Stability of Solutions to Damped Equations with Negative Stiffness

Details Stability of Solutions to Damped Equations with Negative Stiffness Stability of Solutions to Damped Equations with Negative Stiffness

2007-05-31

arxiv.org/abs/0705.4670v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the variable cofficients to prove stability. In particular, we disprove the believe that if the eigenvalues of the system change slowly in time the system remains unstable. We extend some of our results for nonlinear systems.

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