
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 nonlinear systems, the characteristics of which are lost in the process of linearization or quasilinearization. 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 nonlinear inductor and nonlinear 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