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In December 13-15, 2018 Bauman Moscow State Technical University held the International Conference "Fundamental and Applied Problems of Mechanics". The main purpose of this conference is to present new research results in various areas of mechanics held in Russian and foreign scientific and educational institutions. One of the important tasks of the conferences "Fundamental and applied problems of mechanics" (FAPM), which are regularly held at Bauman Moscow State Technical University, is also the disclosure of links with the research of N.Ye. Zhukovsky and the presentation of the development of its results in modern conditions. This year the conference is dedicated to the 140th anniversary of the Department of Theoretical Mechanics, which is one of the oldest departments of Bauman Moscow State Technical University was founded by Nikolay Egorovich Zhukovsky in 1878.

One of the important tasks of the conferences "Fundamental and applied problems of mechanics" (FAPM), which are regularly held at Bauman Moscow State Technical University, is also the disclosure of links with the research of N.Ye. Zhukovsky and the presentation of the development of its results in modern conditions.

Traditions laid by N.E. Zhukovsky in the department, continue to be maintained and developed. New young teachers, graduate students and students are connected to the scientific, pedagogical, methodical and social activities, which is the key to the further successful development of the department in modern conditions.

List of Academician Committee are available in this pdf.

List of international organising committee are available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered bythe proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Using Bayes inversion approach and Markov chain Monte Carlo method (MCMC), we studied the effect of temperature distribution in the lunar mantle on the chemical composition (concentrations of main oxides Al₂O₃, FeO, MgO) and seismic velocities in the mantle. The temperature and concentrations of the main oxides were calculated with thermodynamic methods for phase relations and physical properties modeling in the system CaO-FeO-MgO-Al₂O₃-SiO₂ using the Gibbs free energy minimization method. A set of geophysical data was used for the inversion (slenodetic: mean radius (R), mass (M), normalized moment of inertia (Is / MR²), Love number k2 and seismic data – seismic travel times (TT). The Moon is assumed to be viscoelastic, spherically symmetric, and consists of nine layers with constant physical properties in each layer: megaregolith, crust, four mantle layers, low viscosity zone (LVZ), liquid outer core and solid inner core. Physical properties in each zone are assumed to be constant. The division of the mantle into layers was performed in accordance with the seismic model. The concentrations of the main oxides were set equal in the three upper layers of the mantle; the magma ocean model was used to calculate oxide concentrations in the lower mantle.

Two types of geochemical models of bulk composition of the Moon were considered: 1 -models with similar to silicate Earth Al₂O₃ content, 2 - models enriched in Al₂O₃ (> 4.5 wt.%). Linear temperature profiles in the mantle were considered, the temperature was set in the middle of the mantle layers at depths of 150, 375, 625 and 1000 km. At a depth of 150 km, the temperature was set at 600 ° C; in the lower mantle, it varied from 1000 to 1400 ° C. For both types of models and wide temperature range in the lower mantle, it is possible to obtain distributions of the main oxides concentrations in the mantle which are consistent with a given Al₂O₃ and FeO bulk composition. Calculated concentrations and velocities in the mantle are in good agreement with the results obtained by other authors.

The problem of constructing of shapes of the natural oscillations in a vertical cylindrical basin (vessel) with an elliptic cross-section in linearized form of an ideal incompressible fluid is considered. Only the gravity force is acting on the fluid. It is required to define the frequencies and shapes of the natural oscillations of the fluid as a function of the system's parameters. The solution algorithm represented here is based on the method of separation of variables in elliptic coordinates, and the special developed method for the high-accuracy solution of the boundary problem. It used the variational principle and the procedure of continuation in the parameter. This approach shows its effectiveness and obtains the almost complete solution of the problem. For five lower oscillation modes, the natural shapes are determined with high degree of accuracy for a wide range of the eccentricity values.

In case of possible asteroid Apophis' collision with the Earth, we estimate characteristics of such orbit correction, which will provide asteroid's deflection from the Earth and its collision with the Moon. By this way, we will avoid any danger from this asteroid's close approaches with the Earth in the future. We developed a method for searching these trajectories providing collision with the Moon depending on date of correction. Such trajectories were found for next two decades. Parameters for one-impulse correction were estimated. Additionally an optimization of correction impulse was performed based on the time of collision with the Moon. Parameters of Apophis' collision with the Moon were calculated.

A nonlinear model of the impact of a visco-elastic-plastic body against a fixed obstacle is investigated. This model is reduced to a nonlinear second-order differential equation. The solution of the body motion equation using the special Lambert function is obtained. Within the framework of the model, an elastic and absolutely inelastic impact are possible. In the case of an elastic impact, the coefficient of restitution decreases when of the impact velocity is increasing.

Using a numerical-analytical approach, the Earth pole motion is considered under nonstationary perturbations. A method of refined modeling of the Earth pole motion is proposed, which allows to improve the accuracy of the short-term forecast during the occurrence of irregular effects due to changes in the amplitudes of the fundamental harmonics of the oscillatory process.

The construction of the portrait of the correlation dimension of the attractor in the boundary layer of Earth's atmosphere on the basis of the new theory of stochastic hydrodynamics is presented. This theory is based on the theory of stochastic equations of continuum laws and equivalence of measures between random and deterministic movements. Using these equations a new formula for the correlation dimension of the attractor is applying for conditions in the boundary layer of Earth's atmosphere.

The problem of passing planetesimals through the accretion disks of Jupiter and Saturn and capture of their material into the disks is considered taking into account processes of aerodynamic braking, fragmentation, and ablation of the bodies in the disk's gas medium. We have obtained limitations on planetesimal sizes at which the body remains in the protosatellite disk. Estimates are made for the mass of material captured into the disk for the case of power-law mass (and size) distribution of planetesimals. The narrower size range for the captured bodies and longer duration of satellite formation could yield the low differentiation of Callisto as compared with Ganymede. Only minor planetesimals with radii less than 12 m could be captured into the disk of Saturn in the formation region of Titan. This feature promoted significant lengthening of the process of Titan formation.

The paper adduces theoretical data and results of experimental studies confirming the existence of gravitational radiation predicted by the general theory of relativity. It also shows that studying of gravitational waves detection is based on equations of general relativity and equations of electrodynamics, and for modeling of gravitational waves space by sources, equations of hydrodynamics are used.

The influence of the dynamic effects of the Earth-Moon system spatial motion on the perturbed Chandler wobble of the Earth pole is studied on the basis of the celestial mechanical approach and the analysis of astrometric data of observations of International Earth Rotation and Reference Systems Service. The additional harmonic of the oscillatory process with a frequency close to the Chandler frequency is determined. It is shown that the found harmonic leads to variations in the Chandler wobble amplitude with a period of about 40 years.

The necessary formulae are derived for approximate computation of the Coulomb-type potential and the field strength, generated by system of particles in 2D case. On the one hand, these formulae represent the multipole expansion in which monopole, dipole, quadrupole and octupole terms are taken into account that allows for computing the potential and the field strength, generated by set of the charges with rather high accuracy. On the other hand, polynomial expansions of the obtained formulae are derived up to the cubic terms with respect to the observation point coordinates, which make it possible to compute the field strength at closely located points approximately. The expressions are derived that permit one to compute the multipole moments for the system of charges, which consists of smaller subsystems. Such formulae are required in tree-codes when the hierarchical (tree-type) structure of geometrical regions is introduced in the region of the initial system of the charges. In particular case these expressions allows for changing of the reference point of multipole moments computation (multipole moments shifting). The test problem is considered for rather small number of the charges, which shows the dependency of the relative error of the field strength reconstruction on the type of multipole expansion and number of considered terms in the Taylor expansion.

Earth pole oscillations at the Chandler frequency are studied taking into account nonlinear fluctuation-dissipative moments of forces and disturbances at the Chandler frequency and those close to it. For the stationary mode, the dependence of the external perturbation amplitude at the Chandler frequency on the dissipation coefficients is found. It is shown that the amplitude of the Chandler wobble is sensitive to the difference between the Chandler and close to it frequencies and nonlinear dissipation coefficients.

The article considers paradoxical results of metal chain movement that do not agree with classical theoretical models. We present the results of experiments with the falling U-folded chain and with chain fountain. The velocity and acceleration of chain motion were measured and estimated. The trajectory of the fountaining chain links has been investigated experimentally. A comparison of the experimental data with existing theoretical models is made.

We propose an attitude control system for a telescope utilizing an inverted pendulum. We put a tube with a sharp bottom end on an XY linear translation stage, and surround the top by a ring with 4 pressure gauges inside. We made experiments with a device composed of an inverted pendulum which can move only in one direction. The device is composed of a tube with a conical bottom, a linear translation stage, a monitoring tilt meter, supporting springs, a laser displacement sensor and a frame. The laser displacement sensor which is substitution of pressure gauges measured extension/contraction of the springs between the tube and the frame. We have succeeded in keeping it vertical with the accuracy of better than 1 arc sec.

The problem of the occurrence of irreversible residual deformations is reviewed arising in elements of structures made of carbon fiber reinforced plastic (CFRP) after removing the long and continuous load. These residual deformations impair accuracy of the space structures from CFRP after removing the long load. It is generally known that breaking of the material below the ultimate stress by load cycle reversal in the plastic region is called the Bauschinger effect. Design therefore usually precludes cyclic loading into the plastic region. However, in case of low-cycle loading, the Bauschinger effect can be applied for reduction of the residual deformations in such structures by the pre-loading with opposite sign. CFRP has two plastic deformation stages: the first is ruled by dislocation interactions with the fibers and a real the Bauschinger effect can be observed in repeated tension test. A second stage occurs after 0.6% total strain and is connected with a break of carbon fibers. Examples of the occurrence of residual strain in outer structures from CFRP are shown. A new way of long-term storage in a stressed state of structural elements from CFRP developed on the basis of the Bauschinger effect is presented. The possibility of realization of the proposed method of storage is also shown.

In this paper, the positions of stable and unstable equilibrium of the mechanism moving in the vertical plane are determined. The mechanism consists of a rod, load, counterweight and satellite, rolling without slipping on a fixed cylindrical surface. The potential energy function of the mechanism is examines. Only those variants of the mechanism design for which the ratio of the fixed surface radius to the satellite radius is a rational number are considered. The dependence of the number of equilibrium positions of the mechanism on the radius of the satellite and the distance of the load to the center of the satellite is determined by numerical analysis; and the periods of change in the potential energy of the mechanism for different values of the satellite radius are determined.

In this paper, we consider the problem of free bending vibrations of a rectilinear rod floating on the free surface of a liquid in a rectangular rigid container. This problem is associated with well-known problems, where numerical solutions or asymptotics of the problem of the vibrations of a rod or plates on the free surface of a liquid are considered. On the basis of the accepted assumptions, an exact, analytical solution of this boundary value problem is obtained.

The effect of the upper layer of water-immiscible oil on the process of regularization of breaking standing gravity waves on the free surface of a two-layer system in a rectangular vessel has been experimentally investigated for the first time. A comparison is made with the case of standing gravity waves on the free surface of homogeneous liquids (water and seed oil).

The research object is a harmonic drive with a cam wave generator. Harmonic drive operation is limited by flexible gear (FG) fatigue resistance, flexible bearing (FB) durability and teeth sides wear resistance. The article describes a refined method for determining flexible bearing durability, taking into account the spatial nature of elastic interaction between a rigid gear, a flexible gear and a flexible bearing. According to the suggested method, the impact of the maximum flexible gear deformation and length on the durability of a flexible bearing of a cup-type harmonic drive with a flexible gear has been studied. The dependences of the life of the flexible bearing on the length of the flexible wheel and the maximum deformation of the flexible wheel at the nominal torque and various forms of its deformation are obtained. It is shown that small values of the flexible wheel length can significantly reduce the service life of the flexible bearing. The obtained dependencies expand the knowledge about the impact of various factors on the durability of flexible bearings of harmonic drives.

Free motion of the Earth pole is studied on the base of Euler-Liouville dynamic equations of the deformable Earth motion around its center of mass. The dependence of the external influence amplitude from dissipation coefficients is found for the stationary mode of the Earth pole oscillations on the Chandler frequency and external disturbance with the Chandler frequency. It is shown that the Chandler wobble amplitude is sensitive to the difference between the Chandler frequency and those close to it and to the nonlinear dissipation coefficients. The stability conditions of the steady Chandler wobble are defined.

The article discusses the mechanics of the loss of an athlete transverse steady state when performing a ski turn. The analysis of the loss of stable position of the rod model of the mechanical system "skier-skis" in the lateral sliding of skis and falling in the frontal plane was performed. The conditions and possible ways of preventing the skier from falling and restoring a stable position during turn are quantified.

For the first time experimentally investigated the use of a vision system using the technology of depth maps, infrared depth sensor, laser rangefinder, lidar to determine the relief and geometric dimensions of the object on digital stereo images, which allows continuous monitoring of the state of any process. Methods of digital image processing are presented. The main advantages of such systems are considered.

It is considered the problem of motion of two viscoelastic bodies in the gravitational field of MMP. Earlier we found the displacements of points of bodies caused by the action of centrifugal, elastic and dissipative forces. In this paper we calculated analytically three PP using these displacements for centrifugal, elastic and dissipative forces. These three types of displacements change accordingly the shape of the body. And PP is due to the difference between the shape of deformable bodies and balls. Knowing the PP we can find the torques, which determine the rotational motion of the body. As an example, we have calculated the shape of the body caused by elastic displacements and the torques acting on the body.

A numerical-analytical algorithm for calculating (a type of accelerated convergence method) of eigenvalues and modes of transverse vibrations of a rod of variable cross-section is proposed. The algorithm is implemented as a software package in the Maple symbolic computations language. The use of the package was demonstrated by the example of solving problems of determining the eigen forms and natural frequencies of rods with different dependences of the cross section on the longitudinal distance.

During a numerical integration of motion equations of a constrained mechanical system effect of deviations from initial data can be neglected with the help of Baumgarte stabilization method. According to this method first time derivatives of constraint equations are not considered as first integrals and are equated to an arbitrarily linear form of constraints themselves. The coefficients of these forms are called perturbation parameters. So, the problem of constraint stabilization is reduced to a problem of finding an appropriate range of perturbation parameters' values. This problem can be solved by obtaining these values with the help of stability conditions. The procedure of evaluation is getting even more easier if the perturbation coefficients correspond to the multiple root case of its characteristic equation.