The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration

The inverse problem is posed of stabilizing a spherical pendulum (a mass point at the end weightless solid rod length l ) in given position using high-frequency vibration suspension point. determined by angle between and gravity acceleration vector. For any pendulum, series oblique parameters (amplitude velocity vector vertical) were found that stabilize this position. From obtained solutions, optimal (vibration with minimum amplitude velocity) are selected depending on pendulum. region initial conditions studied, which leads to predetermined stable after sufficiently long time. This area, following N. F.Morozov et al., called area attraction.