Analyzing Periodic Solutions of an ODE Suspension Bridge Model using Difference Equations and Polynomial Methods
Keywords:
suspension bridge, torsional angle, discrete model, periodic solution, equilibrium, bifurcation, elliptic curve, basin of attraction, global attractivity, eigenvaluesAbstract
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.Â
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