Julio G. Dix, César A. Terrero-Escalante
Department of Mathematics
Texas State University
601 University Drive, San Marcos, TX 78666, USA
e-mail: jd01@txstate.edu
Departamento de Física Teórica
Instituto de Física
Universidade do Estado do Rio de Janeiro
Maracanã, 20559-900 RJ, BRAZIL
e-mail: cterrero@dft.if.uerj.br

Abstract.This article concerns the stability of a model for mass-spring systems with positive damping and negative stiffness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the variable coefficients 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.

Received: May 30, 2007

AMS Subject Classification: 34D20, 70J25

Key Words and Phrases: negative stiffness, mass-spring systems, stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 3