12
А.А. Гурченков
Motion of a solid body in a viscous fluid
at high Reynolds numbers
© A.A. Gurchenkov
Bauman Moscow State Technical University, Moscow 105005, Russia
We consider a solid body of an arbitrary geometry moving in a viscous incompressible
fluid. Movement of the body is assumed to be given. We examine the case of perturbed
motion of a solid body relatively to the programmed motion, namely weakly perturbed
libration movement. Two Cartesian coordinate systems are introduced. One is fixed in
inertial space; the other is rigidly connected with the solid body. The position of the related
coordinate system in relation to the fixed one is characterized by the displacement vector
and rotation vector, which are considered to be small in terms of the proximity of the second
order. The problem is solved in the linear formulation. The solution is found by the method
of boundary layer, and the functions satisfying the linearized Navier — Stokes equations
are taken as the initial approximation.
Keywords
: libration movement, viscous liquid, the Navier — Stokes equations, rigid body
dynamics.
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