Application of mode theory to the analysis of machine systems

The mode theory approach is shown to lead to a complete solution of problems involving machine systems under the normal assumptions necessary to give linear differential equations. Only two basic matrix operations, namely inversion and latent root evaluation, suffice to enable determination of the response to any input applied at any set of terminals. It is shown that there are four distinct types of input for a multi-variate system and in some cases superposition does not apply. The effects of open- and short-circuits and of changes in the circuit parameters are analysed in terms of this classification. An indication is given of how the constants of a system may be evaluated if the modes are known.