Models with incomplete correspondence with the prototype

The use of analogies is often advantageous in design and in the prediction of the behavior of complex systems. As developed previously, each component in the model (analog) corresponds to a specific component in the prototype (original system). However, this condition is a consequence of using linear relationships between model and prototype. If the condition of linearity is relaxed, the analog may have components which do not correspond to components in the prototype. Consequently, greater freedom is realized in design of the analog making it possible to overcome conflicting design requirements. Application of the nonlinear prediction equations to a forced vibrating system illustrates the general principles involved.