Initial Conditions in Linear Varying-Parameter Systems
- 1 June 1951
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 22 (6) , 782-786
- https://doi.org/10.1063/1.1700049
Abstract
The problem considered in this paper is that of determining the response of an initially excited linear varying-parameter system to a given input. Mathematically, this problem reduces to solving a linear differential equation (with time-dependent coefficients) subject to prescribed initial conditions. It is shown that these conditions may be satisfied by superposing upon the given input a linear combination of delta-functions and treating the system as if it were initially at rest. Based on this fact and employing the concept of a system function, a general and yet simple expression for the response is developed. The result is similar in form to that obtained by the use of conventional laplace transformation techniques in the case of a linear differential equation with constant coefficients.This publication has 4 references indexed in Scilit:
- Circuit Analysis of Linear Varying-Parameter NetworksJournal of Applied Physics, 1950
- The Generalized Response of Linear Systems for Arbitrary Initial ConditionsJournal of Applied Physics, 1950
- The Determination of the Impulsive Response of Variable NetworksJournal of Applied Physics, 1950
- Frequency Analysis of Variable NetworksProceedings of the IRE, 1950