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Showing papers on "Asymptotology published in 1976"





Book ChapterDOI
01 Jan 1976

11 citations


Journal ArticleDOI
TL;DR: In this article, the existence and asymptotic approximation of second species solutions with any number of near-moon passages during a half-period can be established based on higher-order matching.
Abstract: This paper uses the results of second-order asymptotic matching in the restricted three body problem to establish the existence and first-order asymptotic approximation of various families of second species periodic solutions with one near-moon passage during a half-period. In this way, the existence and asymptotic approximation of second species solutions with any number of near-moon passages during a half-period can be established based on higher order asymptotic matching. Second species solutions with near-moon passages have not been studied numerically due to the difficult nature of this problem.

10 citations





Journal ArticleDOI
01 Jan 1976
TL;DR: In this paper, the authors studied the asymptotic behavior of solutions for the general fourth order linear homogeneous differential equation with bounded coeffi-cients and showed that roughly the same qualitative behavior as in the constant coefficient case holds.
Abstract: Asymptotic behavior of solutions is studied for the general fourth order linear homogeneous differential equation with bounded coeffi- cients. It is shown that roughly the same qualitative behavior as in the constant coefficient case holds.

5 citations




Proceedings ArticleDOI
01 Dec 1976
TL;DR: In this paper, an approach for approximating the uniform asymptotic stability boundary of non-autonomous systems by extending the above-mentioned approach is discussed, which is based on the Lie series method.
Abstract: The application of Lie series method for determination and approximation of asymptotic stability boundary of nonlinear autonomous systems has been reported 1,2,3. However, very little has been published with regard to computing the stability boundary of nonlinear nonautonomous systems. This paper is to discuss an approach for approximating the uniform asymptotic stability boundary of nonautonomous systems by extending the above-mentioned approach.


Journal ArticleDOI
Janos Galambos1
01 May 1976

Journal ArticleDOI
TL;DR: In this paper, a mathematical foundation for the law of gas-parameter stabilization during near-sonic flow of a stream around bodies, which is known in experimental aerodynamics, is presented.
Abstract: A mathematical foundation is presented for the law of gas-parameter stabilization during near-sonic flow of a stream around bodies, which is known in experimental aerodynamics. The quantitative formulation of this law relies on a simple asymptotic analysis of the solutions of the Karman equations. The numerical computation performed for the velocity field around a body of revolution whose meridian section is a Chaplygin profile confirmed the deductions of asymptotic theory to high accuracy.

Proceedings ArticleDOI
01 Dec 1976
TL;DR: In this article, the uniform asymptotic stability of two types of nonautonomous linear systems is characterized in terms of the "richness" of the system elements, and the stability of these equations aries in connection with several adaptive schemes for the idenfication of the parameters of a plant with input and output measurable.
Abstract: The uniform asymptotic stability of two types of nonautonomous linear systems is characterized in terms of the "richness" of the system elements. The stability of these equations aries in connection with several adaptive schemes for the idenfication of the parameters of a plant with input and output measurable.


Journal ArticleDOI
TL;DR: In this article, the problem of asymptotic stability and boundedness of non-linear difference equations is considered, and the authors present results which provide explicit regions of stability for the trivial solution.
Abstract: The problem of asymptotic stability and boundedness of non-linear difference equations is considered, In this paper we shall show some results which guarantee asymptotic stability for the trivial solution. Wo wish to present results which provide explicit regions of asymptotic stability. The results replace these words, 1 sufficiently small', by explicit estimates which are simple. The concept of asymptotic stability to difference equations can be quite useful in the design of system response to arbitrary initial conditions.


Journal ArticleDOI
TL;DR: In this paper, an asymptotic solution of the three-body problem is presented, where the small parameter ε is related to the distance separating the binary and the remaining mass.
Abstract: A three-body problem is considered in which two masses, forming a close binary, orbit a comparatively distant mass. An asymptotic solution of this problem is presented, where the small parameter ε is related to the distance separating the binary and the remaining mass. Accepting certain model constraints, this solution is accurate within a constant errorO(ε11) and uniformly valid for time intervalsO(ε−3). Two specific examples are chosen to verify the literal solution: one relating to the Sun-Earth-Moon configuration of the solar system, the other to an idealized stellar system where the three masses are in the ratio 20:1:1. In both cases close agreement is found when the analytical solution is compared with an equivalent numerically-generated orbit.