Accession Number : AD0255856

Title :   JACOBIAN ELLIPTIC AND OTHER FUNCTIONS AS APPROXIMATE SOLUTIONS TO A CLASS OF GROSSLY NONLINEAR DIFFERENTIAL EQUATIONS

Corporate Author : STANFORD UNIV CALIF STANFORD ELECTRONICS LABS

Personal Author(s) : SOUDACK,A.C.

Report Date : 24 APR 1961

Pagination or Media Count : 1

Abstract : Research is concerned with grossly non-linear systems, the characteristics of which are lost in the process of linearization or quasi-linearization. To this end, methods are here developed for approximating directly the solution to differential equations of the form CH double prime + GH prime + F(H) = 0 or Lq double prime + Rq prime + g(q) = 0 where C = capacitance, G = conductance, L = inductance, R = resistance, H = flux, q = charge, and f(H) and g(q) are polynomials wih constant coefficients. These equations represent, respectively, electric circuits with non-linear inductor and non-linear capacitor. Conservative systems are considered where R or G is zero. The approximate solution emerges in the form of Jacobian Elliptic functions. The approximations are compared quantitatively with those obtained by the Ritz averaging method. Dissipative systems are also considered wherein R or G is not zero. A study of the machine solutions led to some tentative approximations in which f(H) or g(q) contains a linear term and a cubic term only. (Author)

Descriptors :   *NONLINEAR DIFFERENTIAL EQUATIONS, FUNCTIONS(MATHEMATICS), LEAST SQUARES METHOD, NONLINEAR SYSTEMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE