Relationship between Energy Density and Net Power (Intensity) in Coupled One-Dimensional Dynamic Systems.

摘要

A formalism for the power flow vector of a complex composed of a multitude of one-dimensional dynamic systems has been developed using wave propagation concepts. In this formalism, the complex is defined in terms of two diagonal propagator matrices, two terminal position vectors, and two junction matrices. An element in a propagator matrix describes the manner in which power, in a specific dynamic system, propagates toward a junction. An element in a terminal vector defines the terminal position, in a specific dynamic system, at a junction. A junction is the boundary that defines the coupling among the dynamic systems at a common terminal vector. An element in a junction matrix defines either the coupling (transmission action) between two distinct dynamic systems or the self-coupling (reflection action) at the designated junction. The formalism accounts for the energetics of coupled one-dimensional dynamic systems. Neglecting cross terms between linear propagation toward one and the other junction, that the stored energy density vector is the sum of the stored energy density vector associated with propagation of power toward one junction and with that propagating toward the other junction. Under the same conditions, the net power (intensity) vector is the difference between the power vector associated with power propagation toward one junction and with that propagating toward the other. Since the energy stored and the power flow are simply related by a speed of propagation, the stored energy density vector and the net power (intensity) vector are supplemental quantities. (JHD)