The motion of a particle suspended on an ideal thread in a uniform gra
vitational field is investigated. The problem of the orbital stability
of the periodic motion of the particle along the vertical is solved.
The non-linear oscillations in the neighbourhood of the periodic motio
n are considered in the case when the motion is unstable. Normalizatio
n of the Hamilton function using simplectic mappings is employed in th
e investigation. (C) 1996 Elsevier Science Ltd.