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Calculation of the second variation in the problem of the stability of the steady motion of a rigid body containing a liquid

✍ Scribed by P Capodanno

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
298 KB
Volume
61
Category
Article
ISSN
0021-8928

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✦ Synopsis

The stability of equilibrium or of steady motion of a rigid body containing a liquid is studied. A theorem due to Rumyantsev is used to derive the suflkient condition for stability con'ospondin~ to a minimum of the variable potential ener~ for the transformed rigid body. A procedure is presented for expressing the second variation of the variable potential energy as a quadratic form in the parameters that define the position of the body. The calculations are substantially simplified for the problem of the stability of equih'brium or uniform rotation around a fixed axis of a rigid body with fiqnid in a uniform gravitational field. Rumyantsev's results are derived anew.

πŸ“œ SIMILAR VOLUMES

The β€œrestricted” formulation of the prob
The β€œrestricted” formulation of the problem of the motion of a heavy rigid body
✍ A.A. Burov πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 332 KB

The problem of the motion of a heavy rigid body is considered in the so-called "restricted" formulation, which is obtained on the assumption that two dimensions of the body, which we will call its "width" and "thickness", are considerably less than the third dimension, the "length" of the body. They