Evolution of Rotations of a Spheroid with a Cavity Filled with a Fluid of High Viscosity
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ution of Rotations of a Spheroid with a Cavity Filled with a Fluid of High Viscosity L. D. Akulenkoa,*†, D. D. Leshchenkob,**, and E. S. Paliyb,*** aIshlinsky
Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia State Academy of Civil Engineering and Architecture, Odessa, 65029 Ukraine *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected]
bOdessa
Received April 15, 2019; revised July 18, 2019; accepted October 4, 2019
Abstract—In a non-standard setting, motion with respect to the center of mass of a spheroid with a cavity filled with a fluid of high viscosity is considered. The moment of forces acting on the body from the side of a viscous fluid in the cavity is determined by the technique developed in the works of F.L. Chernousko. As a result of original asymptotic and numerical calculations, solutions are obtained that describe the evolution of body motion over an infinite time interval with an asymptotically small error. Keywords: spheroid, cavity, viscous fluid, rigid body, averaging DOI: 10.3103/S0025654420020041
1. INTRODUCTION A satellite or a spaceship in its motion relative to the center of mass is subject to the influence of moments of forces of various nature. They are affected, for example, by moments of forces due to the movement of certain masses inside the body. These movements can be associated with the presence of fluid in cavities located in the body (for example, fluid fuel or an oxidizing agent in rocket tanks). The problems of the dynamics of a rigid body with cavities containing a viscous fluid present greater difficulties than in the case of an ideal fluid. An important contribution to the solution of these problems was made by the work of F.L. Chernousko et al. [1, 2]. They consider the movement of a body with a cavity filled with a viscous fluid. An asymptotic solution is obtained that describes the evolution of the motion of a body having a cavity with a fluid of high viscosity over a long time interval. In the work of A.I. Kobrin [3], the initial section of the rotation of a body with a cavity containing a fluid of high viscosity was studied by the boundary layer method. Article [4] is devoted to the study of the stabilizing effect of a viscous fluid in a cavity on the rotation of a top around a given axis. In [5], oscillations in an elliptical orbit of a solid with a spherical cavity filled with a viscous fluid are studied at small Reynolds numbers. In [6], the inertial motion of a rigid body with a spherical or ellipsoidal cavity filled with a viscous fluid is studied by the asymptotic method. In articles [7, 8, 10] and the book [9], fast rotational motions are studied relative to the center of mass of a dynamically asymmetric satellite with a cavity entirely filled with a fluid of high viscosity, under the action of the moments of gravitational forces, light pressure, and medium resistance. In [11], a numerical analysis of the change in the vector of the kinetic moment of a rigid body with a cavity filled wit
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