Stability of the spherical motion of a solid body with an inhomogeneous fluid performing a uniform vortex motion-Reference-Cited by-同舟云学术

Stability of the spherical motion of a solid body with an inhomogeneous fluid performing a uniform vortex motion

Published:2023-01 Issue:1 (133) Volume: Page:
ISSN:2308-6033
Container-title:Engineering Journal: Science and Innovation
language:
Short-container-title:EJSI

Author:

Win Ko Ko¹,Temnov A.N.¹,Yan Naing Oo¹

Affiliation:

1. Bauman Moscow State Technical University

Abstract

In this paper, the equations of spherical motion of a solid body with a rotating inhomogeneous incompressible fluid that fills a completely ellipsoidal cavity are obtained and investigated. The stability of rotation of a solid with an inhomogeneous fluid having a linear density distribution is considered. Arbitrary fields of density and velocity of fluid particles are represented as a power series by spatial variables with coefficients that depend only on time. Sufficient conditions for the stability of the rotation of a solid body with a fluid around the vertical axis of dynamic symmetry are presented. The obtained equations of motion make it possible to study the stability of stationary motions of the system under consideration in order to assess the effect of fluid separation on the dynamics of the body. By analogy with the motion of a solid body, it is stated that the obtained conditions are also necessary and sufficient conditions for stationary rotations of an inhomogeneous fluid in an ellipsoidal cavity.

Publisher

Bauman Moscow State Technical University

Subject

General Medicine

Reference20 articles.

1. Zhukovsky N.E. O dvizhenii tverdogo tela, imeyuschego polosti, napolnennye odnorodnoi kapelnoi zhidkostyu [On the motion of a rigid body with cavities filled with homogenous drop-like liquid]. Moscow, BMSTU Publ., 2017, 137 p.

2. Sloudsky Th. De la rotation de la terre supposee fluide a son interieur. Bulletin de la Societe Imperiale des naturalistes de Moscou, 1895, Tome IX, pp. 285–318.

3. Hough S.S. The oscillations of a rotating ellipsoidal shell containing fluid. Philosophical Transactions of the Royal Society of London. A, 1895, vol. 186, part 1, pp. 469–506.

4. Poincare H. Sur la precession des corps deformables. Bulletin astronomique, 1910, vol. 27, pp. 321–356.

5. Derendyaev N.V. Ob ustoichivosti statsionarnogo vrashcheniya tsilindra, zapolnennogo stratifitsirovannoy neszhimaemoy zhidkostyu [Stability of the stationary rotation of a cylinder filled with a stratified viscous incompressible fluid]. Doklady AN SSSR (Reports of the USSR Academy of Sciences), 1983, vol. 272, no. 5, pp. 1073–1076.