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| Author | : John H. Lowenstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 203 |
| Release | : 2012-01-19 |
| Genre | : Mathematics |
| ISBN | : 1107005205 |
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.
| Author | : Gaetano Vilasi |
| Publisher | : World Scientific |
| Total Pages | : 457 |
| Release | : 2001 |
| Genre | : Science |
| ISBN | : 9810233086 |
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
| Author | : Kenneth R. Meyer |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 3319536915 |
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)
| Author | : Benedict Leimkuhler |
| Publisher | : Cambridge University Press |
| Total Pages | : 464 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780521772907 |
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.
| Author | : Helmut Hofer |
| Publisher | : Birkhäuser |
| Total Pages | : 356 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034885407 |
Analysis of an old variational principal in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities, and these invariants are the main theme of this book. Topics covered include basic sympletic geometry, sympletic capacities and rigidity, sympletic fixed point theory, and a survey on Floer homology and sympletic homology.
| Author | : Heinz J. Rothe |
| Publisher | : World Scientific |
| Total Pages | : 317 |
| Release | : 2010 |
| Genre | : Science |
| ISBN | : 9814299642 |
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field?antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. All topics are well illustrated with examples emphasizing points of central interest. The book should enable graduate students to follow the literature on this subject without much problems, and to perform research in this field.
| Author | : Alfredo M. Ozorio de Almeida |
| Publisher | : Cambridge University Press |
| Total Pages | : 262 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 9780521386708 |
Hamiltonian Systems outlines the main results in the field, and considers the implications for quantum mechanics.
| Author | : Gaetano Vilasi |
| Publisher | : World Scientific |
| Total Pages | : 460 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9789812386311 |
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations. Contents: Analytical Mechanics: The Lagrangian Coordinates; Hamiltonian Systems; Transformation Theory; The Integration Methods; Basic Ideas of Differential Geometry: Manifolds and Tangent Spaces; Differential Forms; Integration Theory; Lie Groups and Lie Algebras; Geometry and Physics: Symplectic Manifolds and Hamiltonian Systems; The Orbits Method; Classical Electrodynamics; Integrable Field Theories: KdV Equation; General Structures; Meaning and Existence of Recursion Operators; Miscellanea; Integrability of Fermionic Dynamics. Readership: Physicists and mathematicians.
| Author | : Nicholas Woodhouse |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 240 |
| Release | : 2009-12-17 |
| Genre | : Science |
| ISBN | : 1848828160 |
First published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding.
| Author | : Walter Greiner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 574 |
| Release | : 2009-11-13 |
| Genre | : Science |
| ISBN | : 3642034349 |
The series of texts on Classical Theoretical Physics is based on the highly successful courses given by Walter Greiner. The volumes provide a complete survey of classical theoretical physics and an enormous number of worked out examples and problems.
