Chaotic Dynamics in Planetary Systems

Chaotic Dynamics in Planetary Systems
Author: Sylvio Ferraz-Mello
Publisher: Springer Nature
Total Pages: 176
Release: 2023-12-31
Genre: Science
ISBN: 3031458168

The main theme of the book is the presentation of techniques used to identify chaotic behavior in the evolution of conservative mechanical systems and their application to astronomical systems. It results from graduate courses given by the author over the years both at university and at several international summer schools. Along the book surfaces of section, Lyapunov characteristic exponents, frequency maps, MEGNO, dense grid maps, etc., are presented and discussed in connection with the applications. The initial chapter is devoted to the presentation of the main ideas of the chaotic dynamics of conservative systems in plain language so that they can be accessible to a wide range of professionals and students of physical sciences. The applications are mainly related to the motions in the solar system and extrasolar planetary systems. Another chapter is devoted to the applications to asteroids showing how the asteroidal belt is sculpted by chaos and resonances. The contrasting existence of gaps in the distribution of the asteroids and groups of asteroids in resonances is thoroughly discussed. The interest in applications to planetary systems is growing since the discovery of systems of resonant planets around some stars of the solar neighborhood. Exoplanets added a lot of cases to a problem that was before restricted to the planets of our solar system. The book includes an account of results already existing about compact systems.

Solar System Dynamics

Solar System Dynamics
Author: Carl D. Murray
Publisher: Cambridge University Press
Total Pages: 612
Release: 2000-02-13
Genre: Science
ISBN: 1139936158

The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.

Dynamical Chaos in Planetary Systems

Dynamical Chaos in Planetary Systems
Author: Ivan I. Shevchenko
Publisher: Springer
Total Pages: 376
Release: 2021-09-01
Genre: Science
ISBN: 9783030521462

This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.

Chaotic Dynamics

Chaotic Dynamics
Author: Tamás Tél
Publisher: Cambridge University Press
Total Pages: 440
Release: 2006-08-24
Genre: Mathematics
ISBN: 9780521547833

A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.

Dynamical Chaos in Planetary Systems

Dynamical Chaos in Planetary Systems
Author: Ivan I. Shevchenko
Publisher: Springer Nature
Total Pages: 376
Release: 2020-08-31
Genre: Science
ISBN: 3030521443

This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.

Stability and Chaos in Celestial Mechanics

Stability and Chaos in Celestial Mechanics
Author: Alessandra Celletti
Publisher: Springer Science & Business Media
Total Pages: 265
Release: 2010-03-10
Genre: Science
ISBN: 3540851461

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.

Chaos in Astronomy

Chaos in Astronomy
Author: G. Contopoulos
Publisher: Springer Science & Business Media
Total Pages: 493
Release: 2009-01-07
Genre: Science
ISBN: 3540758267

The conference 'Chaos in Astronomy' was held in Athens on 17-20 Sept. 2007. This book contains edited refereed contributions. It offers an overview to students and newcomers entering various fields of dynamical astronomy.

The Dynamical Behaviour of our Planetary System

The Dynamical Behaviour of our Planetary System
Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
Total Pages: 424
Release: 2012-12-06
Genre: Science
ISBN: 9401155100

It is now a well established tradition that every four years, at the end of winter, a group of "celestial mechanicians" from all over the world gather at the "Alpen gasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was held from March 17 to March 23, 1996 and was devoted to the Dynamical Behaviour of our Planetary System. The papers covered a large range of questions of current interest: theoretical questions (re- nances, universal properties, non integrability, transport, ... ) and questions about numerical tools ( symplectic maps, indicators of chaos, ... ) were particularly well represented; the never ending problem of the sculpting of the asteroid belt was also qui te popular. You will find in the following pages a pot-pourri of what we listen to; you will miss of course the diversity of accents with which the tunes were delivered: from China, from Japan, from Brazil, from the United-States of America and from all over Europe, East and West. Let us not forget that the comet 199682 (Hyakutake) came to visit us; many an evening was spent on the deck of the Alpengasthof contemplating this celestial visitor who liked to play hide-and-seek behind the spruce trees.

Dynamics of Planetary Systems

Dynamics of Planetary Systems
Author: Scott Tremaine
Publisher: Princeton University Press
Total Pages: 641
Release: 2023-02-07
Genre: Science
ISBN: 0691244227

An introduction to celestial mechanics for advanced undergraduates, graduate students, and researchers new to the field Celestial mechanics—the study of the movement of planets, satellites, and smaller bodies such as comets—is one of the oldest subjects in the physical sciences. Since the mid-twentieth century, the field has experienced a renaissance due to advances in space flight, digital computing, numerical mathematics, nonlinear dynamics, and chaos theory, and the discovery of exoplanets. This modern, authoritative introduction to planetary system dynamics reflects these recent developments and discoveries and is suitable for advanced undergraduate and graduate students as well as researchers. The book treats both traditional subjects, such as the two-body and three-body problems, lunar theory, and Hamiltonian perturbation theory, as well as a diverse range of other topics, including chaos in the solar system, comet dynamics, extrasolar planets, planetesimal dynamics, resonances, tidal friction and disruption, and more. The book provides readers with all the core concepts, tools, and methods needed to conduct research in the subject. Provides an authoritative introduction that reflects recent advances in the field Topics treated include Andoyer variables, co-orbital satellites and quasi-satellites, Hill’s problem, the Milankovich equations, Colombo’s top and Cassini states, the Yarkovsky and YORP effects, orbit determination for extrasolar planets, and more More than 100 end-of-book problems elaborate on concepts not fully covered in the main text Appendixes summarize the necessary background material Suitable for advanced undergraduates and graduate students; some knowledge of Hamiltonian mechanics and methods of mathematical physics (vectors, matrices, special functions, etc.) required Solutions manual available on request for instructors who adopt the book for a course

Modern Celestial Mechanics

Modern Celestial Mechanics
Author: Alessandro Morbidelli
Publisher: CRC Press
Total Pages: 0
Release: 2002-05-16
Genre: Science
ISBN: 9780415279383

In the last 20 years, researchers in the field of celestial mechanics have achieved spectacular results in their effort to understand the structure and evolution of our solar system. Modern Celestial Mechanics uses a solid theoretical basis to describe recent results on solar system dynamics, and it emphasizes the dynamics of planets and of small bodies. To grasp celestial mechanics, one must comprehend the fundamental concepts of Hamiltonian systems theory, so this volume begins with an explanation of those concepts. Celestial mechanics itself is then considered, including the secular motion of planets and small bodies and mean motion resonances. Graduate students and researchers of astronomy and astrophysics will find Modern Celestial Mechanics an essential addition to their bookshelves.