Analytic Construction of Periodic Orbits in the Restricted Three-body Problem
Title | Analytic Construction of Periodic Orbits in the Restricted Three-body Problem PDF eBook |
Author | Mohammed A. Ghazy |
Publisher | |
Pages | 490 |
Release | 2010 |
Genre | Combinatorial dynamics |
ISBN |
The Three-Body Problem
Title | The Three-Body Problem PDF eBook |
Author | C. Marchal |
Publisher | Elsevier |
Pages | 593 |
Release | 2012-12-02 |
Genre | Science |
ISBN | 0444600744 |
Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions.
Theory of Orbit
Title | Theory of Orbit PDF eBook |
Author | Victory Szebehely |
Publisher | Elsevier |
Pages | 685 |
Release | 2012-12-02 |
Genre | Science |
ISBN | 0323143466 |
Theory of Orbits: The Restricted Problem of Three Bodies is a 10-chapter text that covers the significance of the restricted problem of three bodies in analytical dynamics, celestial mechanics, and space dynamics. The introductory part looks into the use of three essentially different approaches to dynamics, namely, the qualitative, the quantitative, and the formalistic. The opening chapters consider the formulation of equations of motion in inertial and in rotating coordinate systems, as well as the reductions of the problem of three bodies and the corresponding streamline analogies. These topics are followed by discussions on the regularization and writing of equations of motion in a singularity-free systems; the principal qualitative aspect of the restricted problem of the curves of zero velocity; and the motion and nonlinear stability in the neighborhood of libration points. This text further explores the principles of Hamiltonian dynamics and its application to the restricted problem in the extended phase space. A chapter treats the problem of two bodies in a rotating coordinate system and treats periodic orbits in the restricted problem. Another chapter focuses on the comparison of the lunar and interplanetary orbits in the Soviet and American literature. The concluding chapter is devoted to modifications of the restricted problem, such as the elliptic, three-dimensional, and Hill’s problem. This book is an invaluable source for astronomers, engineers, and mathematicians.
The Restricted 3-Body Problem: Plane Periodic Orbits
Title | The Restricted 3-Body Problem: Plane Periodic Orbits PDF eBook |
Author | Alexander D. Bruno |
Publisher | Walter de Gruyter |
Pages | 377 |
Release | 2011-05-03 |
Genre | Mathematics |
ISBN | 3110901730 |
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Periodic Orbits in the Elliptic Restricted Three-body Problem
Title | Periodic Orbits in the Elliptic Restricted Three-body Problem PDF eBook |
Author | R. A. Broucke |
Publisher | |
Pages | 144 |
Release | 1969 |
Genre | Artificial satellites |
ISBN |
Theory of Orbits, the Restricted Problem of Three Bodies
Title | Theory of Orbits, the Restricted Problem of Three Bodies PDF eBook |
Author | Victor G. Szebehely |
Publisher | |
Pages | 684 |
Release | 1967 |
Genre | Science |
ISBN |
Descripción del editor: "Theory of Orbits: The Restricted Problem of Three Bodies is a 10-chapter text that covers the significance of the restricted problem of three bodies in analytical dynamics, celestial mechanics, and space dynamics. The introductory part looks into the use of three essentially different approaches to dynamics, namely, the qualitative, the quantitative, and the formalistic. The opening chapters consider the formulation of equations of motion in inertial and in rotating coordinate systems, as well as the reductions of the problem of three bodies and the corresponding streamline analogies. These topics are followed by discussions on the regularization and writing of equations of motion in a singularity-free systems; the principal qualitative aspect of the restricted problem of the curves of zero velocity; and the motion and nonlinear stability in the neighborhood of libration points. This text further explores the principles of Hamiltonian dynamics and its application to the restricted problem in the extended phase space. A chapter treats the problem of two bodies in a rotating coordinate system and treats periodic orbits in the restricted problem. Another chapter focuses on the comparison of the lunar and interplanetary orbits in the Soviet and American literature. The concluding chapter is devoted to modifications of the restricted problem, such as the elliptic, three-dimensional, and Hill's problem. This book is an invaluable source for astronomers, engineers, and mathematicians ". Academic Press.
Generating Families in the Restricted Three-Body Problem
Title | Generating Families in the Restricted Three-Body Problem PDF eBook |
Author | Michel Henon |
Publisher | Springer Science & Business Media |
Pages | 308 |
Release | 2001-04-24 |
Genre | Language Arts & Disciplines |
ISBN | 3540417338 |
The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.