Moscow University Mechanics Bulletin最新文献

This paper concerned with the motion of two contacting cylinders with dry friction between them. Filippov’s theory of discontinuous differential equations is used to study the system of ordinary differential equations. The forward uniqueness of the solution is proven, the phase portrait is drawn, and its bifurcation is investigated. These results allow describing the motions of the given mechanical system, in particular, the conditions of seizing and permanent rotation.

The problem of motion in a free molecular flow of particles of a rigid body with a fixed point bounded by the surface of an ellipsoid of revolution is considered. Necessary existence conditions for an additional analytic first integral independent of the energy integral are obtained in this problem.

The calibration problem for the accelerometer unit is considered under restrictions on its angular positions (for the plane case). The guaranteeing approach is applied to solve the problem. The solution is found in analytical form.

The paper presents our study on the dilution of precision in the problem of estimating the vehicle’s velocity using a three-beam Doppler lidar. Such a system has been proposed as an addition or replacement to the differential GNSS velocity solution in an airborne gravimetry system. We analytically derive optimal directions of lidar beams and use numerical simulation to obtain their attitude which minimizes the error covariance of estimated vertical velocity.

In this paper, the variational principle of Lagrange, the Ritzmethod and piecewise polynomial serendipity shape functions areused to obtain the stiffness matrix and a system of linearalgebraic equations in the micropolar theory of elasticity fororthotropic and centrally symmetric material.

In this paper, the motion of a spherical body with anisotropic magnetizable elastomer in a viscous liquid under the action of a magnetic field of the coil with current is investigated. A mathematical model of such a body motion taking into account the interaction (rolling, sliding) with the inclined plane is proposed. The calculated trajectories of the body movement from the initial position on the coil axis when the magnetic field is turned on are plotted. The parameters are determined at which the movement over the inclined plane occurs. The maximum deviation of the body from the coil axis for various problem parameters is calculated.

With the growth of various microdefects in bodies, complex systems of cracks of arbitrary configuration can be generated. This paper presents a technique for numerical simulation of complex branched cracks, which makes it possible to analyze such systems. Using the method proposed by the authors, it is possible to find the stress and displacement fields as well as the stress intensity factors, the analysis of which leads to the conclusion about the influence of the considered configuration on the crack stability. The paper also contains the comparison with the results of other authors in the problem of a two-link crack.

The paper studies the temperature conditions under which the emergence and self-development of vortex motion in the real atmosphere are possible.

The paper concerns with the equilibrium of the ideal incompressible liquid situated in a moving cylindrical vertical vessel. It is proved that the equilibrium is unstable with probability one if the vessel movement is defined as the vertical random vibration. Random vibration is simulated by stationary Markov chain.

A plane model of a spherical robot containing a platform with a wheel is considered. Dynamic equations are derived for this robot and some assumptions concerning these equations are also discussed. A control is proposed using a multilayer neural network.