Analyzing Periodic Solutions of an ODE Suspension Bridge Model using Difference Equations and Polynomial Methods

Sukanya Basu

Abstract

In [14], McKenna and Moore studied oscillations in a suspension bridge by investigating periodic solutions to a differential equations model for the bridge and its linearized version numerically. In this paper, the author seeks to build a rigorous mathematical foundation for the numerical experiments of McKenna and Moore in [14] by studying an associated discrete difference equations model using an interplay of ideas from engineering, discrete dynamical systems, algebraic geometry and the theory of polynomials. 

Keywords

suspension bridge, torsional angle, discrete model, periodic solution, equilibrium, bifurcation, elliptic curve, basin of attraction, global attractivity, eigenvalues

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