Stability of one-degree-of-freedom system under velocity and acceleration dependent nonconservative forces

An analysis of the stability of linear and nonlinear nonautonomous single-degree-of-freedom systems loaded with nonconservative forces dependent on the state of their displacements, velocities and accelerations is presented. In the linear case, analytical formulas for the boundaries of the stability regions are generated by means of the Floquet theory and symbolic mapping tools. In stability analysis of a nonlinear system, the cell-to-cell mapping technique and multiresolution with Daubechieus wavelet analysis are used.