Poincare and the Three Body Problem (History of Mathematics, V. 11)

Book Description

The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem--to describe the paths of three bodies in mutual gravitational interaction--is one of those which is simple to pose but impossible to solve precisely.

Poincaré'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 Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm.

Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré'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 Poincaré's subsequent highly influential work in celestial mechanics.

Customer Reviews:

Stiff reading.......2007-01-06

This book is somewhere between an historical essay and a blow-by-blow analysis of one of Poincare's most important papers, which gave rise to many significant developments in 20th-century mathematics. You have to really like the subject of differential equations to get into this.

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Fluctuations Order & Defects
Gene F. Mazenko , and Gene Mazenko
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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Equilibrium Statistical Mechanics
Nonequilibrium Statistical Mechanics (Physics Textbook)

ASIN: 0471328405

Book Description

Fluctuations, order, and defects determine a material's properties. The difference between water and ice is a matter of order. Many of today's high-tech materials in electronics and chemistry engineer order and defects to maximize desired properties. This second of a four volume set discusses phase transitions in a field theoretic context and shows how these methods can be applied to more complex systems such as liquid crystals and polymers. While building on the previous volume, this volume is self-contained and stands alone as a valuable resource.

* Modern treatment includes coverage of effective hamiltonians.
* Focuses on problems in condensed matter physics.
* Author is well-known and respected for his work in statistical mechanics.

Simulating Hamiltonian Dynamics (Cambridge Monographs on Applied and Computational Mathematics)

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Simulating Hamiltonian Dynamics (Cambridge Monographs on Applied and Computational Mathematics)
Benedict Leimkuhler , and Sebastian Reich
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations

ASIN: 0521772907

Book Description

The simulation of matter by direct computation of individual atomic motions has become an important element in the design of new drugs and in the construction of new materials. This book demonstrates how to implement the numerical techniques needed for such simulation, thereby aiding the design of new, faster, and more robust solution schemes. Clear explanations and many examples and exercises will ensure the value of this text for students, professionals, and researchers.

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Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

Mechanics: From Newton's Laws to Deterministic Chaos (Advanced Texts in Physics)

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A very complete book
Excellent, but not as a first contact with Mechanics
The greatest undergratuate book in Mechanics.

Mechanics: From Newton's Laws to Deterministic Chaos (Advanced Texts in Physics)
Florian Scheck
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Course of Theoretical Physics : Mechanics (Course of Theoretical Physics)
Introduction to Quantum Mechanics (2nd Edition)
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition
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Principles of Quantum Mechanics

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Light Scattering and Nanoscale Surface Roughness (Nanostructure Science and Technology)
Quantum Theory: A Wide Spectrum
Lectures on Quantum Mechanics

ASIN: 3540219250

Book Description

This updated and revised fourth edition covers all topics in mechanics from elementary Newtonian mechanics, canonical and rigid body mechanics to relativistic mechanics and nonlinear dynamics.

In particular, symmetries and invariance principles, geometrical structures and continuum mechanics play an important role. Scheck’s Mechanics enables the reader to develop understanding of the general principles from which equations of motions may be derived, to appreciate the importance of symmetries as a basis for quantum mechanics and to get practice in using theoretical tools and concepts that are essential for all branches of physics.

The book contains numerous problems with complete solutions, and some practical examples. This will be appreciated in particular by students using the text to accompany lectures on mechanics. The book ends with some historical remarks on important pioneers in mechanics.

Customer Reviews:

A very complete book.......2006-05-11

Although I agree that one might be scared by the presence of sophisticated chapters like the one devoted to differential geometry, I find that this book is the best for an undergraduate level. It begins with Newtonian mechanics (some knowledge on linear algebra and calculus assumed) and covers all the fundamental points of modern mechanics in a rigorous and straightforward way, including a chapter in special relativity and another on dynamical systems and chaos. As it emphasizes the relevant concepts and formalism of simmetries, it naturally leads to quantum mechanics and can be used by advanced undergrad or graduate students interested in the geometrical foundations of mechanics.
Even though it is certainly not the easiest book available, if you have to buy just one, buy this!

Excellent, but not as a first contact with Mechanics.......2001-11-20

I would agree on the rather high quality of the present
book, as pointed out in the other review.

However, the books seems not appropriate for a first contact
with Newtonian mechanics.

While the book makes every effort to introduce the reader to
modern concepts used in Mechanics, notably its setting in a
differential geometric context and an introduction to nonlinear
dynamical systems, the very basis of vector mechanics receives
only attention from one chapter.

This is clearly inadequate and a thourough understanding of
elementary vector mechanics and a good round of problem solving
is certainly essential before addressing even the simplest
Lagrangian mechanics.

The reason I want to point this out, is that the book is used
at an early level in German universities.

That is scary. I can well imagine people attempting to walk
through tangent spaces, but not able to integrate a simple
dynamics problem in R^2.

Please be careful!

The greatest undergratuate book in Mechanics........1999-11-28

This book is the greatest there is for a study of mechanics on an undergratuate level. This book covers alot of subjects with a unique combination of strictness and easyness. It's a must for all physics and mathematics students. It's index: 1.Elementary Newton Mechanics 2.The Principles of Canonical Mechanics 3.The Mechanics of Rigid Bodies 4.Relativistic Mechanics 5.Geometric Apsects of Mechanics 6.Stability and Chaos 7.Continuous Systems

Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)

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Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)
Walter Dittrich , and Martin Reuter
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Techniques and Applications of Path Integration (Dover Books on Physics)

ASIN: 3540420665

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Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, together with many worked examples throughout the text.
This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.

Elements of Hamiltonian Mechanics (International Series on Nuclear Energy)

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Elements of Hamiltonian Mechanics (International Series on Nuclear Energy)
D. Ter Haar
Manufacturer: Pergamon Pr
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Thermodynamics of Flowing Systems: with Internal Microstructure (Oxford Engineering Science Series)

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Thermodynamics of Flowing Systems: with Internal Microstructure (Oxford Engineering Science Series)
Antony N. Beris , and Brian J. Edwards
Manufacturer: Oxford University Press, USA
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ASIN: 019507694X

Book Description

This much-needed monograph presents a systematic, step-by-step approach to the continuum modeling of flow phenomena exhibited within materials endowed with a complex internal microstructure, such as polymers and liquid crystals. By combining the principles of Hamiltonian mechanics with those of irreversible thermodynamics, Antony N. Beris and Brian J. Edwards, renowned authorities on the subject, expertly describe the complex interplay between conservative and dissipative processes. Throughout the book, the authors emphasize the evaluation of the free energy--largely based on ideas from statistical mechanics--and how to fit the values of the phenomenological parameters against those of microscopic models. With Thermodynamics of Flowing Systems in hand, mathematicians, engineers, and physicists involved with the theoretical study of flow behavior in structurally complex media now have a superb, self-contained theoretical framework on which to base their modeling efforts.

Classical Mechanics: Systems of Particles and Hamiltonian Dynamics (Classical Theoretical Physics)

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Classical Mechanics
good but not enough

Classical Mechanics: Systems of Particles and Hamiltonian Dynamics (Classical Theoretical Physics)
Walter Greiner
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 0387951288

Book Description

The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series provide not only a complete survey of classical theoretical physics but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.

Customer Reviews:

Classical Mechanics.......2005-09-25

I have used some of Greiner's textbooks for my teaching and my students like them very much. Greiner's series of textbooks are comprehensive, comprehensible and contain a lot of non-trivial examples worked out in detail-something that is very important for the students. Just a few gripes-there are quite a number of typos and the notation sometimes does not conform to common English usage. Future editions should make the textbooks better.

good but not enough.......2005-08-03

This book belong to good german teaching tradition, but falls
below Golstein standard.It is a good text for the exercises
but do not expect deep explanation for generatrix function,Hamilton Jacobi resolution methods and Poisson brackets
relaion to differential geomery

Regular and Chaotic Dynamics (Applied Mathematical Sciences)

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Regular and Chaotic Dynamics (Applied Mathematical Sciences)
A.J. Lichtenberg , and M.A. Lieberman
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Classical Many-Body Problems Amenable to Exact Treatments: (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space (Lecture Notes in Physics)

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Classical Many-Body Problems Amenable to Exact Treatments: (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space (Lecture Notes in Physics)
Francesco Calogero
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ASIN: 3540417648

Book Description

This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces.This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.

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