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.     

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 influence of a supporting canopy on the dynamics of opening of a parachute

A mathematical model of the opening of a circular parachute under the action of a supporting canopy was executed on a computer. The proposed model is based on the simultaneous integration of the equations of nonlinear aerodynamics and the theory of soft membranes. It is shown that the supporting canopy may both improve the characteristics of the parachute system and make them worse. The numerical results are presented in the form of graphs. One figure.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 23–26.     

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.     

Nonstationary thermal fields in multilayer parachute spaces

The Green's function method, under assumptions which are more general from the point of view of the phenomenological theory of thermal conductivity, is used to construct a closed-form solution to a nonstationary thermal conductivity problem for a conical body cut from a spherical space and truncated by concentric spheres centered at the apex of the cone. In order to construct the Green's function we apply Legendre-Fourier transforms and Fourier — Bessel transforms (for polar axis with n conjugate points). The results of this work have applications to engineering computations.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 77–87, 1989.     

Qualitative Analysis for Rheodynamic Model of Cardiac Pressure Pulsations

In this paper, we give a rigorous mathematical and complete parameter analysis for the rheodynamic model of cardiac and obtain the conditions and parameter region for global existence and uniqueness of limit cycle and the global bifurcation diagram of limit cycles. We also discuss the resonance phenomenons of the perturbed system.     

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.     

Nonstationary breakaway flow over a permeable parachute

The properties of a uniformly permeable surface that models the canopy of a real parachute are presented. A modernization of the discrete vortex method is proposed that makes it possible to apply it to calculate the flow over uniformly permeable surfaces. The results of computations of the aerodynamic characteristics of permeable parachutes are presented and compared with experimental data.Translated fromDinamichekie Sistemy, No. 6, pp.3–10, 1987.     

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].     

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.     

Exact solution for an optimal impermeable parachute problem

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle—the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.     

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 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.     

Principles of development of an interactive computing system for analyzing the stability and inflatibility of a parachute

This article describes the structure of a software package developed to study the stationary modes of motion of parachute systems and analyze their stability. A brief discussion of optimality criteria for such packages is given. A classification of the instabilities in the mechanics of a parachute is presented.Translated fromDinamicheskie Sistemy, No. 6, pp. 3–10, 1987.     

An interactive method for parametric identification of the mathematical model of a parachute system using computer graphics

A simple mathematical model of the motion of a parachute system in space is described and an interactive algorithm for parametric identification of the model is proposed. The algorithm selects the model parameters that minimize the deviation of the calculated dependences from experimental observations on the computer graphic monitor.Moscow. Translated from Dinamicheskie Sistemy, No. 10, pp. 106–111, 1992.     

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     

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.