CALCULATION OF THE 2ND VARIATION IN THE PROBLEM OF THE STABILITY OF THE STEADY MOTION OF A RIGID-BODY CONTAINING A LIQUID

The stability of equilibrium or of steady motion of a rigid body conta ining a liquid is studied. A theorem due to Rumyantsev is used to deri ve the sufficient condition for stability corresponding to a minimum o f the variable potential energy for the transformed rigid body. A proc edure is presented for expressing the second variation of the variable potential energy as a quadratic form in the parameters that define th e position of the body. The calculations are substantially simplified for the problem of the stability of equilibrium or uniform rotation ar ound a fixed axis of a rigid body with liquid in a uniform gravitation al held. Rumyantsev's results are derived anew. (C) 1997 Elsevier Scie nce Ltd. All rights reserved.