"The subject of computer modeling evolved from analog computing, which gained its majority in the mid twentieth century and was then superseded by digital simulation. In the next five years computer models will serve as the engine that simulates virtual reality within a user interface that exploits the products of the computer games industry. The future may include the increasing use of 3D displays with animation, and computer inputs that come from the user via 3D digital cameras"-- Provided by publisher.
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Description based on print version record and CIP data provided by publisher; resource not viewed.
Contents
1. Introduction -- 1.1 Engineering Uses of Computer Models -- 1.1.1 Mission Statement -- 1.2 The Subject Matter -- 1.3 Mathematical Material -- 1.4 Some Remarks -- Bibliography -- 2 From Computer Hardware to Software -- 2.1 Introduction -- 2.2 Computing Machines -- 2.2.1 The Software Interface -- 2.3 Computer Programming -- 2.3.1 Algebraic Expressions -- 2.3.2 Math Functions -- 2.3.3 Computation Loops -- 2.3.4 Decisionmaking -- 2.3.5 Graphics -- 2.3.6 User Defined Functions -- 2.4 State Transition Machines -- 2.4.1 A Binary Signal Generator -- 2.4.2 Operational Control of an Industrial Plant -- 2.5 Difference Engines -- 2.5.1 Difference Equation to Calculate Compound Interest -- 2.6 Iterative Programming -- 2.6.1 Inverse Functions -- 2.7 Digital Simulation of Differential Equations -- 2.7.1 Rectangular Integration -- 2.7.2 Trapezoidal Integration -- 2.7.3 Second Order Integration -- 2.7.4 An Example -- 2.8 Discussion -- 2.9 Exercises -- References -- 3. Creative Thinking and Scientific Theories -- 3.1 Introduction -- 3.2 The Dawn of Astronomy -- 3.3 The Renaissance -- 3.3.1 Galileo -- 3.3.2 Newton -- 3.4 Electromagnetism -- 3.4.1 Magnetic Fields -- 3.4.2 Electromagnetic Induction -- 3.4.3 Electromagnetic Radiation -- 3.5 Aerodynamics -- 3.5.1 Vector Flow Fields -- 3.6 Discussion -- References -- 4. Calculus and the Computer -- 4.1 Introduction -- 4.2 Mathematical Solution of Differential Equations -- 4.3 From Physical Analogs to Analog Computers -- 4.4 Picard's Method for Solving a Nonlinear Differential Equation -- 4.4.1 Mechanization of Picard's Method -- 4.4.2 Feedback Model of the Differential Equation -- 4.4.3 Approximate Solution by Taylor Series -- 4.5 Exponential Functions and Linear Differential Equations -- 4.5.1 Taylor Series to Approximate Exponential Functions -- 4.6 Sinusoidal Functions and Phasors -- 4.6.1 Taylor Series to Approximate Sinusoids -- 4.7 Bessel's Equation -- 4.8 Discussion -- 4.9 Exercises -- References -- 5. Science and Computer Models -- 5.1 Introduction -- 5.2 A Planetary Orbit around a Stationary Sun -- 5.2.1 An Analytic Solution for Planetary Orbits -- 5.2.2 A Difference Equation to Model Planetary Orbits -- 5.3 Simulation of a Swinging Pendulum -- 5.3.1 A Graphical Construction to Show the Motion of a Pendulum -- 5.3.2 Truncation and Roundoff Errors -- 5.4 Lagrange's Equations of Motion -- 5.4.1 A Double Pendulum -- 5.4.2 A few Comments -- 5.4.3 Modes of Motion of a Double Pendulum -- 5.4.4 Structural Vibrations in an Aircraft -- 5.5 Discussion -- 5.6 Exercises -- References -- 6. Flight Simulators -- 6.1 Introduction -- 6.2 The Motion of an Aircraft -- 6.2.1 The Equations of Motion -- 6.3 Short Period Pitching Motion -- 6.3.1 Case Study of Short Period Pitching Motion -- 6.3.2 State Equations of Short Period Pitching -- 6.3.3 Transfer Functions of Short Period Pitching -- 6.3.4 Frequency Response of Short Period Pitching -- 6.4 Phugoid Motion -- 6.5 User Interfaces -- 6.6 Discussion -- 6.7 Exercises -- References -- 7. Finite Element Models and the Diffusion of Heat -- 7.1 Introduction -- 7.2 A Thermal Model -- 7.2.1 A Finite Element Model Based on an Electrical Ladder Network -- 7.2.2 Free Settling from an Initial Temperature Profile -- 7.2.3 Step Response Test -- 7.2.4 State Space Model of Diffusion -- 7.3 A Practical Application -- 7.4 Two-dimensional Steady-state Model -- 7.5 Discussion -- 7.6 Exercises -- References -- 8. Wave Equations -- 8.1 Introduction -- 8.2 Energy Storage Mechanisms -- 8.2.1 Partial Differential Equation Describing Propagation in a Transmission Line -- 8.3 A Finite Element Model of a Transmission Line -- 8.4 State Space Model of a Standing Wave in a Vibrating System -- 8.4.1 State Space Model of a Multiple Compound Pendulum -- 8.5 A Two-dimensional Electromagnetic Field -- 8.6 A Two-Dimensional Potential Flow Model -- 8.7 Discussion -- 8.8 Exercises -- References -- 9. Uncertainty and Softer Science -- 9.1 Introduction -- 9.2 Empirical and 'Black Box' Models -- 9.2.1 An Imperfect Model of a Simple Physical Object -- 9.2.2 Finite Impulse Response Models -- 9.3 Randomness Within Computer Models -- 9.3.1 Random Number Generators and Data Analysis -- 9.3.2 Statistical Estimation and the Method of Least Squares -- 9.3.3 A State Estimator -- 9.3.4 A Velocity Estimator -- 9.3.5 A FIR Filter -- 9.4 Economic, Geo-, Bio- and other Sciences -- 9.4.1 A Pricing Strategy -- 9.4.2 The Productivity of Money -- 9.4.3 Comments on Business Models -- 9.5 Digital Images -- 9.5.1 An Image Processor -- 9.6 Discussion -- 9.7 Exercises -- References -- 10. Computer Models in a Development Project -- 10.1 Introduction -- 10.1.1 The Scope of this Chapter -- 10.2 A Motor Drive Model -- 10.2.1 A Concepual Model -- 10.2.2 The Motor Drive Parameters -- 10.2.3 Creating the Simulation Model -- 10.2.4 The Electrical and Mechanical Subsystems -- 10.2.5 System Integration -- 10.2.6 Configuration Management -- 10.3 The Definition Phase -- 10.3.1 Selection of a Motor -- 10.3.2 Simulation of Load Disturbances -- 10.4 The Design Phase -- 10.4.1 Calculation of Frequency Response -- 10.4.2 The Current Control Loop -- 10.4.3 Design Review and Further Actions -- 10.4.4 Rate Feedback -- 10.5 A Setback to the Project -- 10.5.1 Elastic Coupling between Motor and Load -- 10.6 Discussion -- 10.7 Exercises -- Reference -- 11. Postscript -- 11.1 Looking Back -- 11.2 The Operation of a Simulation Facility -- 11.3 Looking Forward -- References -- Appendix A Frequency Response Methods -- A.1 Complex Exponential Functions -- A.2 Frequency Response -- A.3 Fourier Series -- A.3.1 Fourier Spectrum and Laplace transform -- A.4 Power Spectra -- A.4.1 Effect of Sampling on a Power Spectrum -- A.5 Pulse Width Modulation -- A.6 Circuit Analysis -- A.7 Transfer Functions of Time Delays -- A.7.1 Time Delays due to Sampling -- A.7.2 Integration of Sampled Signal -- A.7.3 Alternative Analysis of Discrete Integration -- A.8 Feedback Loops -- A.8.1 Digital PI Controllers -- A.8.2 Programming a PI Controller -- References -- Appendix B Vector Analysis -- B.1 The Use of Vector Analysis -- B.2 Vector Analysis of Motion -- B.2.1 Rotation of a Rigid Body -- B.2.2 Center of Gravity -- B.2.3 Moment of Inertia -- B.2.4 Equations of Motion for a Rigid Body -- Appendix C Scalar and Vector Fields -- C.1 One-dimensional Thermal Systems -- C.1.1 The Diffusion Equation -- C.2 Harmonic Analysis of a One-dimensional Diffusion Equation -- C.2.1 Vibration of a Stretched String -- C.3 Transfer Function Analysis of One-dimensional Wave Propagation -- C.3.1 A Finite Transmission Line -- C.3.2 Transfer Function Analysis of Heat Flow -- C.3.3 The Transfer Function of a Transmission Line -- C.4 Two-dimensional Thermal Systems -- C.4.1 Harmonic Analysis of the Laplace Equation -- C.4.2 The Rotation of a Vector Field -- C.4.3 Vector Operations in Polar Coordinates -- Appendix D Probability and Statistical Models -- D.1 The Laws of Chance -- D.2 The Binomial Distributation -- D.3 The Poisson Distributation -- D.4 The Normal Distributation of Errors (Gaussian Law) -- D.5 Inspection by Sampling -- References --
