scholarly journals Estimation of the probability of two consecutive passages through resonance during the descent of an asymmetric rigid body in a rarefied atmosphere

2021 ◽  
Vol 2099 (1) ◽  
pp. 012066
Author(s):  
V V Lyubimov
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Rigid Body ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
System Of Equations ◽  
Principal Resonance ◽  
Aerodynamic Asymmetry ◽  
Asymmetric Rigid Body ◽  
Random Nature

Abstract A two-frequency nonlinear system of ordinary differential equations is considered. This system describes the perturbed motion of a rigid body with considerable asymmetry in a rarefied atmosphere. It is known that when the frequencies of this system of equations coincide, the phenomena of capture or passage through the principal resonance, which have a random nature, are possible. In this case, the probability of a passage through the resonance is calculated from the initial conditions on the separatrix. The objective of this study is to obtain an expression for estimating the probability of two consecutive passages through the resonance regions during the descent in the rarefied atmosphere of Mars of a rigid body with significant geometric and aerodynamic asymmetry.

scholarly journals On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series

2017 ◽  
pp. 169-174
Author(s):  
О.Б. Арушанян ◽  
С.Ф. Залеткин
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Method ◽  
System Of Equations ◽  
Chebyshev Series ◽  
Nonlinear System Of Equations ◽  
Theoretical Substantiation ◽  
Solvability Theorem ◽  
Numerical Analytical Method

Сформулирована и доказана теорема о разрешимости нелинейной системы уравнений относительно приближенных значений коэффициентов Фурье-Чебышёва. Теорема является теоретическим обоснованием ранее предложенного численно-аналитического метода интегрирования обыкновенных дифференциальных уравнений с использованием рядов Чебышёва. A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier-Chebyshev coefficients is formulated and proved. This theorem is a theoretical substantiation for the previously proposed numerical-analytical method of solving ordinary differential equations using Chebyshev series.

scholarly journals Exponential Decay for a System of Equations with Distributed Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Exponential Decay ◽  
Distributed Delay ◽  
Distributed Delays ◽  
System Of Equations ◽  
Activation Functions ◽  
Convergence Of Solutions

We prove convergence of solutions to zero in an exponential manner for a system of ordinary differential equations. The feature of this work is that it deals with nonlinear non-Lipschitz and unbounded distributed delay terms involving non-Lipschitz and unbounded activation functions.

Plumes Above Line Fires in a Cross-Wind

1994 ◽  
Vol 4 (4) ◽  
pp. 201 ◽  
Author(s):  
GN Mercer ◽  
RO Weber
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Velocity Profiles ◽  
Ambient Wind ◽  
Leaf Scorch ◽  
Wind Velocities ◽  
Wind Profiles ◽  
Fire Characteristics ◽  
Temperature Time

A model for the plume above a line fire in a cross wind is constructed. This problem is shown to reduce to numerically solving a system of 6 coupled ordinary differential equations for given initial conditions that depend upon the fire characteristics. The model is valid above the flaming zone and takes inputs such as the width, velocity and temperature of the plume at a given height above the flaming zone, Different horizontal ambient wind velocities are allowed for and a comparison is made between some of these representative wind profiles. The plume trajectory, width, velocity and temperature are calculated for these different representative velocity profiles. This model has application to the calculation of temperature-time exposures of vegetation above line fires and hence can be used in models that predict effects such as leaf scorch and canopy stored seed death. On a larger scale it has application to the problem of tracking burning brands which can cause spotting ahead of the fire.

Application of Ambarzumian’s Method to Radiant Interchange in a Rectangular Cavity

1974 ◽  
Vol 96 (2) ◽  
pp. 191-196 ◽  
Author(s):  
A. L. Crosbie ◽  
T. R. Sawheny
Keyword(s):  
Differential Equation ◽  
Heat Flux ◽  
Integral Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Integral Equation ◽  
Initial Conditions ◽  
Rectangular Cavity ◽  
Wide Range ◽  
First Time

Ambarzumian’s method had been used for the first time to solve a radiant interchange problem. A rectangular cavity is defined by two semi-infinite parallel gray surfaces which are subject to an exponentially varying heat flux, i.e., q = q0 exp(−mx). Instead of solving the integral equation for the radiosity for each value of m, solutions for all values of m are obtained simultaneously. Using Ambarzumian’s method, the integral equation for the radiosity is first transformed into an integro-differential equation and then into a system of ordinary differential equations. Initial conditions required to solve the differential equations are the H functions which represent the radiosity at the edge of the cavity for various values of m. This H function is shown to satisfy a nonlinear integral equation which is easily solved by iteration. Numerical results for the H function and radiosity distribution within the cavity are presented for a wide range of m values.

Exact Equations for the Inextensional Deformation of Cantilevered Plates

1979 ◽  
Vol 46 (3) ◽  
pp. 631-636 ◽  
Author(s):  
J. G. Simmonds ◽  
A. Libai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Independent Set ◽  
Straight Edge ◽  
The Other ◽  
Subsequent Paper ◽  
First Order ◽  
Alternate Forms ◽  
Approximate Equations

A set of first-order ordinary differential equations with initial conditions is derived for the exact, nonlinear, inextensional deformation of a loaded plate bounded by two straight edges and two curved ones. The analysis extends earlier approximate work of Mansfield and Kleeman, Ashwell, and Lin, Lin, and Mazelsky. For a plate clamped along one straight edge and subject to a force and couple along the other, there are 13 differential equations, but an independent set of 9 may be split off. In a subsequent paper, we consider alternate forms of these 9 equations for plates that twist as they deform. Their structure and solutions are compared to Mansfield’s approximate equations and particular attention is given to tip-loaded triangular plates.

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