Stability of the motion of a rigid body in an unsteady flow

The problem of rigid-body motion in an unsteady gas flow is considered using a flow model [1] in which the motion of the body is described by a system of integrodifferential equations. The case in which among the characteristic exponents of the fundamental system of solutions of the linearized equations there are not only negative but also one zero exponent is analyzed. The instability conditions established with respect to the second-order terms on the right sides of the equations are noted. The problem may be regarded as a generalization of the problem of the lateral instability of an airplane in the critical case solved by Chetaev [2], pp. 407–408.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–22, May–June, 1989.     

On the formulation of the problem of the motion of a body in water

The selection of solutions describing steady irrotational flow of an ideal incompressible fluid over bodies is considered. The selection is based on restrictions that follow from the physical properties of a real fluid and from the presence of a boundary layer on the body. In particular, for any body one can specify a minimal Euler number below which flow without cavitation becomes physically impossible. In the limiting case of an Euler number equal to zero, only the Kirchhoff scheme is physical admissible, and the cavity section tends to a circle. An equation is derived for the limiting shapes of cavities at small cavitation numbers, and a comparison is made with known results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–26, September–October, 1980.     

On the problem of stabilization of motion for a parametric family of nonlinear singularly perturbed systems

For nonlinear uncertain singularly perturbed systems, we construct a control guaranteeing their absolute parametric stability and estimate the set of values of the parameters for which this property of the system is preserved.     

Supersonic flow around a body of small elongation

Some results of experimental studies conducted in a wind tunnel at the Mach number M = 1.78 for a blunt body of small elongation are discussed. The effect of the attack angle on the drag and lift coefficients as well as on the static stability and the pressure center position is considered.     

The problem of transonic flow past a convex body

The uniqueness of the asymptotic type of flow in the neighborhood of a corner point in transonic flow past a convex body is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 67–69, March–April, 1971.     

A model problem of deceleration of a body in a resisting medium with a jet flow around the body

A mathematical model is constructed describing the deceleration of a solid body moving in a medium with a jet flow around the body. The regime of translational deceleration is shown to be normally unstable. This has made it possible to develop a relatively simple technique for determining model parameters experimentally. An example of the application of this technique to a cylindrical body is presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 23–27, May–June, 1995.The work was financially supported by the Russian Foundation for Fundamental Research (project No. 93-013-17637).     

Viscous fluid flow created by the helical motion of a body of revolution

An investigation is made into the flow created by the helical, exponentially damped motion of a body of revolution in a viscous incompressible fluid stationary at points remote from the body. The forces exerted by the fluid on a body moving in this way are studied. It is shown that the induced flow is uniformly helical. The exposition is illustrated with reference to the example of the motion of a spherical surface. The exact and approximate (in the Stokes sense) solutions are compared. The classical results for the steady-state slow motions of a sphere (both translational and rotational) follow as particular cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 47–52, March–April, 1985.     

On two linear invariant relationships in the problem of the motion of a body in a magnetic field

Existence conditions are considered for two linear invariant correlations in differential equations relative to gyroscope motion in a magnetic field with regard to the Barnett-London effect. It is proven that only a classical analogue of this case can exist. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 98–104, February, 1999.     

Planar problem of hydrodynamic shaking of a submerged body in the presence of motion in a two-layered fluid

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 32–44, Septerm–October, 1994.     

Comparison of different notation for equations of motion of a body in a medium flow

In [1–6], a model of a nonstationary action of a medium flow on a body moving in this flow was constructed in the form of an associated dynamical system of second order. In the literature, the representation of the aerodynamic force in integral form with a Duhamel type integral is often used (e.g., see [7, 8]). In the present paper, we pay attention to the fact that a system of ODE is equivalent not to a single integro-differential equation but to a family of such equations. Therefore, it is necessary to discuss the problem of the correspondence between their solutions. The integro-differential representation of the aerodynamic force is reduced to a form convenient to realize the procedure of separation of motions. In this case, we single out the first two approximations with respect to a small parameter. It turns out that in the case of actual airfoils one can speak of “detached” rather than “attached” mass. In the problem on the forced drag of an airfoil in a flow, it is shown that for a sufficiently large acceleration the aerodynamic force can change its direction and turn from a drag force into an “accelerating” force for some time. At the same time, in the case of free drag of a sufficiently light plate, the “acceleration” effect is not observed, but in the course of deceleration the plate moves from it original position in the direction opposite to the initial direction of motion.     

Averaging method in the motion stability problem for a rotating body suspended on a long rigid string

We use the averaging method to study the stability of the vertical rotation of a rigid body suspended on a long rigid string.     

Self motion of a body in a fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 111–118, March–April, 1990.     

Stability of spatial motion of a body with flow separation and rotation about the symmetry axis

A model describing the spatial motion (without separation and with nonsymmetric separation of the flow in the medium) of a body rotating about its symmetry axis in a resisting medium is constructed. Several criteria for stability of the body rectilinear motion are obtained in the case of frozen axial velocity. The influence of retardation on the stability of rectilinear motion of a cone is considered.