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Os simuladores de vôo têm sido uma importante ferramenta para treinamento de pilotos e análise de vôo sem ter que se desembolsar grandes quantias monetárias, economizando combustível e evitando acidentes. Conseqüentemente, a demanda por simuladores de vôo tem aumentado tanto na indústria quanto na pesquisa. Com o intuito de futuramente construir um simulador de vôo, foi desenvolvido um projeto para elaboração de um software capaz de simular uma aeronave em vôo, do ponto de vista de dinâmica de vôo. O software SIMAERO foi desenvolvido na linguagem de programação C++ e simula a dinâmica de vôo de uma aeronave. Esta simulação consiste em resolver as equações de movimento da aeronave, utilizando o modelo matemático de equações diferenciais ordinárias proposto por ETKIN & REID, et al (1996). O modelo matemático é solucionado através do método de integração numérica Runge-Kutta de 4ª ordem conforme apresentado em CONTE (1977). Como parâmetros de entrada são informadas as seguintes características da aeronave: dados geométricos, dados aerodinâmicos e derivadas de estabilidade. Os resultados das simulações são apresentados em gráficos cartesianos e gravados em arquivos. Os gráficos são úteis para que possa ser feita uma posterior análise do comportamento da aeronave. Os arquivos gravados com os resultados das simulações podem ser utilizados em alguma aplicação futura, como sinas de entrada para uma plataforma de simulação, por exemplo. Neste trabalho será descrito como o SIMAERO foi desenvolvido e ao final serão apresentados alguns resultados obtidos. / Flight simulators have been an important tool for pilots training and for flight analyses, without having to spend a high quantity of money, saving gas and prevent accidents. Because of this, the demand for flight simulators has increased both in industry and in research centers. With the objective of in future build a flight simulator, a project to develop a software that is able to simulate the dynamics of flight of a flying aircraft was developed. The SIMAERO software was developed using C++ and its principal functionality is to simulate the dynamics of flight of an aircraft. This simulation basically is the solution of the system of motion equations of the aircraft, using the mathematical model described by ETKIN & REID, et al (1996). The mathematical model is solved using the 4th order Runge-Kutta numeric integration method, as presented in CONTE (1977). For the simulation, the geometric data, the aerodynamic data, and the dimensional derivates are passed to the software as input arguments. The results of the simulations are displayed as cartesians graphics and recorded as data files. The graphics are useful for visual analyses of the aircraft behavior, and the file, with the results of the simulation, can be used as input data for ground based simulator, for example. In this work, the development of the software SIMAERO will be presented, and then some results of the simulation of one aircraft will be shown.

Στο πρώτο κεφάλαιο περιγράφονται οι άμεσες μέθοδοι Runge – Kutta και ο προτεινόμενος ελεγκτής που είναι τύπου PI. Όταν το μέγεθος βήματος περιορίζεται από την αριθμητική ευστάθεια, ένα δυναμικό μοντέλο πρέπει να χρησιμοποιηθεί. Ένα τέτοιο μοντέλο παρήχθη και επαληθεύτηκε αριθμητικά για άμεσες μεθόδους Runge – Kutta. Εδώ περιγράφεται αυτό το δυναμικό μοντέλο. Στο δεύτερο κεφάλαιο περιγράφονται το πρόβλημα της επιλογής μεγέθους βήματος στα έμμεσα σχήματα Runge – Kutta και αναλύεται από μια άποψη ελέγχου ανατροφοδότησης. Οι ιδιότητες του νέου μοντέλου και της βελτιωμένης απόδοσης του νέου ελέγχου σφάλματος περιγράφονται χρησιμοποιώντας και ανάλυση και αριθμητικά παραδείγματα. Στο τρίτο κεφάλαιο αναλύεται και υλοποιείται σε περιβάλλον Μathematica η μη γραμμική διαφορική εξίσωση van der Ρol για μια σειρά από διαφορετικές τιμές της παραμέτρου ε. Επιπλέον σ’ αυτό το κεφάλαιο μελετάται η συμπεριφορά του συστήματος με την μέθοδο Runge-Kutta και με βάση τον ολοκληρωμένο αλγόριθμο του P ελέγχου βήματος. Στο τέταρτο κεφάλαιο περιγράφονται οι βασικές μέθοδοι για την επίλυση μη δύσκαμπτων συστημάτων συνήθων διαφορικών εξισώσεων από χαμηλές σε μεσαίες ανοχές. Εδώ δείχνεται πώς κατασκευάζονται μερικά ζεύγη χαμηλής τάξης χρησιμοποιώντας εργαλεία από την υπολογιστική άλγεβρα. Εστιάζεται η προσοχή μας πάνω σε μεθόδους που εξοπλίζονται με ανίχνευση τοπικού σφάλματος (για προσαρμοστικότητα στο μέγεθος βήματος) και με τη δυνατότητα να ανιχνευθεί η δυσκαμψία. Στο πέμπτο κεφάλαιο υλοποιείται σε περιβάλλον Mathematica η σύγκριση δυο αλγορίθμων ελέγχου (P και PI) του βήματος στην μη γραμμική διαφορική εξίσωση van der Pol υλοποιημένη σε RKclassic και RKdopri μέθοδο Στο έκτο κεφάλαιο μελετάται ένα πραγματικό σύστημα της μορφής y'=Α*y με βάση την μεθοδολογία που το προσομοιώνει η μέθοδος Runge-Kutta σε λογισμικό περιβάλλον Mathematica. Στο τελευταίο (έβδομο) κεφάλαιο γίνεται η σύγκριση του πραγματικού συστήματος και του προσομοιωμένου PI έλεγχου βήματος για τη μέθοδο Runge-Kutta. / -

Os simuladores de vôo têm sido uma importante ferramenta para treinamento de pilotos e análise de vôo sem ter que se desembolsar grandes quantias monetárias, economizando combustível e evitando acidentes. Conseqüentemente, a demanda por simuladores de vôo tem aumentado tanto na indústria quanto na pesquisa. Com o intuito de futuramente construir um simulador de vôo, foi desenvolvido um projeto para elaboração de um software capaz de simular uma aeronave em vôo, do ponto de vista de dinâmica de vôo. O software SIMAERO foi desenvolvido na linguagem de programação C++ e simula a dinâmica de vôo de uma aeronave. Esta simulação consiste em resolver as equações de movimento da aeronave, utilizando o modelo matemático de equações diferenciais ordinárias proposto por ETKIN & REID, et al (1996). O modelo matemático é solucionado através do método de integração numérica Runge-Kutta de 4ª ordem conforme apresentado em CONTE (1977). Como parâmetros de entrada são informadas as seguintes características da aeronave: dados geométricos, dados aerodinâmicos e derivadas de estabilidade. Os resultados das simulações são apresentados em gráficos cartesianos e gravados em arquivos. Os gráficos são úteis para que possa ser feita uma posterior análise do comportamento da aeronave. Os arquivos gravados com os resultados das simulações podem ser utilizados em alguma aplicação futura, como sinas de entrada para uma plataforma de simulação, por exemplo. Neste trabalho será descrito como o SIMAERO foi desenvolvido e ao final serão apresentados alguns resultados obtidos. / Flight simulators have been an important tool for pilots training and for flight analyses, without having to spend a high quantity of money, saving gas and prevent accidents. Because of this, the demand for flight simulators has increased both in industry and in research centers. With the objective of in future build a flight simulator, a project to develop a software that is able to simulate the dynamics of flight of a flying aircraft was developed. The SIMAERO software was developed using C++ and its principal functionality is to simulate the dynamics of flight of an aircraft. This simulation basically is the solution of the system of motion equations of the aircraft, using the mathematical model described by ETKIN & REID, et al (1996). The mathematical model is solved using the 4th order Runge-Kutta numeric integration method, as presented in CONTE (1977). For the simulation, the geometric data, the aerodynamic data, and the dimensional derivates are passed to the software as input arguments. The results of the simulations are displayed as cartesians graphics and recorded as data files. The graphics are useful for visual analyses of the aircraft behavior, and the file, with the results of the simulation, can be used as input data for ground based simulator, for example. In this work, the development of the software SIMAERO will be presented, and then some results of the simulation of one aircraft will be shown.

We use the social force model to study the behaviour of two crowds of pedestrians in a bi-directional flow. There are two main goals of the project. The first goal is to study the effects of perception anisotropy on lane formation of the two crowds. The perception anisotropy models the fact that people actually do not perceive their surroundings equally well in all directions, i.e they have a field of vision. The second goal is to develop pedestrian viscosity indices to characterize the motion of the crowds. Our concepts of viscosity indices estimate how fluid the motion of the crowds are. We develop two viscosity indices. A lane viscosity index which gives information of the flow on large timescales, and a space-dependent viscosity index which can pinpoint where in space the motion is less fluid. Our results indicate that there is a small correlation between the perception anisotropy and the lane formation of the two crowds. The two viscosity indices work as intended but more refinement is needed to cope with simultaneous space-time changes.

En esta tesis se estudia la dinámica del control biológico mediante un modelo matemático de cadena alimenticia simple de tres niveles tróficos. Este modelo matemático esta basado en un modelo depredador presa con respuesta funcional Holling tipo II razón dependiente, incluyendo un depredador superior para obtener un sistema de tres ecuaciones diferenciales ordinarias. Para el cual se estudia la existencia y unicidad, invarianza y acotación de las soluciones. La dinámica del control biológico es estudiada de forma local y asintótica, analizando las condiciones para la coexistencia de las tres especies así como también los escenarios de extinción total y parcial del sistema, de donde vemos cuando tiene o no tiene éxito el control biológico. Los resultados obtenidos fueron contrastados con sus respectivas simulaciones realizadas en un programa desarrollado en la tesis el cual aproxima las soluciones utilizando el método de Runge - Kutta de cuarto orden. PALABRAS CLAVE: DEPREDADOR - PRESA, CADENA ALIMENTICIA, CONTROL BIOLÓGICO, ESCENARIOS DE EXTINCIÓN, ESTABILIDAD ASINTÓTICA, RUNGE-KUTTA. / --- In this work, the dynamic of biological control is studied using a mathematical model of simple food chain of three trophic levels. This mathematical model is based on a predator prey model with holling type II functional response rate dependent. including a top predator described by a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundednees of solutions.

Finding a local minimizer in unconstrained nonlinear optimization and a fixed point of a gradient system of ordinary differential equations (ODEs) are two closely related problems. Quasi-Newton algorithms are widely used in unconstrained nonlinear optimization while Runge-Kutta methods are widely used for the numerical integration of ODEs. In this thesis, hybrid algorithms combining low-order implicit Runge-Kutta methods for gradient systems and quasi-Newton type updates of the Jacobian matrix such as the BFGS update are considered. These hybrid algorithms numerically approximate the gradient flow, but the exact Jacobian matrix is not used to solve the nonlinear system at each step. Instead, a quasi-Newton matrix is used to approximate the Jacobian matrix and matrix-vector multiplications are performed in a limited memory setting to reduce storage, computations, and the need to calculate Jacobian information. For hybrid algorithms based on Runge-Kutta methods of order at least two, a curve search is implemented instead of the standard line search used in quasi-Newton algorithms. Stepsize control techniques are also performed to control the stepsize associated with the underlying Runge-Kutta method. These hybrid algorithms are tested on a variety of test problems and their performance is compared with that of the limited memory BFGS algorithm.

The effect of variable inertia flywheel (VIF) on the driving speed fluctuation, and residual vibration of high speed machine systems is investigated in this thesis. Different variable inertia flywheels are proposed to an experimental purpose roller gear cam system and a commercial super high speed paper box folding machine. The effects of time varying inertia and intermittent cam motion on the dynamic responses of different high speed cam droved mechanism systems are simulated numerically. The nonlinear time varied system models are derived by applying the Lagrange¡¦s equation and torque-equilibrium equations. The dynamic responses of these two nonlinear systems under different operating speed are simulated by employing the 4th order Runge-Kutta method. The effects of VIF parameters on the dynamic responses, i.e. the output precision, variation of motor speed, and torque, during the active and dwell periods for these two systems are studied and discussed. The difference between the dynamic responses of constant inertia and variable inertia flywheel systems are also compared. The feasibility and effectiveness of depression of driving speed and torque fluctuations by analying variable inertia flywheel has also been demonstrated.

The purpose of this study is improve the cage net volume deformation during typhoon attacking. A special bottom collar system is to substitute the sinkers system. The Research contents include the numerical development and the hydrodynamic physical model test in a wave tank. The numerical model is based on the lumped mass method to set up the equation of motion of the whole cage net system; meanwhile the solutions of equation have been solved through the Runge-Kutta fifth order method. The hydrodynamic physical model tests have been carried out to verify the goodness of the numerical model. The research results are as follows. The sinker system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is about 4.54% higher than the physical model results, and the error of net deformation rate is about 8.04% higher. While the bottom collar system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is 6.34% lower than physical model results, and the error of net deformation rate is 3.82% lower. The physical model show that the minimum side projection area deformation rates of net in the bottom collar system is about 4~6% higher than the sinker system¡¦s. According to the conclusions of this study, the presented numerical model is capable to predict the whole cage net system performance and indicates that the bottom collar system is practically feasible in improving the cage net volume deformation.

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