Some numerical results obtained by modeling the thermogas displacement of oil from a porous reservoir are discussed. The displacement is performed by a heated water-gas mixture. The injected two-component gas consists of nitrogen and oxygen. Heat, carbon dioxide, and water vapors are released during the reaction process. The heat release decreases the oil viscosity and accelerates the displacement

The minimax problem of stabilization is solved for a line of sight near a programmed trajectory. The motion of this line is described by a system of fourth-order linear differential equations. In this problem, the perturbations are considered as the deviations of the initial position from zero and as time-varying perturbations. The stabilization is performed by a linear feedback. The feedback coefficients

It is assumed that a certain reference frame is inertial for a system of moving and interacting bodies called a large system. In the framework of classical continuum mechanics, some necessary and sufficient conditions are obtained for the existence of a reference frame for a subsystem of this large system considered as an independent large system. The motion of such a new reference frame with respect

The integrability of certain classes of dynamical systems on the tangent bundle of a multidimensional manifold is shown. In this case, the force fields with variable dissipation generalize those considered earlier.

The dynamic behavior of Bernoulli-Euler and Timoshenko beams subjected to a moving concentrated load is considered. Deflection expressions are found in the form of convergent series for a pretensioned beam and for a beam on an elastic foundation. We determine the parameter ranges for which the results of these two models are coincident. It is shown that, under certain conditions, a resonance is possible

The splitting of initial boundary value problems in the theories of elasticity is considered for some anisotropic media. In particular, the initial boundary value problems of the micropolar classical theory of elasticity are represented using the tensor-block matrix operators (or tensor operators). In the case of isotropic micropolar elastic media known also as isotropic or transversally isotropic

The nonstationary processes are considered in a prestressed medium for the case of a sudden viscoelastic break in continuity under the conditions of longitudinal shear. It is assumed that the break proceeds along a semi-infinite strip coincident with the plane of maximum shear stresses. The problem is solved analytically in terms of displacements by the Wiener-Hopf method.

The motion of a puck on a horizontal plane rotating about a vertical axis with dry friction is considered. It is assumed that the Coulomb law of dry friction is locally valid at each point belonging to the lower surface of the puck. The resultant force and friction torque are determined according to the dynamically consistent model of contact stresses. This problem generalizes the problem of motion

The possibility of constructing a mathematical model of disperse systems is discussed. This model is similar to those used in the theory of ideal gases.

The accuracy of stabilization algorithms for a linear system is estimated using maximin testing methods on a finite time interval in the presence of initial and time-varying perturbations.

An algorithm is developed to numerically study the flexible rods (hoses) loaded by concentrated forces and situated in an air or liquid flow. The developed algorithm allows one to solve the static problems with consideration of a liquid flow in a hose. This algorithm can be used to determine an equilibrium rod shape and an axial force in the rod when the velocity vector of the external liquid flow

The equivalence between a possible formulation of an elasticity theory problem in terms of stresses and its classical formulation is shown for rather general domains.

An equation describing a family of stress relaxation curves with arbitrary strain programs at the initial stage generated by the Rabotnov nonlinear constitutive relation with two arbitrary material functions is derived and studied analytically. The effect of the initial stage duration and shape on the properties of relaxation curves is analyzed. Their deviations from each other and from the relaxation

The mutual influence of three-dimensional disk-shaped cracks located in parallel planes of an elastic medium is studied. The medium is under tensile stress directed perpendicular to the crack planes. The cracks are modeled by mathematical cuts of the continuous medium with the possibility of a strong discontinuity of the displacement field on the faces of the cut. The discontinuous displacement method

The programmed motion of an aircraft is considered. The optimization stabilization parameters are sought for this motion. The minimax stabilization problem is formulated and solved. The best parameter is found on the chosen grid and the necessary optimality condition is verified.

The unstable equilibrium positions of four mechanical systems are considered. The following systems are chosen: the system with one degree of freedom (an inverted mathematical pendulum), the systems with two degrees of freedom (an inverted spherical pendulum), the system with a countable number of degrees of freedom (an elastic beam loaded by a compressive force greater than the Eulerian critical load)

The theoretical and experimental results are compared in the classical problem on regular two-dimensional waves in heavy viscous liquid films down a vertical plane. Some similarity transformations are used to perform a comparative analysis of numerical methods to study the nonlinear waves formed in a film during the spatial and time development of disturbances in the main steady flow.

The spouting of vertical submerged axisymmetric jets from under the free surface in relatively narrow channels is experimentally and numerically studied. The existence of self-oscillation regimes with transverse displacements of the free-surface elevation is found for wide ranges of constitutive parameters. Dependencies of the self-oscillation period on the velocities of jets and the initial value

In this paper it is shown that the semi-major axes of the orbits of neighboring planets and of the orbits of large satellites of some planets in the Solar system are close to the orbit radii in the optimal solutions of the problem on a single-impulse transfer in a planetary system from a circular orbit to infinity with a gravitational maneuver.

The problem of motion of a gyroscope in a gimbal suspension is discussed. All steady motions of the system, their stability and branching conditions are given. The results are presented in the form of an atlas of bifurcation diagrams.