INTRODUCTION
One of the wonders of the modern E lectronic Age is the computer or "Giant Brain", as it is
som etim es called. Actually, the computer is not a "B rain ” at all, since it does not think but
must be "told" what to do. It is capable of doing mathematical operations at much greater speed
and with greater accuracy than human beings.
A computer is a machine which perform s physical operations that can be described by mathe
matical operations. In general, computers may be classified as digital or analog. Digital
com puters operate by discrete steps, that is, they actually count. Common exam ples of digital
com puters are the abacus, desk calculator, punched-card machine, and the modern electron ic
digital computer. The fundamental operations perform ed by the digital computer are usually
addition and subtraction. Multiplication, for example, is accomplished by repeated additions.
Analog com puters operate continuously, that is, they measure. Examples of analog com puters
are the slide rule (which m easures lengths), the mechanical differential analyzer, the e le c tro
mechanical analog computer and the a ll-electron ic analog computer. The last three generally
measure electrical voltages or shaft rotations. Physical quantities such as weight, temperature
or area are represented by voltages. Voltage is the electrical analog of the variable being
analyzed. A rbitrary scale factors are set up to relate the voltages in the computer to the var
iables in the problem being solved. For example, 1 volt equals 5 feet or 10 volts equals 1 pound.
The name "analog" com es from the fact that the computer solves by analogy by using physical
quantities to represent numbers.
The fact that the analog computer operates continuously makes it very useful in such operations
as integration; for this reason com puters used this way are som etim es known as Differential
Analyzers.
One of the most powerful applications of analog com puters is simulation in which physical
properties, not easily varied, are represented by voltages which are easily varied. Thus the
"knee action" of an automobile front wheel suspension can be simulated on an analog computer
in which the weight of the automobile, the constant of the spring, the damping of the shock ab
sorb er, the nature of the road surface, the tire pressure and other conditions can be repre
sented by voltages. In practice these factors cannot be readily changed, but on the computer
any one or all of these may be varied at will and the results observed as the changes are made.
Analog com puters are especially useful in solving dynamic problems in which the motion can be
expressed in the form of a differential equation.
All mathematical operations necessary to the solution of ordinary differential equations can be
built up from addition, multiplication by a constant, and integration. * As will be shown later,
the analog computer can perform these operations and thus is a convenient device for the solution
of differential equations.
The combination of the six basic computer operations will perform any continuous function.
Some of the types of problem s which can be solved by these methods are radioactive decay,
chem ical reaction, beam oscillation and heat flow. With the addition of crystal diodes and r e
lays, simulation of discontinuous functions is possible. This makes possible solution of prob
lem s involving saturation, backlash, hysteresis, friction, limit stops, vacuum tube character
istics, and different modes of operation such as sonic vs. subsonic flow.
* Shannon, C ., JOURNAL MATH. AND PHYSICS, Vol. 20, Pages 337-354, 1941.
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