Stability of a Uniform Rotation of an Asymmetric Rigid Body in a Resisting Medium under a Constant Moment

• Published in: International applied mechanics 2021-07, Vol.57 (4), p.432-439
• Main Author: Kononov, Yu. M.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Asymmetry; Asymptotic properties; Engineering; Fluid flow; Incompressible flow; Incompressible fluids; Inequalities; Inertia; Moments of inertia; Rigid structures; Rotating bodies; Rotation; Stability
• ISSN: 1063-7095; 1573-8582
• DOI: 10.1007/s10778-021-01095-1

The conditions of asymptotic stability of the uniform rotation of an asymmetric absolutely rigid body in a resisting medium are obtained in the form of a system of three inequalities. The rotation of the rigid body is maintained by a constant moment that is directed along the third principal axis. These inequalities are estimated analytically. It is shown that these conditions are reduced to three inequalities if the moment is overturning and to two inequalities of the moment is restoring. Conditions for the constant moment and the moment of inertia of the third principal axis are obtained, which under the restoring moment are sufficient for the asymptotic stability of the uniform rotation of the rigid body in the resisting medium. If the body rotates around the axis of the largest moment of inertia and the smallest of the doubles, then for the restoring moment, asymptotic stability is observed if the constant moment is sufficiently large. The stability conditions are generalized to the case where the body contains a cavity with an ideal incompressible fluid that undergoes irrotational motion.