Shape of the parachute canopy

The article presents new equations of equilibrium of an axisymmetric parachute canopy generalizing Kh. A. Rakhmatulin's well-known equations. The equations take the biaxial nature of the state of stress near the pole of the canopy into account, and this leads to a finite value of the tension of the tissue and to a finite value of the radius of curvature at the pole.Translated from Dinamicheskie Sistemy, No. 5, pp. 21–25, 1986.     

Pulsations of the parachute canopy

The problem of pulsations of the canopy of a parachute is considered. Equations which are linearized in a neighborhood of the stationary state of motion are given, the algorithm of solution that is based on the composition of the methods of discrete curls and finite differences is described. The results of computations of the characteristics of frequency of the canopy are given in the form of graphs.Translated from Dinamicheskie Sistemy, No. 9, pp. 87–94, 1990.     

Mathematical model of the dynamics of the canopy of an axisymmetric parachute

The article presents a mathematical model of the dynamics of the canopy of an axisymmetric parachute taking into account the biaxiality of the state of complex stress of the tissue, the effect of the rigging lines of the annular carcass, viscous deformation, riffling. For the solution a threelayered symmetric implicit difference schema is suggested. The method of accelerated attainment of a stable solution without distortion of the dynamic pattern is explained.Translated from Dinamicheskie Sistemy, No. 5, pp. 25–32, 1986.     

The effect of the center suspension line and canopy rotation on the shape of a parachute

We consider the effect of the center suspension line and the rotation of an axisymmetric parachute on the shape of the canopy and the drag. The boundary-value problem of the parachute shape is stated, a solution algorithm is described, and some results are discussed.Simferopol' University. Translated from Dinamicheskie Sistemy, No. 10, pp. 31–34, 1992.     

A simplified method of computing the process of opening of a parachute

We propose a simplified method of determining the integral characteristics of the opening of a parachute which makes it possible to compute the maximal stress on a parachute and the trajectory parameters of the motion of the load in the region of the opening of the parachute, and to determine the size of the portion of the canopy at the time of maximal stress.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 38–41.     

Aerodynamic characteristics of a spherical canopy with a pole opening

Aerodynamic characteristics of a rigid half-sphere with different pole openings in an aerodynamic setup AT-2 are considered. Some relationships between the lifting force and an arbitrary resistance under different angles of incidence from 0 to 70° are given.Translated from Dinamicheskie Sistemy, No. 9, pp. 77–81, 1990.     

Studies of the dynamics of space motion of a class of parachute systems

A mathematical model of space motion of a mechanical system that consists of a load and a parachute is presented. With the help of the apparatus of the Lyapunov functions, a particular case of the model is studied when the load can be considered as a mass point that does not have resistance. A sufficient condition of stability is obtained. The results can be applied to the model/ing and construction of parachute systems.Translated from Dinamicheskie Sistemy, No. 9, pp. 99–102, 1990.     

Numerical study of forebody wake effect on axisymmetric parachute opening shock and drag reduction

ABSTRACT

Parachute–forebody distance is a parameter which is amongst the most critical factors to be considered in forebody wake effect. In this study, a new axisymmetric parachute–forebody coupling model is developed. Axisymmetric wrinkling membrane element is built to assess the dynamic response of the parachute canopy membrane under fluid pressure. Besides, fluid model and its further implementation on the fluid structure analysis are discussed. With the proposed method, the wake effect on both the opening shock during inflation state and the drag reduction during steady state can be obtained efficiently. Finally, numerical model is validated with published experimental result and further employed to investigate the influence of distance parameters on fluid–parachute coupling behaviour. On the basis of numerical results, failure distance during the inflation process and critical forebody–parachute distance are determined. The results show that forebody–parachute distance has a strong influence on flow behaviour around the parachute in both inflation state and steady descent state.     

The influence of friction forces on the dynamics of a two-link mobile robot

Controlled periodic motions of a planar two-link robot in a horizontal plane when there is dry friction are considered. The two-link is controlled by means of an internal torque applied to the joint connecting the links. The dynamics of the two-link, taking into account the influence of friction forces and the constrained nature of the control torque, is analysed assuming that the angle between the links is small. The conventional locomotion algorithm of a two-link is modified to ensure rectilinear displacement of the two-link. The influence of various geometrical and mechanical parameters of the system on the average rate of locomotion and on the power consumption during the motion of the two-link robot in a plane is investigated.     

The influence of noise on synchronous dynamics in a diluted neural network

We study the influence of noise on the dynamics of a simple model of excitatory leaky integrate – and – fire neurons in a diluted network. The stochastic process amounts to a random walk with boundaries acting on the external current, whose average value plays the role of a control parameter identifying different dynamical phases. Above a given threshold value one observes a gaussian statistics of synchronous firing events, that changes to an asymmetric long-tail distribution below threshold. For uncorrelated noise the distribution below threshold exhibits an exponential tail for large rare events, while for strongly correlated noise the long-tail turns to a power-law. This interesting dynamical scenario is shown to persist also when short-term plasticity is introduced in the model. Synchronous firing events change to population bursts and the model with plasticity is shown to reproduce quantitatively what observed in in vitro experiments. We also discuss the persistence of this scenario in the thermodynamic limit.     

The use of the simplex method in the design of parachute systems with use of a prototype

We develop a formal mathematical apparatus that makes it possible using the simplex method (linear programming) to carry out the design of parachute systems with use of a prototype, the experimental development of parachute systems using a computer, the analysis of a technical problem, and the identification of mathematical models of an automated parachute design system.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 46–49.     

A parachute for the degree of a polynomial in algebraically independent ones

We give a simpler proof as well as a generalization of the main result of an article of Shestakov and Umirbaev. This latter article being the first of two that solve a long-standing conjecture about the non-tameness, or “wildness”, of Nagata’s automorphism. As corollaries we get interesting informations about the leading terms of polynomials forming an automorphism of K[x ₁, . . . , x _n ] and reprove the tameness of automorphisms of K[x ₁, x ₂].     

The large-particle method in arbitrary nets and its application to the solution of problems in the aeroelasticity of a parachute

Modifications are introduced into the large-particle method to make it possible to use the method in arbitrary nonrectangular computing nets in the study of the flow of an ideal compressible gas over mobile thin permeable membranes. A problem in the aeroelasticity of a parachute is stated. An example is given of the solution of a problem in the stationary formulation for an axially symmetric parachute in the wake of a cylindrical leading body for supersonic flow.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 16–22     

On the influence of aggressive driving behavior on the dynamics of traffic flow

The car following model under discussion is a system of ordinary differential equations describing N cars moving around a circular road. We extend the stability analysis of the model in two directions: variable reaction time (depending on the headway) and an additional part describing the aggressive driving tendency. We study the global bifurcation dynamics and in particular its dependence on these two new ingredients. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering on a resonator with a small opening

By the methods of the theory of extensions, one constructs an explicitly solvable resonator model with a small opening. One computes the high-frequency resonances, i.e., the eigenvalues of the dissipative operator, associated with the considered problem of resonance scattering in the framework of the Lax-Phillips theory.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 159–169, 1983.     

A mathematical model of Helmholtz type for a parachute profile in the presence of gravity

A model of Helmholtz type for a plane inviscid incompressible and potential fluid flow past a curvilinear obstacle of parachute in the presence of gravity is considered. Assuming that the “attack” (wind) flow is unsteady, it is shown that a bounded cavity zone should occur behind the obstacle. The determination of the fluid flow is reduced to a boundary value problem of Volterra type, for a half plane whose solution is explicitly set up, once the unknown separation (jet) lines are found under some approximation hypotheses.     

The influence of stratospheric polar vortex dynamics upon lower tropospheric circulation

In this paper, we explore how the extratropical troposphere responds to a polar stratospheric temperature decrease, accompanied by strengthening polar vortex. For this purpose, use is made of a spectral general circulation model with zonally symmetric boundary conditions on surface and a heat source given analytically.     

The influence of a crack in a medium on the interference waves

The interference Kr-waves in an elastic half-space with a crack are considered. The processes of dispersion and attenuation of such waves are described and theoretical seismograms are constructed. A number of frequency and velocity characteristics are discussed, which can help to identify the waves in mining investigations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 110–115, 1989.