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Том 73, № 1 (2018)
- Год: 2018
- Статей: 4
- URL: https://journals.rcsi.science/0027-1330/issue/view/10022
Article
1-6
Stationary Shape of a Moving Heavy Flexible Thread
Аннотация
A model describing the shape of the stationary segment of a heavy flexible inextensible thread moving in a fixed vertical plane down to a given depth from a fixed position to a fixed position is considered. The parametric equations of the stationary curve are derived. The shape of the stationary segment and its properties are in a qualitative agreement with those observed in experiments.
7-10
Line-of-Sight Guidance Control Using Video Images
Аннотация
A mathematical formulation of the line-of-sight control problem is proposed for the case when this line is directed at a target. An operator situated on a moving platform controls the line of sight using the data received from video images. Some functionals determining the quality of control by the operator are introduced. It is proved that, in the case of plane motion of the platform and an infinitely distant target, the problem has a saddle point.
11-17
Formulation of Problems in the Bernoulli—Euler Theory of Anisotropic Inhomogeneous Beams
Аннотация
A procedure of reducing the three-dimensional problem of elasticity theory for a rectilinear beam made of an anisotropic iuhomogeueous material to a one-dimensional problem on the beam axis is studied. The beam is in equilibrium under the action of volume and surface forces. The internal force equations are derived on the basis of equilibrium conditions for the beam from its end to any cross section. The internal force factors are related to the characteristics of the strained axis under the prior assumptions on the distribution of displacements over the cross section of the beam. To regulate these assumptions, the displacements of the beam’s points are expanded in two-dimensional Taylor series with respect to the transverse coordinates. Some physical hypotheses on the behavior of the cross section under deformation are used. The well-known hypotheses of Bernoulli—Euler, Timoslienko, and Reissner are considered in detail. A closed system of equations is proposed for the theory of anisotropic iuhomogeueous beams on the basis of the Bernoulli—Euler hypothesis. The boundary conditions are formulated from the Lagrange variational principle. A number of particular cases are discussed.
18-26