The Mechanical Differential Analyser: Its Principles, Development, and Applications

Abstract

In the physical sciences differential equations are encountered which are either extremely difficult or impossible to solve by formal methods. For the evaluations of such equations a number of numerical and graphical methods have been developed, together with electrical and other analogues for their direct assessment when the numerical or graphical methods are not practicable. Each analogue will evaluate but one type of equation; the differential analyser—which is not an analogue in this sense but a machine for performing mathematical operations—will, however, evaluate any differential equation (within the capacity of the machine) and present the solution in graphical or tabular form. In the paper the mechanization of integration and other algebraic operations are discussed, and a “non-linear” vibration problem is used as an example of the setting-up and operation of the machine for the solution of a differential equation. Points of special interest in the design and construction of these machines are discussed together with an account of the existing machines. A number of problems of special interest that have been solved by use of the machines are considered and possible lines of development are discussed.