Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications
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Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications
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Author : Alessandra Celletti
language : en
Publisher: Springer Verlag
Release Date : 2006-10-30
Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications written by Alessandra Celletti and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-30 with Science categories.
Selected papers from the Fourth Meeting on Celestial Mechanics, CELMEC IV San Martino al Cimino (Italy), 11-16 September 2005
Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications
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Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-02
Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications written by Alessandra Celletti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-02 with Science categories.
The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.
Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications
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Author : Alessandra Celletti
language : en
Publisher: Springer
Release Date : 2010-10-19
Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications written by Alessandra Celletti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with Science categories.
The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.
Capture Dynamics And Chaotic Motions In Celestial Mechanics
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Author : Edward Belbruno
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05
Capture Dynamics And Chaotic Motions In Celestial Mechanics written by Edward Belbruno and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Mathematics categories.
This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.
From Ordered To Chaotic Motion In Celestial Mechanics
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Author : Yi-sui Sun
language : en
Publisher: World Scientific
Release Date : 2015-10-27
From Ordered To Chaotic Motion In Celestial Mechanics written by Yi-sui Sun and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Science categories.
This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.
Stable And Random Motions In Dynamical Systems
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Author : Jurgen Moser
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Stable And Random Motions In Dynamical Systems written by Jurgen Moser and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Science categories.
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
Chaos In Nature
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Author : Christophe Letellier
language : en
Publisher: World Scientific
Release Date : 2013
Chaos In Nature written by Christophe Letellier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory — a three-body problem — and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using “Newtonian” mechanics. Henri Poincaré's deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, etc.
Stability And Chaos In Celestial Mechanics
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Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Stability And Chaos In Celestial Mechanics written by Alessandra Celletti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Science categories.
This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
New Frontiers Of Celestial Mechanics Theory And Applications
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Author : Giulio Baù
language : en
Publisher: Springer Nature
Release Date : 2023-02-09
New Frontiers Of Celestial Mechanics Theory And Applications written by Giulio Baù and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
Regular And Chaotic Motions In Dynamic Systems
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Author : A. S. Wightman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Regular And Chaotic Motions In Dynamic Systems written by A. S. Wightman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
The fifth International School ~ Mathematical Physics was held at the Ettore Majorana Centro della Culture Scientifica, Erice, Sicily, 2 to 14 July 1983. The present volume collects lecture notes on the session which was devoted to'Regular and Chaotic Motions in Dynamlcal Systems. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. Many of the fundamental problems of this subject go back to Poincare and have been recognized in recent years as being of basic importance in a variety of physical contexts: stability of orbits in accelerators, and in plasma and galactic dynamics, occurrence of chaotic motions in the excitations of solids, etc. This period of intense interest on the part of physicists followed nearly a half a century of neglect in which research in the subject was almost entirely carried out by mathematicians. It is an in dication of the difficulty of some of the problems involved that even after a century we do not have anything like a satisfactory solution.