Accession Number:

AD0255856

Title:

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

Descriptive Note:

Corporate Author:

STANFORD UNIV CALIF STANFORD ELECTRONICS LABS

Personal Author(s):

Report Date:

1961-04-24

Pagination or Media Count:

1.0

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 FH 0 or Lq double prime Rq prime gq 0 where C capacitance, G conductance, L inductance, R resistance, H flux, q charge, and fH and gq 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 fH or gq contains a linear term and a cubic term only. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE