On asymptotic motions of a heavy rigid body in the Bobylev--Steklov case
The Bobylev--Steklov solution belongs to one of the most well-known particular solutions of the Euler--Poisson equation of the problem of motion of a heavy rigid body with a ﬁxed point. It is characterized by two linear invariant relations and can be expressed as elliptic functions of time. The interpretation of the motion of the Bobylev--Steklov gyroscope was carried out by P. V. Kharlamov using the Poinsot method. Analysis of the neighborhood of the Bobylev--Steklov solution in the integral manifold of the Euler--Poisson equations was presented by B. S. Bardin for the case where this solution describes pendulum motions. It is therefore of interest to study the general case of the above-mentioned manifold. Using the ﬁrst Lyapunov method, a new class of asymptotic motions is obtained for a heavy rigid body whose limit motions are described by the Bobylev--Steklov solution.