Showing papers in "Journal of Applied Mathematics and Mechanics in 2004"

TL;DR: In this article, the Cole-Hopf transformation was used to obtain exact solutions of the Burgers-Huxley equation, which occurs in the description of many non-linear wave phenomena.

TL;DR: In this article, several numerical methods are applied to solve the Savage-Hutter (SH) equations and compared, including traditional difference schemes, as well as high-resolution NOC (Non-Oscillatory Central Differencing) schemes, in which several second-order TVD (Total Variation Diminishing) limiters and a third-order ENO (Essentially non-oscillation) cell reconstruction scheme are used.

TL;DR: In this article, the results obtained by Poincare's small parameter method and by direct separation of motions, which require laborious computations, can be obtained much more simply by using an extended formulation of the integral stability criterion.

TL;DR: In this paper, the instability of oscillations of a weightless rod with a concentrated mass, sliding periodically along the rod axis is investigated, where the amplitude of the displacement of the mass and viscous friction, due to the air resistance, is assumed to small, while the periodic excitation function is arbitrary.

TL;DR: In this article, the diffraction of plane surface waves by a floating semi-infinite elastic plate at oblique incidence in a fluid of finite depth is investigated, and an exact solution of this problem is constructed by the Wiener-Hopf method.

TL;DR: In this paper, the deterministic problem of constructing synthesized control strategies from the results of available observations under unknown but bounded disturbances subjected in advance to hard bounds on the uncertain parameters is considered.

TL;DR: In this paper, the motion of a mechanical system of coaxial axisymmetrical bodies of variable mass in a translating system of coordinates is considered and a theorem on the change in the angular momentum of such a system with respect to translating axes is given.

TL;DR: In this paper, an algorithm is proposed for constructing optimal trajectories and their properties are investigated based on results obtained by solving a special case of the optimal control problem with a closed trajectory of motion.

TL;DR: In this paper, a method of calculating the rate of thermophoresis of large bodies in gases is briefly described, focusing on the features of the mechanism of the thermophoreis of highly heat-conducting bodies, which were subject to the attempts made over many years to explain the anomalies.

TL;DR: A model of transient single-lane traffic flows is proposed, taking into account the basic components used to control road traffic (traffic lights and “sleeping policemen”), which is radically different from those traditionally considered in continuum mechanics.

TL;DR: In this paper, it was shown that the number of independent compatibility equations in terms of stresses involved in formulating the basic problem in the mechanics of deformable solids in termsof stresses in ℝn, is the same as the independent components of the Kroner and Riemann-Christoffel tensors and the existence of the Bianchi identities does not reduce this number.

TL;DR: In this article, the authors considered the case of a heavy rigid body with a single fixed point in a uniform gravity field, and the problem of the orbital stability of such motions is solved.

TL;DR: In this paper, the basic ideas of the renormalization-group (RG) method are presented, the results of which are the functional and differential RG equations are explained, and ways of solving the RG differential equation, as well as some technical aspects of the RG method, such as the method of ϵ-expansion, are outlined.

TL;DR: In this article, the authors considered the coupled problem of stability for a rectangular plate of a shape-memory alloy undergoing a direct thermo-elastic phase transition when compressive loads are applied.

TL;DR: In this paper, the deformation of the microprotuberances of the elastic surface in contact with a rigid punch is assumed to be non-linear (for example, it obeys a power law) and the solution of the problems is reduced to investigating nonlinear Hammerstein integral equations.

TL;DR: In this article, it is shown that the inequality first derived by Metelitsyn (1952) is a sufficient but not necessary condition for asymptotic stability of linear mechanical systems.

TL;DR: In this article, the authors considered the plane problem of the limit equilibrium of a crack, where constant normal and shear stresses of cohesion act between the crack surfaces in the end regions when uniformly distributed normal stresses are applied at infinity.

TL;DR: In this article, the motion of a carriage with two wheeled pairs over a rough horizontal plane is investigated in the following cases: (1) inertial motion, (2) when there is an elastic constraint which produces a restoring moment of the forces when the axis of rotation of the leading wheeled pair deviates from the unperturbed position.

TL;DR: In this paper, a new method of constructing canonical replacements of variables in parametric form, which differs from the existing constructive methods in the Hamiltonian procedure: the method of derivatives and generators, is proposed.

TL;DR: In this paper, a norm-bounded locally optimal control is constructed which minimizes the frequency and phase deviations from resonance in a non-linear system affected by bounded perturbations, independent of the form of the perturbation and the structure of the conservative part of the system.

TL;DR: In this article, the problem of the motion of a heavy rigid body is considered in the so-called "restricted" formulation, which is obtained on the assumption that two dimensions of the body, which we will call its "width" and "thickness", are considerably less than the third dimension, the "length" of a body.

TL;DR: In this paper, a design for constructing control strategies using extremal aiming in the direction of the coinvariant gradients of auxiliary functionals of the Lyapunov-Krasovskii type is presented for problems of controlling hereditary dynamical systems when there is interference.

TL;DR: In this article, the Lyapunov-Poincare method was used to calculate the period and initial value of the velocity of the self-sustained oscillator for small and moderately large values of the feedback factors.

TL;DR: In this article, the authors considered a system whose configuration space is a Lie group and whose Lagrangian is invariant to left translations on that group and assumed that the mass geometry of the system may change under the action of only internal forces.

TL;DR: In this paper, the authors investigated the controlled oscillatory and rotational motions of a rigid body on a plane-parallel bifilar suspension, where the controlled object, the relative position of which can be regulated, is connected to the body.

TL;DR: In this paper, a periodic model of rail track in the form of an infinite Timoshenko beam held by massive elastoviscous supports with constant spacing is considered, where the sprung part of the carriage is separated from the wheel by an elastic spring, and its action on the wheel in a first approximation is represented by a static load.

TL;DR: In this paper, an autonomous system when the frequencies of the linear system satisfy a relation which is close, with a frequency detuning e, to an exact two-frequency internal resonance is investigated and the fact that there is an isolated periodic solution in the general situation is established.

TL;DR: In this paper, exact solutions of some three-dimensional problem of the deformation of a thin annular plate fixed along the outer contour and loaded along the inner contour in a certain way are obtained using functions of a complex variable.

TL;DR: The main element of the proposed approach to constructing a theory of the stability of canonical systems is an index function (defined below), which contains all the necessary information on the system as mentioned in this paper, and the fundamental results of existing theory, in particular, the necessary and sufficient condition for strong stability, are expressed in new terms.

TL;DR: In this paper, an accurate non-linear theory of the three-dimensional bending of cylindrical (prismatic) elastic solids is proposed, where each material straight line parallel to the axis of a prismatic beam is converted into a helical line after deformation.