The stability of uniformly accelerated motions

Differential equations with quadratic right-hand sides and additional const ant terms are considered. Important examples are self-driven gyroscopes and the problem of the motion of a rigid body in an unbounded volume of ideal fluid subject to a force and a torque which are constant in an attached fra me of reference. Under certain simple conditions, these equations have solu tions that increase linearly with time. In problems of dynamics they descri be uniformly accelerated motions of mechanical systems. The stability of su ch motions is investigated in the first approximation and using bundles of integrals. The general results are used to investigate the stability of uni formly accelerated screw motions of a rigid body in a fluid. (C) 1999 Elsev ier Science Ltd. All rights reserved.