Moscow University Mechanics Bulletin最新文献

The paper investigates the possibility of pulsed control of an asteroid approaching the Earth. The control scheme is fixed: this is a two-pulse flight with a gravitational maneuver near the Earth. The purpose of the first pulse is to correct the approach to the Earth. With the help of a gravitational maneuver, the asteroid is transferred to an osculating heliocentric orbit with a period close to the period of the Earth’s revolution around the Sun. The purpose of the second pulse is to transfer the asteroid to an osculating orbit, the period of rotation of which makes long-period fluctuations near the period of the Earth. An approximate method for evaluating the feasibility of a flight is proposed. Two examples are considered: the asteroids Apophis 2004 MN4 and Duende 2012 DA14.

A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.

A variant of the constitutive equations for describing complex loading processes with deformation trajectories of arbitrary geometry and dimension is considered. The vector constitutive equations and a new method of mathematical modeling the five-dimensional complex loading processes are obtained. This method is validated for two- and three-dimensional processes of constant curvature. The constitutive equations describe the stages of active loading and unloading. Explicit representations of the stress vector in an arbitrary deformation process are obtained. It is shown that the state parameters of the model in the five-dimensional deformation space are the four angles from the representation of the stress director vector in the Frenet frame, not directly, but in the form of four special functions whose form is known. These functions are called the Vasin functions. The process of complex loading along a three-dimensional helical trajectory of deformation is also considered, where, after diving and subsequent additional loading, the equations of the steady-state loading process are established. Similar results are obtained for five-dimensional helical deformation trajectories. Hence, for this class of processes there exists a correspondence between the geometries of the deformation and reaction paths in the form of a loading path.

The trigger factors of various nature that lead to the excitation of seismic and volcanic activity are briefly considered. Based on the solution of the generalized Boussinesq problem for half-space and typical pressure differences in medium-power typhoons, some estimates of the trigger effect of such differences on the provocation of earthquakes are given. The possible mechanisms of the trigger effect of typhoons on seismicity, before they move from the sea area to the land, are discussed.

The paper considers parametric oscillations of a classical system under nonconservative loading—a flexible pipeline with a flowing liquid. The parametric effect on the system is determined by the variability of the fluid flow rate. The stability of the rectilinear form of the pipeline equilibrium according to the Floquet–Lyapunov theory is investigated by the monodromy matrix method. The main focus is the study of the influence the characteristics of the parametric effect have on the stability boundary position of the pipeline, assuming a harmonic deviation of the flow rate from a certain constant, in particular, the amplitude and frequency.

The article examines how the filtration theory should look from the point of view of the modern theory of disperse systems, which is a nontrivial generalization of the classical theory of Brownian motion.

We consider a mathematical model of a catamaran with a wind turbine consisting of a hull equipped with an air propeller and a water propeller. The wind-receiving propeller converts wind energy into rotational energy and transfers it via the transmission system to the propeller, which creates a pulling force. The superiority of this force over the sum of the sailing resistance of the propeller and the hydrodynamic resistance of the catamaran hull provides the possibility of upwind acceleration. The shaft system connecting the air and water propeller suggests the possibility of changing the rotation transmission ratio. Steady modes of motion have been studied, their stability has been analyzed, and parameters have been found that provide the highest hull speed when moving upwind.

In the present paper assumptions are formulated, and, on the basis of the moment theory of elasticity with independent fields of displacements and rotations, general variation principle of Hu–Washizu type is established and basic equations with boundary conditions of the moment-membrane theory of shells are set out. For the moment-membrane theory of shells particular variation principles of Lagrange and Castigliano type are proved, equations of continuity of deformations of the middle surface of the shell are derived.

The article shows a theoretical (part 1) improvement in thestabilization of the gaze in galvanic vestibular stimulation.

The problem of motion by inertia of a rigid body with an ellipsoidal cavity filled with a liquid in the presence of the internal friction is discussed. The global qualitative analysis of the system dynamics and the limiting motions is given.