Chaotic Dynamics In Planetary Systems PDF Download
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Author | : Sylvio Ferraz-Mello |
Publisher | : Springer Nature |
Total Pages | : 176 |
Release | : 2023-12-31 |
Genre | : Science |
ISBN | : 3031458168 |
Download Chaotic Dynamics in Planetary Systems Book in PDF, ePub and Kindle
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.
Author | : Ivan I. Shevchenko |
Publisher | : Springer Nature |
Total Pages | : 376 |
Release | : 2020-08-31 |
Genre | : Science |
ISBN | : 3030521443 |
Download Dynamical Chaos in Planetary Systems Book in PDF, ePub and Kindle
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.
Author | : Carl D. Murray |
Publisher | : Cambridge University Press |
Total Pages | : 612 |
Release | : 2000-02-13 |
Genre | : Science |
ISBN | : 1139936158 |
Download Solar System Dynamics Book in PDF, ePub and Kindle
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.
Author | : B.A. Steves |
Publisher | : Springer Science & Business Media |
Total Pages | : 342 |
Release | : 2006-09-22 |
Genre | : Science |
ISBN | : 1402047061 |
Download Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems Book in PDF, ePub and Kindle
Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.
Author | : Rudolf Dvorak |
Publisher | : Springer Science & Business Media |
Total Pages | : 304 |
Release | : 2006-01-13 |
Genre | : Science |
ISBN | : 9783540282082 |
Download Chaos and Stability in Planetary Systems Book in PDF, ePub and Kindle
This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Author | : Rudolf Dvorak |
Publisher | : Springer |
Total Pages | : 281 |
Release | : 2009-09-02 |
Genre | : Science |
ISBN | : 9783540814078 |
Download Chaos and Stability in Planetary Systems Book in PDF, ePub and Kindle
This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Author | : Rudolf Dvorak |
Publisher | : Springer Science & Business Media |
Total Pages | : 375 |
Release | : 2013-06-29 |
Genre | : Science |
ISBN | : 9401724148 |
Download New Developments in the Dynamics of Planetary Systems Book in PDF, ePub and Kindle
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 in the Austrian Alps at the invitation of R. Dvorak. This time the colloquium was held at Badhofgastein from March 19 to March 25, 2000 and was devoted to the 'New Developments in the Dynamics of Planetary Systems'. The papers covered a large range of questions of current interest: t- oretical questions (resonances, KAM theory, transport, ... ) and questions about numerical tools (synthetic elements, indicators of chaos, ... ) were particularly well represented; of course planetary theories and Near Earth Objects were also quite popular. Three special lectures were delivered in honor of deceased colleagues whom, to our dismay, we will no longer meet at the 'Austrian Colloquia'. W. Jefferys delivered the Heinrich Eichhorn lecture on 'Statistics for the Twenty-first Century Astrometry', a topic on which Heinrich Eichhorn was a specialist. A. Roy delivered a lecture honoring Victor Szehebely on 'Lifting the Darkness: Science in the Third Millenium', in which in wove anecdotes and remembrances of Victor which moved the audience very much. A. Lemaitre spoke in honor of Michele Moons on 'Mech anism of Capture in External Resonance'. The end of her talk was devoted to a short and moving biography of Michele illustrated by many slides.
Author | : Scott Tremaine |
Publisher | : Princeton University Press |
Total Pages | : 640 |
Release | : 2023-02-07 |
Genre | : Science |
ISBN | : 0691207127 |
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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.
Author | : Suman Satyal |
Publisher | : |
Total Pages | : 139 |
Release | : 2015 |
Genre | : Extrasolar planets |
ISBN | : |
Download Orbital Stability Analysis and Chaotic Dynamics of Exoplanets in Multi-stellar Systems Book in PDF, ePub and Kindle
The advancement in detection technology has substantially increased the discovery rate of exoplanets in the last two decades. The confirmation of thousands of exoplanets orbiting the solar type stars has raised new astrophysical challenges, including the studies of orbital dynamics and long-term stability of such planets. Continuous orbital stability of the planet in stellar habitable zone is considered vital for life to develop. Hence, these studies furthers one self-evident aim of mankind to find an answer to the century old question: Are we alone? This dissertation investigates the planetary orbits in single and binary star systems. Within binaries, a planet could orbit either one or both stars as S-type or P-type, respectively. I have considered S-type planets in two binaries, Cephei and HD 196885, and compute their orbits by using various numerical techniques to assess their periodic, quasi-periodic or chaotic nature. The Hill stability (HS) function, which measures the orbital perturbation induced by the nearby companion, is calculated for each system and then its efficacy as a new chaos indicator is tested against Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO). The dynamics of HD 196885 AB is further explored with an emphasis on the planet's higher orbital inclination relative to the binary plane. I have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space, which indicates a likely regime of the planet's inclination. In, addition, the resonant angle is inspected to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a large inclination. The studies of planetary system in GJ 832 shows potential of hosting multiple planets in close orbits. The phase space of GJ 832c (inner planet) and the Earth-mass test planet(s) are analyzed for periodic-aperiodic orbits. The stability of the system is defined in terms of its lifetime and maximum eccentricity during the integration period then a regime is established for the known and injected planet's orbital parameters. The de-stabilizing resonances due to the outer planet extend by 1.36 AU towards the star, nonetheless, existence of two Earth-mass planets seems plausible. The radial velocity (RV) curves generated for the test planets reveals a weak RV signal that cannot be measured by currently available instruments. A theory has been developed by extrapolating the radio emission processes in the Jupiter-Io system, which could reveal the presence of exomoons around the giant exoplanets. Based on this theory, maximum distance, radius and masses of exoplanets and exomoons are calculated that could be detected by the available radio telescopes. Observation time at the Low Frequency Array (LOFAR) radio telescope has been proposed to detect exomoon in five different stellar systems. Subjects of my future studies include analysis of the data from LOFAR, search for the additional transiting planets in Kepler 47 circumbinary system and observation at the Subaru telescope to verify the predicted planets in GJ 832 system by the method of direct imaging.
Author | : Geoffrey R. Goodson |
Publisher | : Cambridge University Press |
Total Pages | : 419 |
Release | : 2016-12-28 |
Genre | : Mathematics |
ISBN | : 1316943070 |
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This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text.