Vol 205 (2022)
Articles
3-9
On nonstationary and nonlinear heating of a spherical body rotating in a viscous fluid with a constant angular speed
Abstract
In this paper, we shown a stationary rotation of a ball in a viscous liquid with a constant angular speed, an increase in the temperature of the body surface at the boundary is accompanied by a nonstationary heat conduction process, which leads to a spontaneous increase in temperature. We prove that this process of temperature increase is nonlinear and has a limiting point of growth on the temperature scale.
10-15
Asymptotics of the independence number of a random subgraph of the graph G(n, r, < s)
Abstract
In this paper, we discuss the probabilistic version of the classical problem of extremal combinatorics stated appeared in the middle of the 20th century by P. Erdos, C. Ko, and R. Rado.
16-21
Integrable homogeneous dynamical systemswith dissipation on the tangent bundle of a three-dimensional manifold
Abstract
In many problems of dynamics, the position spaces of systems considered are threedimensional manifolds and hence the phase spaces of such systems are the corresponding tangent bundles. In this paper possess, we consider dynamical systems with variable (alternating) dissipation. We prove the integrability of general classes of homogeneous dynamical systems with variable dissipation on the tangent bundles of three-dimensional manifolds.
22-54
Systems with four degrees of freedom with dissipation: analysis and integrability
Abstract
This paper is a survey on integrable systems with four degrees of freedom whose phase spaces are tangent bundles of four-dimensional smooth manifolds. First, we discuss in detail the original problem from the dynamics of a multidimensional rigid body in a nonconservative force field; then we consider general dynamical systems on the tangent bundles of a sufficiently large class of smooth manifolds and prove sufficient conditions for the integrability of the dynamical systems considered in the class of transcendental.
55-94
Algorithms for diagnosing the motion of aircrafts
Abstract
In this paper, we perform qualitative and numerical mathematical experiments on diagnosing the control system of an aircraft during its planning from nearly orbital altitudes with an initial speed close to the first escape speed. We show that diagnostic algorithms proposed are effective in the search for various types of reference malfunctions, in particular, malfunctions in sensors of control signals from a gyro-stabilized platform, almost reference malfunctions in trajectory measurements with errors, and also in the case of continuous express diagnostics.
95-106
Diagnostic algorithms in some systems of direct and indirect control
Abstract
We discuss the diagnostics of malfunctions in a system of indirect control of an object whose motion is governed by third-order nonlinear ordinary differential equations (B. V. Bulgakov’s problem).
We also consider diagnostics of malfunctions in one system of direct control of the aircraft described by second-order nonlinear differential equations. Using methods developed earlier, we construct a diagnostic algorithm.
107-118