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Mathematics and Mechanics of Solids
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Dynamics of a Chain of Springs with Nonconvex Potential Energy

Franco Cardin

Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Belzoni, 7-35131, Padova, Italy

Marco Favretti

Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Belzoni, 7-35131, Padova, Italy

We study the dynamics of a discretized model of an elastic bar in a hard device formed by a chain of point masses connected by nonlinear springs whose total length is a controlled parameter. We compare the description of the system dynamics given by the first-order (gradient) dynamics, the second-order (Newtonian) dumped dynamics and the Relaxation Oscillation Theory. Using a technique based on Liapunov's second method, we prove a dynamic stability result concerning the above-mentioned ODEs.

Key Words: Relaxation Oscillation Theory • nonconvex potential energy • springs

Mathematics and Mechanics of Solids, Vol. 8, No. 6, 651-669 (2003)
DOI: 10.1177/1081286503031176
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