Inertial motion of a body in an ideal fluid from the state at rest

Abstract

UDC 532; 533 O. V. VoinovThe motion of a body in an ideal incompressible fluid flow without vortices in the absence of external forces is considered. It is demonstrated that the body can move inertially from the state at rest if its shape satisfies certain conditions. Key words: ideal incompressible fluid, vortex-free flow, motion of a body in a fluid, inertia.Introduction. The first studies of motion of various bodies in fluids under the action of internal forces were performed with modeling the motion of living organisms in water. Models of fish motion were developed, based on models of motion of bodies in a vortex-free flow of an inviscid fluid. Such a model of motion due to finite deformations of the body in a fluid was proposed in [1].The general features of motion of deformable bodies in an ideal fluid from the state at rest were summarized in [2]. The possibility of motion of the body in an ideal fluid due to body deformations and changes in the mass distribution inside the body was verified in [3]. Examples of motion of a pulsing sphere and an ellipsoid with a variable eccentricity and examples of motion of a body due to small deformations defined by two parameters were also given in [3].The motion of a deformable body in a fluid can be described by the Lagrangian equations. Based on these equations, axisymmetric and plane flows around bodies were studied, and conditions were found, which restrict the possibility of body motion for arbitrary given laws of variation of the body shape and changes in the mass distribution inside the body [4].A problem of motion of a nondeformable body with variable internal characteristics in an ideal fluid was considered in [5]. It follows from the known solutions that the body displacement in a fluid can be provided by periodic changes in parameters determining the body shape. The motion is nonuniform: the translational velocity is not constant, and the body stops if internal forces cease to act and deformation is terminated (in the case of a deformable body). Until now, the theory of self-induced motion of a body in a fluid predicted that it is impossible to reach uniform motion on the basis of available solutions of the problem of self-induced motion of the body [3]. It is demonstrated below that a body, being at rest at the initial time, can uniformly move in an ideal fluid under the action of internal forces.1. Shape of the Body that can Ensure its Inertial Motion in a Fluid from the State at Rest. Let us consider the motion of a body in an unbounded ideal incompressible fluid with the state at rest at infinity. The fluid motion does not contain vortices, and there are no external forces. The motion in the gravity field with neutral buoyancy of the body also refers to this case. The body is at rest at the initial time.Let us find the body shape that can ensure inertial motion of the body from the state at rest. We consider arbitrary symmetric shapes. The symmetry of the body surface is necessary for solutions of dynamic equations corresponding to straight-line motion o...

Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid

“…Отметим, что тела с винтовой симметрией могут иметь применение в мобильной робо-тотехнике, поскольку такая форма дает преимущества при самопродвижении тела [24].…”