This work aims to study the rotational stability of a tower crane left free to rotate. Indeed, in case of important wind velocities, small oscillations can increase and build up into autorotations due to autoparametric excitation of the structure. Many references in the literature describe the limit between oscillation and autorotation for simple cases like the deterministic pendulum and evidence the importance of the Hamiltonian of a system on its stability. In this context the susceptibility of the structure to this dynamical instability is characterized by the average time necessary to reach a given energy barrier departing from an initial energy level. This first passage time is the solution of the Pontryagin equation and is approached by an asymptotic expansion. First- and second-order terms are calculated as well as the boundary layer solution providing a correction when the initial energy is close to the barrier level.
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