Network models for the numerical solution of coupled ordinary non-lineal differential equations

Many apparently simple problems in mechanics or mechanical engineering, particularly problems related to chaotic systems, are governing by coupled differential equations, generally non-lineal, that have to be solved numerically by specialists in this field. The network model, a tool very used in the last decades for numerical problems in different fields of science and engineering, allows that non-specialists, and even students familiarized with circuits theory, to design networks whose governing equations are just those of the engineering phenomenon, assuming a suitable or formal equivalence between electrical and physical variables. The design of the model, which is composed of a principal network, which implements a balance between the addends of the differential equations, and auxiliary networks to implement the derivative terms, follows a standard procedure. Non-lineal terms of the differential equations are implemented by a controlled source, a kind of device whose operation is quite intuitive. In this communication the models of two characteristic non-lineal mechanical problems are designed step by step with a detailed explanation: the elastic pendulum and the chaotic double pendulum: Solutions are presented graphically by using MATLAB