Modeling and Simulation: An Application-Oriented Introduction (Springer Undergraduate Texts in Mathematics and Technology)

By Stefan Zimmer, Martin Buchholz, Dirk Pflüger

Die Autoren führen auf anschauliche und systematische Weise in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik ein. Es geht um Klassen von Modellen und um die Vielfalt an Beschreibungsarten. Aber es geht immer auch darum, wie aus Modellen konkrete Simulationsergebnisse gewonnen werden können. Nach einem kompakten Repetitorium zum benötigten mathematischen Apparat wird das Konzept anhand von Szenarien u. a. aus den Bereichen „Spielen – entscheiden – planen" und „Physik im Rechner" umgesetzt.

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10. 2. 1 Linear version with Saturation .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . 10. 2. 2 Logistic progress . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 10. three Species types . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 10. four A Discrete unmarried Species Model.. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 241 242 242 243 243 245 250 xii Contents eleven keep watch over Engineering .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 1 the fundamentals of keep watch over thought . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 1. 1 regulate Loop .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 1. 2 Description of Linear Dynamical structures . . . . . . . . . . . . . . . . eleven. 1. three necessities for the Controller . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 1. four PID Controller . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 2 Exemplary Modeling of a Multibody process . . .. . . . . . . . . . . . . . . . . . . . eleven. 2. 1 Linearized version with Conservation of Linear and Angular Momentum . . . .. . . . . . . . . . . . . . . . . . . . eleven. 2. 2 whole version with Lagrange Equations . . . . . . . . . . . . . . . eleven. 2. three Simulation of the Pendulum . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. three Fuzzy Set conception .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. three. 1 club in Fuzzy units . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. three. 2 Operations with Fuzzy units . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. three. three Linguistic Variables . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. three. four Fuzzy good judgment .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. four Rule-Based Fuzzy procedure . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. four. 1 Fuzzification . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. four. 2 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. four. three Defuzzification.. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. four. four instance .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. five Fuzzy regulate of the Inverted Pendulum .. . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. five. 1 Parameters and Constraints . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. five. 2 Swinging Up the Pendulum .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. five. three Stabilizing the Pendulum .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . eleven. 6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 263 266 270 271 271 274 276 277 280 281 282 283 284 284 285 286 288 288 12 Chaos conception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. 1 advent .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. 2 From Order to Chaos .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. 2. 1 Logistic Mapping and Its mounted issues . . . . . . . . . . . . . . . . . . . . 12. 2. 2 Numerical research and Bifurcations... . . . . . . . . . . . . . . . . . . . 12. 2. three Transition into Chaos . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. three unusual Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. three. 1 Self-Similarity and Fractal size . . . . . . . . . . . . . . . . . . . . 12. three. 2 Hénon Mapping.. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. three. three common Two-Dimensional Quadratic Mapping . . . . . . . . . . . 12. four Chaotic habit of a pushed Pendulum .. . . . . . .. . . . . . . . . . . . . . . . . . . . 12. four. 1 version of the Pendulum . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 12. four. 2 Discretization .

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