Аннотация:Nonlinear spatial oscillations of a material point on a weightless elastic suspension are
considered. The frequency of vertical oscillations is assumed to be equal to the doubled
swinging frequency (the 1:1:2 resonance). In this case, vertical oscillations are unstable,
which leads to the transfer of the energy of vertical oscillations to the swinging energy of
the pendulum. Vertical oscillations of the material point cease, and, after a certain period
of time, the pendulum starts swinging in a vertical plane. This swinging is also unstable,
which leads to the back transfer of energy to the vertical oscillation mode, and again vertical
oscillations occur. However, after the second transfer of the energy of vertical oscillations to the pendulum swinging energy, the apparent plane of swinging is rotated through a certain
angle. These phenomena are described analytically by the normal form method.