Abstract :
For any linear, constant-coefficient, electrical network, it is shown that a general functional matrix exists which may be used to determine a very large class of functionals of the free motion of network variables directly in terms of component values without an intermediate determination of the explicit form of network behaviour. This general-functional matrix is formed in a systematic way from the network linear functional matrix, and the effect of time-weighting functions is formally interpreted in terms of a matrix Laplace transform of the time-weighting function. The functional calculation method developed is extended to the investigation of impulse-, step- and ramp-response functionals by the use of equivalent free-motion systems. The use of functionals in engineering dynamical system investigations is briefly reviewed.
