Spatial Oscillations of a Physical Pendulum

The motions of a heavy rigid body with one fixed point and a center of gravity located in the main plane of the energy ellipsoid are investigated. The body admits the motions of a physical pendulum containing a family of pendulum oscillations. The existence of the second spatial family of pendulum oscillations is proved, which, together with Mlodzievskii’s pendulum oscillations, proceed from the lower equilibrium and adjoin the upper equilibrium of the body. The Euler-Poisson equations are used.