  We determine the general form of the potential of the problem of motion of a
rigid body about a fixed point, which allows the angular velocity to remain
permanently in a principal plane of inertia of the body. Explicit solution of
the problem of motion is reduced to inversion of a single integral. A
several-parameter generalization of the classical case due to Bobylev and
Steklov is found. Special cases solvable in elliptic and ultraelliptic
functions of time are discussed.
