Abstract
The stability of modes at rest in non-linear mechanical systems which have one active mode undergoing chaotic oscillations is considered. A general formulation is developed for these systems. Results from the theory of almost sure stability (Infante [1]) for stochastic systems are briefly reviewed in order to determine the minimal statistical measures of the chaos which are required to determine the stability of the inactive modes. A specific non-linear two-degree-of-freedom system is then considered for which these measures can be explicitly estimated by using a method developed by Brunsden et al. [2, 3]. Analytical results for the almost sure stability of the inactive mode are obtained and compared with simulation results.
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