Abstract
The motion of a mathematical pendulum whose point of suspension performs small-amplitude horizontal harmonic oscillations is considered. The non-integrability of the equation of motion of the pendulum is established. The periodic motion of the pendulum originating from a stable position of equilibrium is obtained and its stability is investigated. Unstable periodic motions originating from unstable positions of equilibrium are indicated and the separatrice surfaces asymptotic to these motions are determined. The problem of the existence and stability of periodic motions of the pendulum originating from its oscillations with arbitrary amplitude and rotations with arbitrary mean angular velocity is investigated.
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