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The Three Body Problem And The Equations Of Dynamics
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Book Synopsis The Three-Body Problem and the Equations of Dynamics by : Henri Poincaré
Download or read book The Three-Body Problem and the Equations of Dynamics written by Henri Poincaré and published by Springer. This book was released on 2017-05-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.
Book Synopsis Dynamical Systems by : Wang Sang Koon
Download or read book Dynamical Systems written by Wang Sang Koon and published by Springer. This book was released on 2011-06-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.
Book Synopsis The Three-Body Problem by : Mauri J. Valtonen
Download or read book The Three-Body Problem written by Mauri J. Valtonen and published by Cambridge University Press. This book was released on 2006-03-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.
Book Synopsis The Three-Body Problem and the Equations of Dynamics by : Henri Poincaré
Download or read book The Three-Body Problem and the Equations of Dynamics written by Henri Poincaré and published by . This book was released on 2017 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. .
Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth R. Meyer
Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Book Synopsis Poincare and the Three Body Problem by : June Barrow-Green
Download or read book Poincare and the Three Body Problem written by June Barrow-Green and published by American Mathematical Soc.. This book was released on 1997 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.
Download or read book The Dark Forest written by Cixin Liu and published by Tor Books. This book was released on 2015-08-11 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inspiration for the Netflix series 3 Body Problem! Over 1 million copies of the Three-Body Problem series sold in North America PRAISE FOR THE THREE-BODY PROBLEM SERIES: “A mind-bending epic.”—The New York Times • “War of the Worlds for the 21st century.”—The Wall Street Journal • “Fascinating.”—TIME • “Extraordinary.”—The New Yorker • “Wildly imaginative.”—Barack Obama • “Provocative.”—Slate • “A breakthrough book.”—George R. R. Martin • “Impossible to put down.”—GQ • “Absolutely mind-unfolding.”—NPR • “You should be reading Liu Cixin.”—The Washington Post The Dark Forest is the second novel in the groundbreaking, Hugo Award-winning series from China's most beloved science fiction author, Cixin Liu. In The Dark Forest, Earth is reeling from the revelation of a coming alien invasion-in just four centuries' time. The aliens' human collaborators may have been defeated, but the presence of the sophons, the subatomic particles that allow Trisolaris instant access to all human information, means that Earth's defense plans are totally exposed to the enemy. Only the human mind remains a secret. This is the motivation for the Wallfacer Project, a daring plan that grants four men enormous resources to design secret strategies, hidden through deceit and misdirection from Earth and Trisolaris alike. Three of the Wallfacers are influential statesmen and scientists, but the fourth is a total unknown. Luo Ji, an unambitious Chinese astronomer and sociologist, is baffled by his new status. All he knows is that he's the one Wallfacer that Trisolaris wants dead. The Three-Body Problem Series The Three-Body Problem The Dark Forest Death's End Other Books by Cixin Liu Ball Lightning Supernova Era To Hold Up the Sky The Wandering Earth A View from the Stars At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.
Book Synopsis Analytical Mechanics of Space Systems by : Hanspeter Schaub
Download or read book Analytical Mechanics of Space Systems written by Hanspeter Schaub and published by AIAA. This book was released on 2003 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Orbital Mechanics for Engineering Students by : Howard D Curtis
Download or read book Orbital Mechanics for Engineering Students written by Howard D Curtis and published by Elsevier. This book was released on 2009-10-26 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 New examples and homework problems
Book Synopsis The Three-body Problem from Pythagoras to Hawking by : Mauri Valtonen
Download or read book The Three-body Problem from Pythagoras to Hawking written by Mauri Valtonen and published by Springer. This book was released on 2016-05-03 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal gravitation was discovered by Newton, it became immediately a problem to understand why these three-bodies form a stable system, in spite of the pull exerted from one to the other. In fact, it was a big question whether this system is stable at all in the long run. Leading mathematicians attacked this problem over more than two centuries without arriving at a definite answer. The introduction of computers in the last half-a-century has revolutionized the study; now many answers have been found while new questions about the three-body problem have sprung up. One of the most recent developments has been in the treatment of the problem in Einstein’s General Relativity, the new theory of gravitation which is an improvement on Newton’s theory. Now it is possible to solve the problem for three black holes and to test one of the most fundamental theorems of black hole physics, the no-hair theorem, due to Hawking and his co-workers.
Book Synopsis The Restricted Three-Body Problem and Holomorphic Curves by : Urs Frauenfelder
Download or read book The Restricted Three-Body Problem and Holomorphic Curves written by Urs Frauenfelder and published by Springer. This book was released on 2018-08-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Celestial Encounters by : Florin Diacu
Download or read book Celestial Encounters written by Florin Diacu and published by Princeton University Press. This book was released on 2020-12-08 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.
Book Synopsis Solar System Dynamics by : Carl D. Murray
Download or read book Solar System Dynamics written by Carl D. Murray and published by Cambridge University Press. This book was released on 2000-02-13 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis A Treatise on the Analytical Dynamics of Particles and Rigid Bodies by : Edmund Taylor Whittaker
Download or read book A Treatise on the Analytical Dynamics of Particles and Rigid Bodies written by Edmund Taylor Whittaker and published by . This book was released on 1904 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automated Rendezvous and Docking of Spacecraft by : Wigbert Fehse
Download or read book Automated Rendezvous and Docking of Spacecraft written by Wigbert Fehse and published by Cambridge University Press. This book was released on 2003-11-13 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive reference for space engineers on rendezvous and docking/berthing (RVD/B) related issues, this book answers key questions such as: How does the docking vehicle accurately approach the target spacecraft? What technology is needed aboard the spacecraft to perform automatic rendezvous and docking, and what systems are required by ground control to supervise this process? How can the proper functioning of all rendezvous-related equipment, systems and operations be verified before launch? The book provides an overview of the major issues governing approach and mating strategies, and system concepts for rendezvous and docking/berthing. These issues are described and explained such that aerospace engineers, students and even newcomers to the field can acquire a basic understanding of RVD/B. The author would like to extend his thanks to Dr Shufan Wu, GNC specialist and translator of the book's Chinese edition, for his help in the compilation of these important errata.
