Watt regulator dynamics

Abstract

The nonlinear problem on Watt regulator motion mounted on a machine subjected to set vertical harmonic small-amplitude vibrations is considered. The problem on the existence and stability of the periodic motions of the regulator is investigated by the methods of the classical perturbation theory and the Kolmogorov‒Arnold‒Moser (KAM) theory. Under additional assumptions that the regulated-machine vibrations are high-frequency, an integrable approximate set of equations is obtained and it is shown that the majority of its trajectories are retained also in the complete set.