Analog and Hybrid Computer Programming 2nd Edition by Bernd Ulmann ISBN 3110787881 9783110787887

1 Introduction

1.1 What is an analog computer?

1.2 Direct vs. indirect analogies

1.3 A short history of analog computing

1.4 Characteristics of analog computers

2 Computing elements

2.1 Machine units

2.2 Summer

2.3 Integrators

2.4 Free elements

2.5 Potentiometers

2.6 Function generators

2.7 Multiplication

2.8 Comparators and switches

2.9 Input/output devices

3 Analog computer operation

4 Basic programming

4.1 Radioactive decay

4.1.1 Analytical solution

4.1.2 Using an analog computer

4.1.3 Scaling

4.2 Harmonic functions

4.3 Sweep

4.4 Mathematical pendulum

4.4.1 Straightforward implementation

4.4.2 Variants

4.5 Mass-spring-damper system

4.5.1 Analytical solution

4.5.2 Using an analog computer

4.5.3 RLC-circuit

5 Special functions

5.1 Stieltjes integral

5.2 Inverse functions

5.2.1 Square root

5.2.2 Division

5.3 f(t) = 1/t

5.4 Powers and polynomials

5.5 Low pass filter

5.6 Triangle/square wave generator

5.7 Ideal diode

5.8 Absolute value

5.9 Limiters

5.10 Dead zone

5.11 Hysteresis

5.12 Maximum and minimum

5.13 Bang-bang

5.14 Minimum/maximum holding circuits

5.15 Sample & Hold

5.16 Time derivative

5.17 Time delay

5.17.1 Historic approaches to delay

5.17.2 Digitization

5.17.3 Sample and hold circuits

5.17.4 Analog delay networks

5.18 Transfer functions

5.19 Exponentially mapped past

6 Examples

6.1 Displaying polynomials

6.2 Chemical kinetics

6.3 SEIR model

6.4 Damped pendulum with external force

6.5 Mathieu’s equation

6.6 Van der Pol’s equation

6.7 Generating Bessel functions

6.8 Solving the one-dimensional Schrödinger equation

6.9 Ballistic trajectory

6.10 Charged particle in a magnetic field

6.11 Rutherford-scattering

6.12 Celestial mechanics

6.13 Bouncing ball

6.14 Zombie apocalypse

6.15 Rössler attractor

6.16 Lorenz attractor

6.17 Another Lorenz attractor

6.18 Chua attractor

6.19 Nonlinear chaos

6.20 Aizawa attractor

6.21 Nosé-Hoover oscillator

6.22 The SQM model

6.23 The Duffing oscillator

6.24 Rotating spiral

6.25 Generating an Euler spiral

6.26 Hindmarsh-Rose model

6.27 Simulating the flight of a glider

6.28 Flow around an airfoil

6.29 Heat transfer

6.30 Two-dimensional heat transfer

6.31 Systems of linear equations

6.32 Human-in-the-loop

6.33 Inverted pendulum

6.34 Elastic pendulum

6.35 Double pendulum

6.36 Making Music

6.37 Neutron kinetics

6.38 Smooth sorting

7 Hybrid computing

7.1 Hybrid controllers

7.2 Basic operation

7.3 Shell trajectory

7.4 Data gathering

7.5 Training an AI with an analog computer

7.6 Hybrid solution of systems of linear equations

7.7 Solving PDEs with random walks

8 Summary and outlook

A The Laplace transform

A. 1 Basic functions

A. 1.1 Step function

A. 1.2 Delta function

A. 1.3 Ramp function

A. 1.4 Exponential and trigonometric functions

A. 2 Laplace transforms of basic operations

A. 3 Further characteristics

A. 4 Inverse Laplace transform

A. 5 Example

A. 6 Block diagrams and transfers functions

B Solving the heat equation with a passive network

C A simple hybrid controller for THE ANALOG THING

D An oscilloscope multiplexer

E A log() function generator

F A sine/cosine generator

G A simple joystick interface

H The Analog Paradigm bus system

I HyCon commands

Bibliography

Index