Average customer rating:
|
Poincare and the Three Body Problem (History of Mathematics, V. 11)
June Barrow-Green Manufacturer: American Mathematical Society ProductGroup: Book Binding: Paperback ASIN: 0821803670 |
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
Average customer rating: |
Fluctuations Order & Defects
Gene F. Mazenko , and Gene Mazenko Manufacturer: Wiley-Interscience ProductGroup: Book Binding: Hardcover Similar Items: 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.
Average customer rating: |
Simulating Hamiltonian Dynamics (Cambridge Monographs on Applied and Computational Mathematics)
Benedict Leimkuhler , and Sebastian Reich Manufacturer: Cambridge University Press ProductGroup: Book Binding: Hardcover Similar Items:
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.Download Description
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.
Average customer rating:
|
Mechanics: From Newton's Laws to Deterministic Chaos (Advanced Texts in Physics)
Florian Scheck Manufacturer: Springer ProductGroup: Book Binding: Hardcover Similar Items:
Accessories:
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
Excellent, but not as a first contact with Mechanics.......2001-11-20
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
Average customer rating: |
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 Similar Items: ASIN: 3540420665 |
Book Description
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.
Average customer rating: |
Elements of Hamiltonian Mechanics (International Series on Nuclear Energy)
D. Ter Haar Manufacturer: Pergamon Pr ProductGroup: Book Binding: Paperback ASIN: 0080167268 |
Average customer rating: |
Thermodynamics of Flowing Systems: with Internal Microstructure (Oxford Engineering Science Series)
Antony N. Beris , and Brian J. Edwards Manufacturer: Oxford University Press, USA ProductGroup: Book Binding: Hardcover 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.
Average customer rating:
|
Classical Mechanics: Systems of Particles and Hamiltonian Dynamics (Classical Theoretical Physics)
Walter Greiner Manufacturer: Springer ProductGroup: Book Binding: Paperback Similar Items:
Accessories:
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
good but not enough.......2005-08-03
Average customer rating: |
Regular and Chaotic Dynamics (Applied Mathematical Sciences)
A.J. Lichtenberg , and M.A. Lieberman Manufacturer: Springer ProductGroup: Book Binding: Hardcover ASIN: 0387977457 |
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.
Average customer rating: |
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 Manufacturer: Springer ProductGroup: Book Binding: Hardcover 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.Books:
Recommended Books