Dynamics And Mission Design Near Libration Points Vol Ii Fundamentals The Case Of Triangular Libration Points

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Dynamics And Mission Design Near Libration Points - Vol Ii: Fundamentals: The Case Of Triangular Libration Points

Author : Gerard Gomez
Publisher : World Scientific
ISBN 13 : 9814493295
Total Pages : 159 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Dynamics And Mission Design Near Libration Points - Vol Ii: Fundamentals: The Case Of Triangular Libration Points by : Gerard Gomez

Download or read book Dynamics And Mission Design Near Libration Points - Vol Ii: Fundamentals: The Case Of Triangular Libration Points written by Gerard Gomez and published by World Scientific. This book was released on 2001-02-12 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, μ, below Routh's critical value, μ1. It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L4, L5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains “practical stability” in the sense that the massless particle remains close to the equilibrium point for a big time interval (some millions of years, for example).According to the literature, what has been done in the problem follows two approaches: (a) numerical simulations of more or less accurate models of the real solar system; (b) study of periodic or quasi-periodic orbits of some much simpler problem.The concrete questions that are studied in this volume are: (a) Is there some orbit of the real solar system which looks like the periodic orbits of the second approach? (That is, are there orbits performing revolutions around L4 covering eventually a thick strip? Furthermore, it would be good if those orbits turn out to be quasi-periodic. However, there is no guarantee that such orbits exist or will be quasi-periodic). (b) If the orbit of (a) exists and two particles (spacecraft) are put close to it, how do the mutual distance and orientation change with time?As a final conclusion of the work, there is evidence that orbits moving in a somewhat big annulus around L4 and L5 exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable.

Dynamics and Mission Design Near Libration Points

Author : Gerard Gómez
Publisher : World Scientific
ISBN 13 : 9789812810632
Total Pages : 466 pages
Book Rating : 4.8/5 (16 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points by : Gerard Gómez

Download or read book Dynamics and Mission Design Near Libration Points written by Gerard Gómez and published by World Scientific. This book was released on 2001 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the Earth-Moon system. The second chapter gives a complete description of the orbits near the collinear point, L 1, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy for the qua

Dynamics and Mission Design Near Libration Points

Author : Gerard G¢mez
Publisher : World Scientific
ISBN 13 : 9789812810649
Total Pages : 170 pages
Book Rating : 4.8/5 (16 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points by : Gerard G¢mez

Download or read book Dynamics and Mission Design Near Libration Points written by Gerard G¢mez and published by World Scientific. This book was released on 2001 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the Earth-Moon system. The second chapter gives a complete description of the orbits near the collinear point, L 1, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy for the qua

Dynamics and Mission Design Near Libration Points: Fundamentals : the case of triangular libration points

Author : Gerard G¢mez
Publisher : World Scientific
ISBN 13 : 9810242743
Total Pages : 159 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points: Fundamentals : the case of triangular libration points by : Gerard G¢mez

Download or read book Dynamics and Mission Design Near Libration Points: Fundamentals : the case of triangular libration points written by Gerard G¢mez and published by World Scientific. This book was released on 2001 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, ?, below Routh's critical value, ?1. It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L4, L5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains ?practical stability? in the sense that the massless particle remains close to the equilibrium point for a big time interval (some millions of years, for example).According to the literature, what has been done in the problem follows two approaches: (a) numerical simulations of more or less accurate models of the real solar system; (b) study of periodic or quasi-periodic orbits of some much simpler problem.The concrete questions that are studied in this volume are: (a) Is there some orbit of the real solar system which looks like the periodic orbits of the second approach? (That is, are there orbits performing revolutions around L4 covering eventually a thick strip? Furthermore, it would be good if those orbits turn out to be quasi-periodic. However, there is no guarantee that such orbits exist or will be quasi-periodic). (b) If the orbit of (a) exists and two particles (spacecraft) are put close to it, how do the mutual distance and orientation change with time?As a final conclusion of the work, there is evidence that orbits moving in a somewhat big annulus around L4 and L5 exist, that these orbits have small components out of the plane of the Earth-Moon system, and that they are at most mildly unstable.

Dynamics And Mission Design Near Libration Points - Vol I: Fundamentals: The Case Of Collinear Libration Points

Author : Gerard Gomez
Publisher : World Scientific
ISBN 13 : 9814493228
Total Pages : 462 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Dynamics And Mission Design Near Libration Points - Vol I: Fundamentals: The Case Of Collinear Libration Points by : Gerard Gomez

Download or read book Dynamics And Mission Design Near Libration Points - Vol I: Fundamentals: The Case Of Collinear Libration Points written by Gerard Gomez and published by World Scientific. This book was released on 2001-04-02 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the problem of station keeping is studied for orbits near libration points in the solar system. The main focus is on orbits near halo ones in the (Earth+Moon)-Sun system. Taking as starting point the restricted three-body problem, the motion in the full solar system is considered as a perturbation of this simplified model. All the study is done with enough generality to allow easy application to other primary-secondary systems as a simple extension of the analytical and numerical computations.

Dynamics and Mission Design Near Libration Points: Advanced methods for triangular points

Author : Gerard G¢mez
Publisher : World Scientific
ISBN 13 : 9810242107
Total Pages : 274 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points: Advanced methods for triangular points by : Gerard G¢mez

Download or read book Dynamics and Mission Design Near Libration Points: Advanced methods for triangular points written by Gerard G¢mez and published by World Scientific. This book was released on 2001 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions. The methodology developed here is not specific to astrodynamics problems. The techniques are developed in such a way that they can be used to study problems that can be modeled by dynamical systems.

Dynamics And Mission Design Near Libration Points, Vol Iii: Advanced Methods For Collinear Points

Author : Gerard Gomez
Publisher : World Scientific
ISBN 13 : 9814493651
Total Pages : 203 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Dynamics And Mission Design Near Libration Points, Vol Iii: Advanced Methods For Collinear Points by : Gerard Gomez

Download or read book Dynamics And Mission Design Near Libration Points, Vol Iii: Advanced Methods For Collinear Points written by Gerard Gomez and published by World Scientific. This book was released on 2001-02-12 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the Earth-Moon system. The second chapter gives a complete description of the orbits near the collinear point, L1, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy for the quasiperiodic halo orbits. In the last chapter, the transfer from the Earth to a halo orbit is studied.

Dynamics and Mission Design Near Libration Points

Author :
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (128 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points by :

Download or read book Dynamics and Mission Design Near Libration Points written by and published by . This book was released on 2001 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamics and Mission Design Near Libration Points

Author : Gerard G¢mez
Publisher : World Scientific
ISBN 13 : 9789812794628
Total Pages : 206 pages
Book Rating : 4.7/5 (946 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points by : Gerard G¢mez

Download or read book Dynamics and Mission Design Near Libration Points written by Gerard G¢mez and published by World Scientific. This book was released on 2001 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies several problems related to the analysis of planned or possible spacecraft missions. It is divided into four chapters. The first chapter is devoted to the computation of quasiperiodic solutions for the motion of a spacecraft near the equilateral points of the EarthOCoMoon system. The second chapter gives a complete description of the orbits near the collinear point, L 1, between the Earth and the Sun in the restricted three-body problem (RTBP) model. In the third chapter, methods are developed to compute the nominal orbit and to design and test the control strategy for the quasiperiodic halo orbits. In the last chapter, the transfer from the Earth to a halo orbit is studied. Contents: Quasi-periodic Solutions Near the Equilateral Points of the Earth-Moon System; Global Description of the Orbits Near the L 1 Point of the EarthOCoSun System in the RTBP; Quasi-periodic Halo Orbits; Transfer from the Earth to a Halo Orbit; Appendices: The JPL Model; Reference Systems and Equations of Motion; The Model Equations Near the Equilateral Points in the EarthOCoMoon System; Transfer Between Halo Orbits of the RTBP. Readership: Applied mathematicians, computational physicists and aerospace engineers.

Twenty Years of Bialowieza

Author : Syed Twareque Ali
Publisher : World Scientific
ISBN 13 : 9812561463
Total Pages : 275 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Twenty Years of Bialowieza by : Syed Twareque Ali

Download or read book Twenty Years of Bialowieza written by Syed Twareque Ali and published by World Scientific. This book was released on 2005 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1-7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience.This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view.

Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties

Author : Fedor S Rofe-beketov
Publisher : World Scientific
ISBN 13 : 9814480673
Total Pages : 463 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties by : Fedor S Rofe-beketov

Download or read book Spectral Analysis Of Differential Operators: Interplay Between Spectral And Oscillatory Properties written by Fedor S Rofe-beketov and published by World Scientific. This book was released on 2005-08-29 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals).The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators.

Perturbation Theory

Author : Giuseppe Gaeta
Publisher : Springer Nature
ISBN 13 : 1071626213
Total Pages : 601 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Perturbation Theory by : Giuseppe Gaeta

Download or read book Perturbation Theory written by Giuseppe Gaeta and published by Springer Nature. This book was released on 2022-12-16 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Dynamics and Mission Design Near Libration Points

Author :
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points by :

Central Configurations, Periodic Orbits, and Hamiltonian Systems

Author : Jaume Llibre
Publisher : Birkhäuser
ISBN 13 : 3034809336
Total Pages : 240 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Central Configurations, Periodic Orbits, and Hamiltonian Systems by : Jaume Llibre

Download or read book Central Configurations, Periodic Orbits, and Hamiltonian Systems written by Jaume Llibre and published by Birkhäuser. This book was released on 2015-12-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notes of this book originate from three series of lectures given at the Centre de Recerca Matemàtica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems. The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.

Space Manifold Dynamics

Author : Ettore Perozzi
Publisher : Springer Science & Business Media
ISBN 13 : 1441903488
Total Pages : 265 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Space Manifold Dynamics by : Ettore Perozzi

Download or read book Space Manifold Dynamics written by Ettore Perozzi and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an overview of the outcomes resulting from applying the dynamical systems approach to space mission design, a topic referred to as "Space Manifold Dynamics" (SMD). It is a natural follow-on to the international workshop "Novel Spaceways for Scientific and Exploration Missions," which was held in October 2007 at the Telespazio Fucino Space Centre (Italy) under the auspices of the Space OPS Academy. The benefits and drawbacks of using the Lagrangian points and the associated trajectories for present and future space missions are discussed. The related methods and algorithms are also described in detail. Each topic is presented in articles that were written as far as possible to be self consistent; the use of introductory sections and of extended explanations is included in order to address the different communities potentially interested in SMD: space science, the aerospace industry, manned and unmanned exploration, celestial mechanics, and flight dynamics.

Dynamics and Mission Design Near Libration Points - Vol Ii

Author : J. Llibre
Publisher :
ISBN 13 : 9789812810649
Total Pages : 0 pages
Book Rating : 4.8/5 (16 download)

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Book Synopsis Dynamics and Mission Design Near Libration Points - Vol Ii by : J. Llibre

Download or read book Dynamics and Mission Design Near Libration Points - Vol Ii written by J. Llibre and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, æ, below Routh's critical value, æ 1 . It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L 4, L 5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains "practical stability" in the sense that the massless partic.

The Earth-Moon System as a Dynamical Laboratory

Author : Elisa Maria Alessi
Publisher : Frontiers Media SA
ISBN 13 : 2889630447
Total Pages : 156 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis The Earth-Moon System as a Dynamical Laboratory by : Elisa Maria Alessi

Download or read book The Earth-Moon System as a Dynamical Laboratory written by Elisa Maria Alessi and published by Frontiers Media SA. This book was released on 2019-09-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Earth-Moon neighborhood is the scene of a large variety of applications that concern asteroids, lunar exploration and space debris in Earth orbit. In particular, recent efforts by the scientific community have focused on the possibility of extending the human operations beyond the radiation belts; of exploiting in-situ resources, either on the lunar surface or on asteroids retrieved to the vicinity of the Earth; and of mitigating the space debris concern by taking advantage of the lunar perturbation. The characteristic dynamics in the cislunar space represents an opportunity for the mission designer, but also a challenge in terms of theoretical understanding and operational control. This Research Topic covers the Earth-Moon dynamics in its complexity and allure, considering the most relevant aspects for both natural and artificial objects, in order to get a new comprehension of the dynamics at stake along with the operational procedures that can handle it.