Free work and control of equilibrium configurations

Let C* be a equilibrium configuration of a thermo-visco-elastic material. The paper aims to reach three objectives; i) control of perturbations to C* in terms of the data, if forces are conservatives, and C* is a local proper minimum for the total energy ε; ii) asymptotic decay to zero of perturbations to C*, in case of dissipative systems if C* is a local proper minimum for ε; iii) non-linear instability, if forces are conservatives, and C* is a local proper maximum for ε. In order to reach these goals we adopt qualitative methods in the wake of direct Lyapunov methods. Precisely, first we use the concept of power to construct a Lyapunov functional appropriate to furnish stability in the mean (control of perturbations to velocity and positions), when ε has a minimum at C*; then introducing thefree work we deduce apivot equation for the study of nonlinear stability. In particular, the pivot equation provides and asymptotic stability for dissipative systems toward C*, if C* is a local p...