Isolated stable initial perturbations of unstable equilibria of some mechanical systems (Q2291270)

The author considers four different mechanical systems that differ in the number of degrees of freedom: one, two, countable number and continuum. For each of these systems, unstable equilibrium positions are studied and a class of perturbations is established that lead to an exponential tendency to an unstable equilibrium or an oscillatory regime. It is shown that, despite the significant differences between these systems, they are united by the similarity of conditions that characterize such a class of perturbations.