On the Probability of the Outcomes in Buckling of an Elastic Beam

A nonlinear time-varying one-degree-of-freedom system, which is used for the modelling of the buckling of a loaded beam in Euler’s problem, is considered. For a slowly changing load, the deterministic approach in this problem fails if the trajectories pass through the separatrix. An expression for the probability of possible outcomes of the evolution of the oscillations is obtained. The analytical and numerical results are compared.