Dynamical behavior of a nonlinear single-degree-of-freedom system with negative viscous and positive frictional damping. (English) Zbl 1238.70017

From the text (conclusion): This short note presents the dynamical behavior of an autonomous nonlinear s.d.o.f. system. A negative viscous damping model and the Coulomb dry friction model are added to the undamped linear system. Where \(-1 < \delta <0\) an unstable limit cycle appears, dividing the phase-plane into the region of stable motion (inside the limit cycle) and unstable motion (outside the limit cycle). In the case of \(\delta \leq -1\) heteroclinic orbits divide the phase-plane into regions of stable and unstable motion. Criteria are established to find out the stability of the the given initial condition.


70K40 Forced motions for nonlinear problems in mechanics
70F40 Problems involving a system of particles with friction
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