Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publsiher: Springer Science & Business Media
Total Pages: 520
Release: 2013-04-09
ISBN 10: 1475720637
ISBN 13: 9781475720631
Language: EN, FR, DE, ES & NL

Mathematical Methods of Classical Mechanics Book Review:

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Mathematical Methods of Analytical Mechanics

Mathematical Methods of Analytical Mechanics
Author: Henri Gouin
Publsiher: Elsevier
Total Pages: 320
Release: 2020-11-27
ISBN 10: 0128229861
ISBN 13: 9780128229866
Language: EN, FR, DE, ES & NL

Mathematical Methods of Analytical Mechanics Book Review:

Mathematical Methods of Analytical Mechanics uses tensor geometry and geometry of variation calculation, includes the properties associated with Noether's theorem, and highlights methods of integration, including Jacobi's method, which is deduced. In addition, the book covers the Maupertuis principle that looks at the conservation of energy of material systems and how it leads to quantum mechanics. Finally, the book deduces the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry. Helps readers understand calculations surrounding the geometry of the tensor and the geometry of the calculation of the variation Presents principles that correspond to the energy conservation of material systems Defines the invariance properties associated with Noether's theorem Discusses phase space and Liouville's theorem Identifies small movements and different types of stabilities

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V. I. Arnold
Publsiher: Springer Science & Business Media
Total Pages: 464
Release: 2013-11-11
ISBN 10: 1475716931
ISBN 13: 9781475716931
Language: EN, FR, DE, ES & NL

Mathematical Methods of Classical Mechanics Book Review:

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

Methods of Differential Geometry in Analytical Mechanics

Methods of Differential Geometry in Analytical Mechanics
Author: M. de León,P.R. Rodrigues
Publsiher: Elsevier
Total Pages: 482
Release: 2011-08-18
ISBN 10: 9780080872698
ISBN 13: 0080872697
Language: EN, FR, DE, ES & NL

Methods of Differential Geometry in Analytical Mechanics Book Review:

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint. Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publsiher: Springer Science & Business Media
Total Pages: 520
Release: 1997-09-05
ISBN 10: 9780387968902
ISBN 13: 0387968903
Language: EN, FR, DE, ES & NL

Mathematical Methods of Classical Mechanics Book Review:

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Analytical Mechanics

Analytical Mechanics
Author: Ioan Merches,Daniel Radu
Publsiher: CRC Press
Total Pages: 456
Release: 2014-08-26
ISBN 10: 148223940X
ISBN 13: 9781482239409
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive a

A Student s Guide to Analytical Mechanics

A Student s Guide to Analytical Mechanics
Author: John L. Bohn
Publsiher: Cambridge University Press
Total Pages: 226
Release: 2018-09-30
ISBN 10: 1107145767
ISBN 13: 9781107145764
Language: EN, FR, DE, ES & NL

A Student s Guide to Analytical Mechanics Book Review:

An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.

Symplectic Geometry and Analytical Mechanics

Symplectic Geometry and Analytical Mechanics
Author: P. Libermann,Charles-Michel Marle
Publsiher: Springer Science & Business Media
Total Pages: 526
Release: 2012-12-06
ISBN 10: 9400938071
ISBN 13: 9789400938076
Language: EN, FR, DE, ES & NL

Symplectic Geometry and Analytical Mechanics Book Review:

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Analytical Mechanics

Analytical Mechanics
Author: Louis N. Hand,Janet D. Finch
Publsiher: Cambridge University Press
Total Pages: 329
Release: 1998-11-13
ISBN 10: 1139643312
ISBN 13: 9781139643313
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

Analytical Mechanics, first published in 1999, provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and prepares the reader thoroughly for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early on in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many 'e-mail questions', which are intended to facilitate dialogue between the student and instructor. Many worked examples are given, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.

Analytical Mechanics

Analytical Mechanics
Author: Nivaldo A. Lemos
Publsiher: Cambridge University Press
Total Pages: 470
Release: 2018-08-09
ISBN 10: 1108416586
ISBN 13: 9781108416580
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

An Introduction to Information Theory

An Introduction to Information Theory
Author: John Robinson Pierce
Publsiher: Courier Corporation
Total Pages: 305
Release: 1980-01-01
ISBN 10: 0486240614
ISBN 13: 9780486240619
Language: EN, FR, DE, ES & NL

An Introduction to Information Theory Book Review:

Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permeated the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter. Even more revolutionary progress is expected in the future. To give a solid introduction to this burgeoning field, J. R. Pierce has revised his well-received 1961 study of information theory for an up-to-date second edition. Beginning with the origins of the field, Dr. Pierce follows the brilliant formulations of Claude Shannon and describes such aspects of the subject as encoding and binary digits, entropy. language and meaning, efficient encoding , and the noisy channel. He then goes beyond the strict confines of the topic to explore the ways in which information theory relates to physics, cybernetics, psychology, and art. Mathematical formulas are introduced at the appropriate points for the benefit of serious students. A glossary of terms and an appendix on mathematical notation are provided to help the less mathematically sophisticated. J. R. Pierce worked for many years at the Bell Telephone Laboratories, where he became Director of Research in Communications Principles. He is currently affiliated with the engineering department of the California Institute of Technology. While his background is impeccable, Dr. Pierce also possesses an engaging writing style that makes his book all the more welcome. An Introduction to Information Theory continues to be the most impressive non-technical account available and a fascinating introduction to the subject for laymen. "An uncommonly good study. . . . Pierce's volume presents the most satisfying discussion to be found."? Scientific American.

Analytical Mechanics

Analytical Mechanics
Author: Joseph S. Torok
Publsiher: John Wiley & Sons
Total Pages: 376
Release: 1999-11-04
ISBN 10: 9780471332077
ISBN 13: 0471332070
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

A stimulating, modern approach to analytical mechanics Analytical Mechanics with an Introduction to Dynamical Systems offers a much-needed, up-to-date treatment of analytical dynamics to meet the needs of today's students and professionals. This outstanding resource offers clear and thorough coverage of mechanics and dynamical systems, with an approach that offers a balance between physical fundamentals and mathematical concepts. Exceptionally well written and abundantly illustrated, the book contains over 550 new problems-more than in any other book on the subject-along with user-friendly computational models using MATLAB. Featured topics include: * An overview of fundamental dynamics, both two- and three-dimensional * An examination of variational approaches, including Lagrangian theory * A complete discussion of the dynamics of rotating bodies * Coverage of the three-dimensional dynamics of rigid bodies * A detailed treatment of Hamiltonian systems and stability theory Ideal for advanced undergraduate and graduate students in mechanical engineering, physics, or applied mathematics, this distinguished text is also an excellent self-study or reference text for the practicing engineer or scientist.

Mathematical Physics Classical Mechanics

Mathematical Physics  Classical Mechanics
Author: Andreas Knauf
Publsiher: Springer
Total Pages: 683
Release: 2018-02-24
ISBN 10: 3662557746
ISBN 13: 9783662557747
Language: EN, FR, DE, ES & NL

Mathematical Physics Classical Mechanics Book Review:

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

Mathematical Methods of Classical Physics

Mathematical Methods of Classical Physics
Author: Vicente Cortés,Alexander S. Haupt
Publsiher: Springer
Total Pages: 99
Release: 2017-05-29
ISBN 10: 3319564633
ISBN 13: 9783319564630
Language: EN, FR, DE, ES & NL

Mathematical Methods of Classical Physics Book Review:

This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.

Probability Theory

Probability Theory
Author: Y. A. Rozanov
Publsiher: Courier Corporation
Total Pages: 148
Release: 2013-05-27
ISBN 10: 0486321142
ISBN 13: 9780486321141
Language: EN, FR, DE, ES & NL

Probability Theory Book Review:

This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.

Advanced Classical Mechanics

Advanced Classical Mechanics
Author: Bijan Bagchi
Publsiher: CRC Press
Total Pages: 260
Release: 2017-05-08
ISBN 10: 1351690434
ISBN 13: 9781351690430
Language: EN, FR, DE, ES & NL

Advanced Classical Mechanics Book Review:

This book is designed to serve as a textbook for postgraduates, researchers of applied mathematics, theoretical physics and students of engineering who need a good understanding of classical mechanics. In this book emphasis has been placed on the logical ordering of topics and appropriate formulation of the key mathematical equations with a view to imparting a clear idea of the basic tools of the subject and improving the problem solving skills of the students. The book provides a largely self-contained exposition to the topics with new ideas as a smooth continuation of the preceding ones. It is expected to give a systematic and comprehensive coverage of the methods of classical mechanics.

Analytical Mechanics

Analytical Mechanics
Author: A.I. Lurie
Publsiher: Springer Science & Business Media
Total Pages: 864
Release: 2002-03-26
ISBN 10: 9783540429821
ISBN 13: 3540429824
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

This is a translation of A.I. Lurie classical Russian textbook on analytical mechanics. Part of it is based on courses formerly held by the author. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the XX century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems. This book will help researchers and graduate students to acquire a deeper insight into analytical mechanics.

Classical Mechanics

Classical Mechanics
Author: R. Douglas Gregory
Publsiher: Cambridge University Press
Total Pages: 329
Release: 2006-04-13
ISBN 10: 1139450042
ISBN 13: 9781139450041
Language: EN, FR, DE, ES & NL

Classical Mechanics Book Review:

Gregory's Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author's clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether's theorem.

Analytical Mechanics

Analytical Mechanics
Author: Carl S. Helrich
Publsiher: Springer
Total Pages: 349
Release: 2016-10-01
ISBN 10: 3319444913
ISBN 13: 9783319444918
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.

Analytical Mechanics

Analytical Mechanics
Author: John G. Papastavridis
Publsiher: World Scientific Publishing Company Incorporated
Total Pages: 1392
Release: 2014
ISBN 10: 9789814338714
ISBN 13: 9814338710
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

This is a comprehensive, state-of-the-art, treatise on the energetic mechanics of Lagrange and Hamilton, that is, classical analytical dynamics, and its principal applications to constrained systems (contact, rolling, and servoconstraints). It is a book on advanced dynamics from a unified viewpoint, namely, the kinetic principle of virtual work, or principle of Lagrange. As such, it continues, renovates, and expands the grand tradition laid by such mechanics masters as Appell, Maggi, Whittaker, Heun, Hamel, Chetaev, Synge, Pars, Luré, Gantmacher, Neimark, and Fufaev. Many completely solved examples complement the theory, along with many problems (all of the latter with their answers and many of them with hints). Although written at an advanced level, the topics covered in this 1400-page volume (the most extensive ever written on analytical mechanics) are eminently readable and inclusive. It is of interest to engineers, physicists, and mathematicians; advanced undergraduate and graduate students and teachers; researchers and professionals; all will find this encyclopedic work an extraordinary asset; for classroom use or self-study. In this edition, corrections (of the original edition, 2002) have been incorporated.