'Twixt Earth and Sky with Rod and Tube; the Mobility and Classical Impedance Analogies

Abstract

The techniques which comprise the mobility analogy have been introduced into the classical impedance analogy. The mobility and impedance analogies are set forth in form for practical use. The completely dual character of these two analogies is rendered evident by placing the elements of the mobility analogy on a series of left-hand pages and the dual elements of the impedance analogy on the facing right-hand pages. In each analogy a set of mechanical and acoustical symbols is provided so that mechanical and acoustical schematic diagrams can be drawn without the necessity of drawing either of the analogous electrical schematic diagrams. These mechanical and acoustical symbols resemble somewhat their analogous electrical symbols so as to indicate to anyone familiar with circuit theory the algebraic operations which are to be performed in the analysis. Whereas in an electrical schematic straight line represents an ideal wire, in a mobility schematic a straight line represents an ideal incompressible massless rod; in an impedance schematic a line represents a hydraulic tube filled with ideal massless incompressible liquid which can sustain either tension or compression. Correct mobility schematics are obtained by inspection through considering each mass as having one terminal fixed in a frame of reference called the earth which has zero mobility and infinite mass and is analogous to electrical ground; correct impedance schematics are obtained by inspection through considering each spring as having one terminal fixed in a force of reference (P0, etc.) called the sky which has zero impedance and infinite compliance (in both cases the analogous electrical element is a conducting sphere in free space, not a condenser). Although it is recommended that analogous electrical circuits not be used in routine analysis, they can be copied directly from a mobility schematic by considering mechanical earth analogous to electrical ground, or copied directly from an impedance schematic by considering mechanical sky analogous to electrical ground.