Network models for the numerical solution of coupled ordinary non-lineal differential equations
Document typeConference report
Rights accessOpen Access
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.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder