Showing papers in "Journal of Applied Mathematics and Mechanics in 1980"

TL;DR: In this paper, an exact solution of Stokes equations is derived in the case of two spherical drops moving in a viscous medium at velocities normal to their line of centers.

TL;DR: In this article, it is shown that for obtaining an unambiguous local solution of Euler's equation, it is sufficient to define along the whole boundary of the flow region the normal component of the velocity vector and supplement this at the in-flow section by two tangent components of the vortex vector.

TL;DR: In this paper, the degeneration conditions associated with the rearrangement of separatrices are determined, which made it possible to define all bifurcation sequences of the general form.

TL;DR: In this paper, effective elastic constants of a medium with cracks are determined and the results obtained in the plane case are compared with published experimental data and construction of the first moment of solution is shown on the example of an elastic medium containing Poisson set of plane elliptic cracks.

TL;DR: In this paper, the problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system, where the control plant's motion is described by a system of linear periodic finite-difference equations.

TL;DR: In this article, the contact of elastic bodies, taking account of friction on the contact surface, is investigated and a new formulation is constructed, which is based on reducing the problem to some nonclassical problem of the calculus of variations.

TL;DR: In this paper, the stability of the equilibrium position of a non-autonomous Hamiltonian system with periodic coefficients was analyzed in a nonlinear setting, and the stability in the finite approximation and formal Liapunov stability or instability were proved, depending on the Hamiltonian's coefficients.

TL;DR: In this article, an extension of the equations obtained earlier for plates, to shells /1/, was given, and the corresponding extension for straight rods was given in /2/, where /2 is the length of the shell.

TL;DR: In this article, the kinematic equations of a rigid body screw-motion are examined in parameters the complex combinations of which are components of the biquaternion of the body screw motion.

TL;DR: In this article, the stability problem for the equilibrium position of a holonomic mechanical system subject to stationary geometric constraints and to potential and non-conservative position forces was solved for the first nonlinear approximation in the absence of degeneracy.

TL;DR: In this paper, the results of the analysis of Chaplygin's nonholonomic system /1/ were extended to the case of non-holonomic systems of a general form.

TL;DR: In this paper, the stability of the equilibrium position of a non-autonomous 2λ pperiodic Hamiltonian system with two degrees of freedom was examined in the case when the multipliers of the linearized system are equal and correspond to a combination-type parametric resonance.

TL;DR: In this paper, the authors derived asymptotic equations that define unsteady processes in a three-dimensional boundary layer with self-induced pressure, where the pressure gradient under conditions of free interaction is calculated not by the solution of the external problem of flow over a body, but on the assumption that it is due to growth of streamline displacement thickness near the body surface.

TL;DR: In this paper, the generalized Korteweg-DeVries-Burgers equation is analyzed for continuous medium mechanics and solutions belonging to the class of invariant solutions are obtained.

TL;DR: Singularities of solutions of equations for unsteady boundary layer, for the boundary layer on a moving surface, and for a wake generated by a specified positive pressure gradient are investigated in this paper.

TL;DR: In this paper, a theory for the solution of an optimal motion control problem when reactive forces are taken as controls was developed for a mechanical system with variable masses and superimposed constraints, whose responses are reactive forces.

TL;DR: In this article, a nonlinear approximation of the Hugoniot curve is proposed for weak shock wave propagation over an arbitrary elastic medium in lightly deformed (stressed) state.

TL;DR: In this article, the problem of motion control in differential games with mixed strategies has been studied and conditions guaranteeing a successful completion of the search are established, where a control of the first object's motion is determined, under which a second controlled object is found whose motion the first one does not know.

TL;DR: In this paper, a criterion of guaranteed evasion from contact with an estimate not tending to zero as l →+ ∞ is derived for a linear many-person differential game with integral constraints.

TL;DR: In this article, approximate equations describing the evolution of translational-rotational motion of a visco-elastic sphere in a central Newtonian force field are obtained, and their stability is investigated.

TL;DR: In this article, the fundamental criticisms in the review are: 1) separation of self-similar solutions into solutions of the first and second kinds, which is considered the fundamental idea underlying the book, and 2) questions of priority: realizations of the tendency to introduce invented myths about the achievements of some authors with the disparagement of the value and meaning of the results of other authors.

TL;DR: A way is suggested for the approximate realization of the extremal aiming method that essentially lowers the required rapidity of the computing device used in the control loop to simulate quasi-optimal control processes for the flight path of an aircraft at landing.

TL;DR: In this article, the problem of flexure of a piston ring in contact with the inner surface of a rigid cylinder and moving in the direction of its generatrix is solved.

TL;DR: In this article, a smooth rigid stamp penentration into an elastic halfplane is considered with allowance for initial stresses produced by the half-plane own weight, and an integral equation is derived for the contact pressure, whose solution is obtained by the asymptotic method.

TL;DR: In this paper, the instability of equilibrium of a mechanical system when the force function is not a maximum is proved by using Poincare's recurrence theorem and the principle of least action in Jacobi's form.

TL;DR: In this article, the saddle point of the differential game is constructed in the form of optimal mixed position strategies for a specific class of functionals designated as position functionals, which can be specified by functions depending solely on the current position and on a certain parameter.

TL;DR: In this article, the authors considered the problem of stationary distribution of particles in a disperse phase according to size, where the particles are subjected to coagulation and disintegration processes, and analytic expressions were obtained for the mean number of particles of arbitrary mass in a stationary distribution.

TL;DR: In this article, a foundation is given for asymptotic expansions for the axisymmetric precritical equilibrium of a very thin elastic, strictly-convex, shell of revolution with fixed clamping of the edge.

TL;DR: In this article, the stability of a gyrostat about its principal axis is investigated with the use of the Arnol'd-Moser theorem extended to stationary motions, and it is shown that steady rotations are stable for all parameter values that belong to the region where the necessary stability conditions are satisfied, except for some manifold of lesser dimension.

TL;DR: In this paper, the buckling and post-critical behavior of elastic conservative, shallow shells with very small initial imperfections in the middle-surface shape are investigated for several coincident critical loads.