part, la politique de numérisation des services publics induit la nécessité de disposer de logiciels adaptés aux métiers de l'ensemble des établissements publics. Ces logiciels sont complexes et particulièrement riches comparativement aux logiciels de bureautique classiquement utilisés. D'autre part, on observe que les dispositifs utilisés pour interagir avec ces logiciels n'évoluent que très peu. Depuis plusieurs décennies, la souris et le clavier restent la norme dans un environnement fixe. Or, ces dispositifs ne possèdent que peu de degrés de libertés en entrée. La manipulation de données multidimensionnelles avec ceux-ci induit un plus grand nombre d'étapes pour réaliser une tâche, rallongeant ainsi le chemin d'interaction. Dans ce contexte, l'objectif de ces travaux de thèse est de contribuer à la fluidification de l'interaction avec des données multidimensionnelles, contenues dans les logiciels du service public, au travers de l'augmentation des degrés de libertés en entrée proposés par les dispositifs. En effet, une plus grande quantité de degrés de libertés en entrée réduirait le nombre d'étapes nécessaires à la réalisation d'une tâche donnée, fluidifiant ainsi l'interaction. Nous proposons 3 contributions majeures : un dispositif à multiples degrés de libertés, la Roly-Poly Mouse ; un espace de conception, DECO ; ainsi qu'un ensemble de techniques d'interaction avec dispositifs mobiles basées sur le principe du stacking. Une première contribution de nos travaux consiste en la conception d'un nouveau dispositif à multiples degrés de liberté : la Roly-Poly Mouse (RPM). Ce dispositif, dont la base est arrondie, vise à remplacer la souris traditionnelle. Il possède 6 degrés de libertés (3 translations dont 2 exploitées et 3 rotations). Nous avons évalué ses performances et l'avons comparé à d'autres dispositifs pour une tâche nécessitant 6 degrés de libertés (manipulation d'objet 3D). Une seconde contribution de nos travaux consiste en la définition d'un espace de conception se focalisant sur l'aspect physique de la composition de dispositifs : DECO. DECO s'appuie sur deux axes : l'arrangement physique et la manipulation physique. À partir de cet espace de conception, nous avons conçu un dispositif composé : la Roly-Poly Mouse 2, un dispositif composé d'une Roly-Poly Mouse et d'une souris traditionnelle. Nous avons évalué ses performances et l'avons comparé à d'autres dispositifs au travers d'une tâche de RST (Rotate-Scale-Translate, tâche 5D). [...] / The work of this thesis is part of a collaboration with the company Berger-Levrault, a major actor in the development of administrative management software for public services. This work is based on two observations. On the first hand, the policy of digitization of public services induces the need for software adapted to the professions of all public institutions. These software are complex and particularly rich compared to classically used office software (Office, mailbox, etc.). On the other hand, we observe that the devices used to interact with these software did not evolve. Since several decades, the mouse and the keyboard remain the norm in a fixed environment. However, these devices have only few input degrees of freedom. The manipulation of multidimensional data with these devices induces a greater number of steps to perform a task, thus lengthening the interaction path. In this context, the objective of these thesis work is to improve the interaction flow with multidimensional data contained in the software of the public service through the increase of the input degrees of freedom proposed by the devices. Indeed, a larger amount of input degrees of freedom would reduce the number of steps necessary to the accomplishment of a given task, thus improving the interaction flow. We propose three major contributions: a device with multiple degrees of freedom, the Roly-Poly Mouse; a design space, DECO; as well as a set of interaction techniques with mobile devices based on the principle of stacking. A first contribution of our work is the design of a new device with multiple degrees of freedom: the Roly-Poly Mouse (RPM). This device, whose base is rounded, aims to replace the traditional mouse. It has 6 degrees of freedom (3 translations of which 2 exploited and 3 rotations). We evaluated its performance and compared it to other devices for a task requiring 6 degrees of freedom (3D object manipulation). A second contribution of our work is the definition of a design space focusing on the physical aspect of the composition of devices: DECO. DECO relies on two axes: physical arrangement and physical manipulation. From this design space, we designed a compound device: the Roly-Poly Mouse 2, a device consisting of the combination of a Roly-Poly Mouse and a traditional mouse. We evaluated its performance and compared it to other devices through a RST task (Rotate-Scale-Translate, 5D task). [...]

<p>The aim of this thesis is to investigate how the absolute accuracy of an industrial robot can be increased by monitoring the position of the robot. The motive is to automate high precision, low volume production such as aircraft industry. A laser tracker that can measure both position and orientation with very high accuracy isused to monitor the robot tool position. The robot and laser tracker are integrated via a standard computer. </p><p>The abilities and performance of the robot, with and without feedback from the laser tracker, are investigated. Robotic drilling is performed with supervision and control from the laser tracker. </p><p>The system is implemented and tested on parts of a demonstrator for new aircraft assembly techniques. The ability to position components with internal friction to (+/-)0.05 mm absolute accuracy is shown.</p>

Thesis (M.S.)--Air Force Institute of Technology, 2005. / "September 2005" Also available as a PDF file on the Air Force Institute of Technlogy website.

The aim of this thesis is to investigate how the absolute accuracy of an industrial robot can be increased by monitoring the position of the robot. The motive is to automate high precision, low volume production such as aircraft industry. A laser tracker that can measure both position and orientation with very high accuracy isused to monitor the robot tool position. The robot and laser tracker are integrated via a standard computer. The abilities and performance of the robot, with and without feedback from the laser tracker, are investigated. Robotic drilling is performed with supervision and control from the laser tracker. The system is implemented and tested on parts of a demonstrator for new aircraft assembly techniques. The ability to position components with internal friction to (+/-)0.05 mm absolute accuracy is shown.

Η διερεύνηση της περιοχής χωρητικότητας και της περιοχής επιτεύξιμων ρυθμών μετάδοσης καναλιών αποτελεί βασικό αντικείμενο της Θεωρίας Πληροφορίας. Η Ευθυγράμμιση Παρεμβολών είναι μια καινούρια ιδέα που δίνει μια εναλλακτική οπτική στο αντικείμενο αυτό, μέσω της διαφορετικής λογικής που εισάγει σχετικά με την κωδικοποίηση και τη μετάδοση της πληροφορίας. Σε πρόσφατες δημοσιεύσεις έχουν προταθεί μοντέλα που επιτρέπουν την εφαρμογή της θεωρίας της Ευθυγράμμισης Παρεμβολών και τη χρήση της σε πρακτικά συστήματα επικοινωνιών και καταδεικνύουν την υπεροχή της σε σχέση με συμβατικές μεθόδους. Παράλληλα, παρόλο που προς το παρόν έχει δοθεί έμφαση στην εδραίωση της Ευθυγράμμισης Παρεμβολών στις επικοινωνίες, η μαθηματική της βάση καθιστά δυνατή την εφαρμογή της σε αντικείμενα που ανήκουν σε άλλους τομείς. Σκοπός της παρούσας εργασίας είναι η μελέτη και η εφαρμογή της Αναδρομικής Ευθυγράμμισης Παρεμβολών για μετάδοση πληροφορίας σε Συστήματα Επικοινωνιών, καθώς και η διερεύνηση της απόδοσης της μεθόδου σε πρακτικά συστήματα. / The study of the channel capacity region and the achievable rate region is one of the main topics of Information Theory. Interference Alignment is a new idea that provides new insights through the introduction of a different viewpoint on data encoding and transmission. In recent publications, models have been proposed that allow the application of the theory of Interference Alignment to practical communication systems and demonstrate its superiority compared to traditional approaches. Furthermore, although for the time being emphasis has been put on establishing the use of Interference Alignment to communication systems, its mathematical formulation makes possible its use to other areas. The purpose of this thesis is to study and to apply Retrospective Interference Alignment to data transmission in communication systems and to evaluate the performance of the method in practical systems.

Το κύριο μέρος της διατριβής αρχίζει στο Κεφάλαιο 4 όπου παρουσιάζονται πρωτότυπα ερευνητικά αποτελέσματα της διατριβής που αφορούν στην κανονική και χαοτική δυναμική Χαμιλτώνιων συστημάτων λίγων βαθμών ελευθερίας. Περιγράφονται αποτελέσματα πάνω στη συμπεριφορά δεικτών διάκρισης οργανωμένης και χαοτικής δυναμικής στα συστήματα αυτά και γίνεται σύγκριση με τα αντίστοιχα της διεθνούς βιβλιογραφίας. Τέλος, αναφέρονται αποτελέσματα από τη θεωρία και την εφαρμογή της μεθόδου του Γενικευμένου Δείκτη Ευθυγράμμισης GALI, που αποτελεί ένα από τα πιο βασικά νέα στοιχεία της διατριβής, σε μη ολοκληρώσιμα Χαμιλτώνια συστήματα δύο και τριών βαθμών ελευθερίας. Το Κεφάλαιο 5 ασχολείται με την παρουσίαση πρωτότυπων ερευνητικών αποτελεσμάτων σε Χαμιλτώνια δυναμικά συστήματα πολλών βαθμών ελευθερίας. Εδώ, εισάγονται νέες μέθοδοι για την μελέτη των περιοχών κανονικής και χαοτικής συμπεριφοράς συστημάτων πολλών βαθμών ελευθερίας με σκοπό να κατανοηθεί η συμπεριφορά των συστημάτων αυτών στο θερμοδυναμικό όριο και να δοθεί μια απάντηση στο καίριο ερώτημα αν οι νόμοι της Στατιστικής Μηχανικής ισχύουν στην περίπτωση των πολυδιάστατων Χαμιλτώνιων συστημάτων που εξετάζονται εδώ. Ελέγχεται πως αυξάνουν οι χαοτικές περιοχές γύρω από ασταθείς Απλές Περιοδικές Λύσεις (ΑΠΛ) στον χώρο φάσεων, μετά από μία κρίσιμη τιμή της ολικής ενέργειας, η δε μετάβαση από περιορισμένο σε εκτεταμένο χάος, προκύπτει από το ότι συχνά σε περιοχές διαφορετικών ασταθών ΑΠΛ συγκλίνουν τα αντίστοιχα φάσματα Lyapunov στην ίδια εκθετική συνάρτηση. Υπολογίζοντας κατόπιν το άθροισμα των θετικών εκθετών Lyapunov, που αντιστοιχεί στην εντροπία Kolmogorov - Sinai και διαπιστώνεται ότι για τα συστήματα που εξετάζονται στη διατριβή αυτή, η εντροπία KS αυξάνει γραμμικά, συναρτήσει των βαθμών ελευθερίας N, επιβεβαιώνοντας έτσι ότι είναι εκτεταμένη ποσότητα της Στατιστικής Μηχανικής. Τέλος εισάγεται η νέα μέθοδος του Δείκτη Γραμμικής Εξάρτησης (LDI) για τον διαχωρισμό χαοτικών και οργανωμένων τροχιών και αναφέρονται τα συγκριτικά της πλεονεκτήματα σε σχέση με τις μεθόδους των Κεφαλαίων 3 και 4. Αξίζει επίσης να αναφερθεί ότι πολλά αποτελέσματα της διατριβής μπορούν να εφαρμοσθούν για τη μελέτη της δυναμικής συμπλεκτικών απεικονίσεων, για τις οποίες ο κ .Αντωνόπουλος ανέπτυξε μια νέα μέθοδο που συνδυάζει τη χρήση δικών του μεθόδων και των λεγόμενων Διαφοροεξελικτικών Αλγορίθμων, για την εύρεση της δυναμικής ακτίνας ευστάθειας συμπλεκτικών απεικονίσεων που περιγράφουν επιταχυντές σωματιδίων υψηλών ενεργειών. / The main part of the thesis begins with Chapter 3, where new research results are presented which concern the regular and chaotic dynamics of Hamiltonian systems of few degrees of freedom. Results are described on the behavior of indices distinguishing organized from chaotic motion in these systems and a comparison is made with corresponding results in the international literature. Then, new findings are reported on the theory and application of the method of the Generalized Alignment Index GALI, which is one of the most basic discoveries of the thesis in nonintegrable Hamiltonian systems of 2 and 3 degrees of freedom. Chapter 5 deals with the presentation of original research results in Hamiltonian systems of many degrees of freedom. Here new methods are introduced for the study of regions of regular and chaotic behavior of multi degree of freedom systems with the primary aim of understanding the behavior of these systems in the thermodynamic limit to give an answer to the crucial question of whether the laws of Statistical mechanics hold in the case of multi dimensional Hamiltonian systems. The author studies how chaotic regions increase in size around unstable Simple Periodic Orbits (SPOs) in phase space, beyond a critical value of the energy, while the transition from limited to widespread chaos is indicated by the fact that in regions of different unstable SPOs the corresponding Lyapunov spectra converge to the same exponential – like function. Computing then the sum of the positive Lyapunov exponents, which corresponds to the so called Kolmogorov – Sinai entropy, it is shown that the systems that are studied in this thesis the KS entropy increases linearly as a function of the number of degrees of freedom N, thus confirming that it is an extensive quantity of Statistical Mechanics. Finally, the new method of the Linear Dependence Index (LDI) is introduced for distinguishing between regular and chaotic orbits and its advantages are described when compared with the methods of Chapters 3 and 4. It is worth mentioning also that many of the results of this thesis can be applied to the study of the dynamics of symplectic mappings, for which Mr. Antonopoulos developed a new method which combines his techniques with those of Evolutionary Algorithms, for determining the dynamical aperture radius for the stability of symplectic maps which describe the dynamics of high energy particle accelerators.

Στην παρούσα διπλωματική εργασία μελετάμε την κλασική δυναμική ατόμου υδρογόνου σε γενικευμένο δυναμικό Van der Waals. Το πρόβλημα ανήκει στην ευρύτερη κατηγορία των μη γραμμικών Χαμιλτώνιων δυναμικών συστημάτων. Σκοπός της μελέτης είναι η ανάλυση των ιδιομορφιών της κανονικής και χαοτικής κίνησης του συστήματος στο μιγαδικό πεδίο του χρόνου και η εξαγωγή συμπερασμάτων σχετικά με την ολοκληρωσιμότητα και επιλυσιμότητά του. Εκείνο που θέλουμε να κατανοήσουμε, επίσης, είναι τον ρόλο που παίζει η εμφάνιση ιδιομορφιών σε κάποια σημεία του χώρου των φάσεων και κατά πόσο μπορούν αυτές να επηρεάσουν συνολικά τις ιδιότητες των λύσεων. Για πρώτη φορά, επίσης, στην διπλωματική αυτή εργασία εφαρμόζεται σε ένα Χαμιλτώνιο δυναμικό σύστημα μία νέα αριθμητική μέθοδος διάκρισης μεταξύ κανονικής και χαοτικής συμπεριφοράς σε διαφορετικές περιοχές του χώρου φάσεων, η μέθοδος των Μικρότερων Δεικτών Ευθυγράμμισης (Smaller Alignment Indices method ή SALI). Η μέθοδος αυτή έχει χρησιμοποιηθεί κατά το πρόσφατο παρελθόν σε απεικονίσεις δύο, τεσσάρων και έξι διαστάσεων με πολύ ενδιαφέροντα αποτελέσματα. Χαρακτηριστικά της είναι η αποτελεσματικότητα και η δυνατότητα εξαγωγής χρήσιμων συμπερασμάτων ως προς την κανονική και χαοτική φύση των τροχιών ενός δυναμικού συστήματος με μεγαλύτερη ταχύτητα και αξιοπιστία από την μέθοδο των χαρακτηριστικών εκθετών Lyapunov καθώς και άλλων νεότερων μεθόδων στην σύγχρονη βιβλιογραφία. Εδώ θα παρουσιασθεί η μέθοδος αυτή με ορισμένες βελτιώσεις ώστε να μπορεί να εφαρμοσθεί σε συστήματα μη γραμμικών διαφορικών εξισώσεων οποιασδήποτε διάστασης ελέγχοντας συστηματικά ένα όσο πυκνό πλέγμα αρχικών συνθηκών του χώρου φάσεων επιθυμούμε, αντιστοιχώντας σε κάθε μία από αυτές ένα χρώμα. Κάθε χρώμα αντιστοιχεί και σε ένα διαφορετικό εύρος τάξεων του SALI δημιουργώντας έτσι μία συνολική εικόνα στο χώρο φάσεων που μας επιτρέπει να γνωρίζουμε τη φύση της τροχιάς κάθε συγκεκριμένης αρχικής συνθήκης. Σχηματίζεται με αυτόν τον τρόπο το "μωσαϊκό" του χώρου φάσεων και αποκαλύπτονται περιοχές κανονικής κίνησης, χαοτικής κίνησης καθώς και νησίδες ή περιοχές στις οποίες δεν αντιστοιχεί καθόλου κίνηση. / In this master thesis we study the classical dynamics of hydrogen atoms in a generalized Van der Waals potential. The problem belongs to the class of non linear Hamiltonian systems. Our aim is the singularity analysis of the ordered and chaotic motion of the system in the complex plain of time and the extraction of valuable conclusions concerning its integrability and solvability. What we want to understand, also, is the role of the emergence of singularities in some points of the phase space of the aforementioned system and how the singularities can affect globally the properties of the solutions. For the first time, in this master thesis, we introduce and apply in a Hamiltonian system a new numerical method for the fast and efficient discrimination between ordered and chaotic motion in different parts of phase space, namely the method of the Smaller Alignment Index (SALI). The method has been introduced and applied recently in mappings of two, four and six dimensions with very satisfactory results. Its main characteristics are the effectiveness and the ability of extracting valuable conclusions about the ordered and chaotic nature of trajectories of a dynamical system faster than the traditional method of Lyapunov exponents as well as of other indices in the bibliography. We will introduce SALI with appropriate modifications that help using it in non linear systems of differential equations of arbitrary dimensions checking systematically a dense grid of initial conditions and corresponding in every orbit a different color. Every color corresponds to a different range of SALI values creating by that way a global picture of the phase space that allows us to know the dynamic nature of initial conditions. By that way, we construct a “mosaic” of the phase space and reveal parts of ordered motion as well as parts of chaotic motion and islands of stability.