Some Background Material
The study of the stability of linear dynamical systems is a well-established field and there are many references available in the literature on this subject (see, e.g., [48–50]). In this chapter, a brief review of the relevant material to the subsequent study of the dynamical systems with friction is presented. An important tool in the study of the stability of mechanical systems is the eigenvalue analysis method. The local stability of the system’s equilibrium point is determined by studying the sign of the real part of the eigenvalues of the system’s Jacobian matrix. As parameters are changed, one or more eigenvalues may cross the imaginary axis marking the onset of the instability.