This paper presents the stability analysis of a single degree-of-freedom elastic system following a rate-and state-dependent friction law. Normal force is assumed to depend on the displacement, velocity and acceleration of the sliding interface. The history dependence of friction on normal force is included in the analysis. It is shown that to achieve steady sliding, system stiffness must exceed a critical value which depends on the expression for normal force. A system in which normal force depends on spring displacement is analyzed in detail. These results indicate that the functional dependence of normal force on system state can have a significant effect on the stability of low-velocity motion.

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