Blocks, bridges, boilers and graph theory

John Hogan

Several important physical systems have dynamics governed by piecewise linear differential equations. In this talk we shall discuss theoretical approaches to three different problems. In particular we shall demonstrate the excellent agreement with experimental observations in the case of rigid block vibrations and the continuation analysis of equations governing suspension bridge dynamics, including the Tacoma Narrows disaster. Finally we show how graph theory can be used to find all permissible periodic solutions to certain piecewise linear systems and how this can be used to explore the dynamics of a high dimensional system (a heat exchanger boiler).

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