JACOBIAN ELLIPTIC AND OTHER FUNCTIONS AS APPROXIMATE SOLUTIONS TO A CLASS OF GROSSLY NONLINEAR DIFFERENTIAL EQUATIONS
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 24, 1961
- Accession Number
- AD0255856
Entities
People
- A.c. Soudack
Organizations
- Stanford University