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Stability and Chaos in Celestial Mechanics - Alessandra Celletti
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Alessandra Celletti:

Stability and Chaos in Celestial Mechanics - neues Buch

ISBN: 9783540851462

ID: 9783540851462

The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di erent directions. The stability theory of nearlyintegrable systems (a class of problems which includes many models of - lestial Mechanics) pro ted from the breakthrough represented by the Kolmogorov ArnoldMoser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con nement of the actions for exponential times was guaranteed by Nekhoroshevs theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies. Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics. Stability and Chaos in Celestial Mechanics: The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di erent directions. The stability theory of nearlyintegrable systems (a class of problems which includes many models of - lestial Mechanics) pro ted from the breakthrough represented by the Kolmogorov ArnoldMoser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con nement of the actions for exponential times was guaranteed by Nekhoroshevs theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies. Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics., Springer-Verlag Gmbh

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Stability and Chaos in Celestial Mechanics - Alessandra Celletti
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Alessandra Celletti:

Stability and Chaos in Celestial Mechanics - neues Buch

ISBN: 9783540851462

ID: 9783540851462

This book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers. First paradigmatic models are used to introduce the reader to the concepts of order, chaos, invariant curves, cantori. Next the main numerical methods to investigate a dynamical system are presented. Then the author reviews the classical two-body problem and proceeds to explore the three-body model in order to investigate orbital resonances and Lagrange solutions. In rotational dynamics the author details the derivation of the rigid body motion, and continues by discussing related topics, from spin-orbit resonances to dumbbell satellite dynamics.Perturbation theory is then explored in full detail including practical examples of its application to finding periodic orbits, computation of the libration in longitude of the Moon. The main ideas of KAM theory are provided including a presentation of long-term stability and converse KAM results. Celletti then explains the implementation of computer-assisted techniques, which allow the user to obtain rigorous results in good agreement with the astronomical expectations. Finally the study of collisions in the solar system is approached. Stability and Chaos in Celestial Mechanics: This book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers. First paradigmatic models are used to introduce the reader to the concepts of order, chaos, invariant curves, cantori. Next the main numerical methods to investigate a dynamical system are presented. Then the author reviews the classical two-body problem and proceeds to explore the three-body model in order to investigate orbital resonances and Lagrange solutions. In rotational dynamics the author details the derivation of the rigid body motion, and continues by discussing related topics, from spin-orbit resonances to dumbbell satellite dynamics.Perturbation theory is then explored in full detail including practical examples of its application to finding periodic orbits, computation of the libration in longitude of the Moon. The main ideas of KAM theory are provided including a presentation of long-term stability and converse KAM results. Celletti then explains the implementation of computer-assisted techniques, which allow the user to obtain rigorous results in good agreement with the astronomical expectations. Finally the study of collisions in the solar system is approached., Springer-Verlag Gmbh

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Stability and Chaos in Celestial Mechanics - Celletti, Alessandra
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Celletti, Alessandra:
Stability and Chaos in Celestial Mechanics - neues Buch

2010

ISBN: 3540851461

ID: 9783540851462

In englischer Sprache. Verlag: Springer Berlin, PC-PDF, 264 Seiten, XVI Seiten, 264 Seiten, [GR: 9647 - Nonbooks, PBS / Physik, Astronomie/Astronomie], [SW: - Astronomie, Raum und Zeit ], [Ausgabe: 2010][PU:Springer Berlin], [PU: Springer, Berlin/Heidelberg]

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Stability and Chaos in Celestial Mechanics - Celletti,  Alessandra
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Celletti, Alessandra:
Stability and Chaos in Celestial Mechanics - neues Buch

ISBN: 9783540851462

ID: 9783540851462

[KW: PDF ,ASTRONOMIE] PDF ,ASTRONOMIE, [PU: Springer, Berlin/Heidelberg]

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Stability and Chaos in Celestial Mechanics. Springer Praxis Books - Alessandra Celletti
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Alessandra Celletti:
Stability and Chaos in Celestial Mechanics. Springer Praxis Books - Erstausgabe

2009, ISBN: 9783540851462

ID: 21682369

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Details zum Buch
Stability and Chaos in Celestial Mechanics
Autor:

Celletti, Alessandra

Titel:

Stability and Chaos in Celestial Mechanics

ISBN-Nummer:

3540851461

Detailangaben zum Buch - Stability and Chaos in Celestial Mechanics


EAN (ISBN-13): 9783540851462
ISBN (ISBN-10): 3540851461
Erscheinungsjahr: 2010
Herausgeber: Springer Berlin
264 Seiten
Sprache: eng/Englisch

Buch in der Datenbank seit 08.08.2011 09:20:13
Buch zuletzt gefunden am 16.08.2015 18:54:48
ISBN/EAN: 3540851461

ISBN - alternative Schreibweisen:
3-540-85146-1, 978-3-540-85146-2

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