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Vol 74, No 3 (2019)
- Year: 2019
- Articles: 6
- URL: https://journals.rcsi.science/0027-1330/issue/view/10038
Article
Minimax Optimization of Stabilization Parameters during the Programmed Flight
Abstract
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.
55-59
Isolated Stable Initial Perturbations of Unstable Equilibria of Some Mechanical Systems
Abstract
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), and a continual system (a gravitationally unstable two-layer system of incompressible inviscid liquids). For each of these cases, we find an isolated class of perturbations leading to an exponential tendency to the unstable equilibrium or to an exponential tendency to an oscillatory regime in the initial phase space. The conditions characterizing such a class of perturbations are similar for the four considered systems.
60-64
Spouting of Vertical Submerged Axisymmetric Jets in Relatively Narrow Channels
Abstract
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 of the jet submergence are analyzed for various jet diameters. Some spouting regimes are numerically analyzed. A new class of self-oscillation spouting regimes known also as quasiregular is discovered for high-speed small-diameter jets when the depth of their submergence is relatively small. A comparison is made with the results obtained for plane submerged jets.
65-68
Limiting Wave Regimes during the Spatial and Time Development of Disturbances in Falling Liquid Films
Abstract
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.
69-74
Bifurcation Analysis of Gyroscope Dynamics in a Gimbal Suspension
Abstract
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.
75-78
An Extremal Property of Orbits in the Solar System
Abstract
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.
79-82