ПРО СТІЙКІСТЬ РІВНОМІРНОГО ОБЕРТАННЯ У СЕРЕДОВИЩІ З ОПОРОМ НЕСИМЕТРИЧНОГО ТВЕРДОГО ТІЛА ПІД ДІЄЮ ПОСТІЙНОГО МОМЕНТУ У ІНЕРЦІАЛЬНІЙ СИСТЕМІ ВІДЛІКУ

Abstract

Assuming that the center of mass of a rigid asymmetric body is on the third main axis of inertia of a rigid body, the conditions for the asymptotic stability of uniform rotation of a dynamically asymmetric solid rigid body with a fixed point are obtained. These conditions are obtained in the form of a system of three inequalities based on the Lénard-Shipar test, written in innormal form. The rigid body is under the action of gravity, dissipative moment and constant moment in the inertial frame of reference. The rotation of a rigid asymmetric body around the center of mass is studied. Uniform rotation around the center of mass of a rigid asymmetric body will be unstable in the absence of a constant moment. Cases of absence of dynamic or dissipative asymmetry are considered. It is shown that the equilibrium position of a rigid body will be stable only under the action of the reducing moment. Dynamic asymmetry has a more significant effect on the stability of rotation of an asymmetric rigid body than dissipative asymmetry. Stability conditions have been studied for various limiting cases of small or large values of restoring, overturning, or constant moments. It is noted that for sufficiently large values of the modulus of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. If the axial moment of inertia is the greatest or the smallest moment of inertia, then at sufficiently large values of angular velocity, both under the action of the overturning moment and under the action of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. Analytical studies of the influence of dissipative, constant, overturning and restorative moments on the stability of uniform rotations of asymmetric and symmetric solids have been carried out. It is shown that in the absence of dynamic and dissipative symmetries, the obtained stability conditions coincide with the known ones.