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 Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publsiher: Springer
Total Pages: 520
Release: 2010-12-01
ISBN 10: 9781441930873
ISBN 13: 1441930876
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.

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.

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.

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

Analytical Mechanics

Analytical Mechanics
Author: Louis N. Hand,Janet D. Finch
Publsiher: Cambridge University Press
Total Pages: 135
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.

The Elements of Mechanics

The Elements of Mechanics
Author: Giovanni Gallavotti
Publsiher: Springer Science & Business Media
Total Pages: 575
Release: 2013-04-17
ISBN 10: 3662007312
ISBN 13: 9783662007310
Language: EN, FR, DE, ES & NL

The Elements of Mechanics Book Review:

The word "elements" in the title of this book does not convey the implica tion that its contents are "elementary" in the sense of "easy": it mainly means that no prerequisites are required, with the exception of some basic background in classical physics and calculus. It also signifies "devoted to the foundations". In fact, the arguments chosen are all very classical, and the formal or technical developments of this century are absent, as well as a detailed treatment of such problems as the theory of the planetary motions and other very concrete mechanical problems. This second meaning, however, is the result of the necessity of finishing this work in a reasonable amount of time rather than an a priori choice. Therefore a detailed review of the "few" results of ergodic theory, of the "many" results of statistical mechanics, of the classical theory of fields (elasticity and waves), and of quantum mechanics are also totally absent; they could constitute the subject of two additional volumes on mechanics. This book grew out of several courses on meccanica razionaie, i.e., essentially, theoretical mechanics, which I gave at the University of Rome during the years 1975-1978.

Introduction to Classical Mechanics

Introduction to Classical Mechanics
Author: Roy, Nikhil Ranjan
Publsiher: Vikas Publishing House
Total Pages: 135
Release: 2022
ISBN 10: 932599402X
ISBN 13: 9789325994027
Language: EN, FR, DE, ES & NL

Introduction to Classical Mechanics Book Review:

The book deals with the mechanics of particles and rigid bodies. It is written for the undergraduate students of physics and meets the syllabus requirements of most Indian universities. It also covers the entire syllabus on classical/analytical mechanics for various national and state level examinations like NET, GATE and SLET. Some of the topics in the book are included in the curricula of applied mathematics in several institutions as well.KEY FEATURES• Main emphasis is on the evolution of the subject, the underlying ideas, the concepts, the laws and the mathematical methods• Written in the style of classroom teaching so that the students may benefit from it by way of self-study• Step-by-step derivation of concepts, with each step clearly numbered• Concepts explained with the help of relevant examples to aid understanding

Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics
Author: Oliver Johns
Publsiher: OUP Oxford
Total Pages: 656
Release: 2011-05-19
ISBN 10: 0191001627
ISBN 13: 9780191001628
Language: EN, FR, DE, ES & NL

Analytical Mechanics for Relativity and Quantum Mechanics Book Review:

An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It presents classical mechanics in a way designed to assist the student's transition to quantum theory.

Quantum Mechanics for Mathematicians

Quantum Mechanics for Mathematicians
Author: Leon Armenovich Takhtadzhi͡an
Publsiher: American Mathematical Soc.
Total Pages: 387
Release: 2008
ISBN 10: 0821846302
ISBN 13: 9780821846308
Language: EN, FR, DE, ES & NL

Quantum Mechanics for Mathematicians Book Review:

This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

Analytical Mechanics

Analytical Mechanics
Author: J.L. Lagrange
Publsiher: Springer Science & Business Media
Total Pages: 594
Release: 2013-04-17
ISBN 10: 9401589038
ISBN 13: 9789401589031
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.

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.

Classical Mechanics with Calculus of Variations and Optimal Control

Classical Mechanics with Calculus of Variations and Optimal Control
Author: Mark Levi
Publsiher: American Mathematical Soc.
Total Pages: 299
Release: 2014-03-07
ISBN 10: 0821891383
ISBN 13: 9780821891384
Language: EN, FR, DE, ES & NL

Classical Mechanics with Calculus of Variations and Optimal Control Book Review:

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Classical Mechanics

Classical Mechanics
Author: R. Douglas Gregory
Publsiher: Cambridge University Press
Total Pages: 135
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.

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: Grant Robert FOWLES
Publsiher: Unknown
Total Pages: 278
Release: 1962
ISBN 10: 1928374650XXX
ISBN 13: OCLC:559266851
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

Classical Mechanics

Classical Mechanics
Author: Matthew J. Benacquista,Joseph D. Romano
Publsiher: Springer
Total Pages: 546
Release: 2018-02-27
ISBN 10: 3319687808
ISBN 13: 9783319687803
Language: EN, FR, DE, ES & NL

Classical Mechanics Book Review:

This textbook provides an introduction to classical mechanics at a level intermediate between the typical undergraduate and advanced graduate level. This text describes the background and tools for use in the fields of modern physics, such as quantum mechanics, astrophysics, particle physics, and relativity. Students who have had basic undergraduate classical mechanics or who have a good understanding of the mathematical methods of physics will benefit from this book.

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.

Mechanical Systems Classical Models

Mechanical Systems  Classical Models
Author: Petre P. Teodorescu
Publsiher: Springer Science & Business Media
Total Pages: 772
Release: 2009-09-30
ISBN 10: 9048127645
ISBN 13: 9789048127641
Language: EN, FR, DE, ES & NL

Mechanical Systems Classical Models Book Review:

All phenomena in nature are characterized by motion. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature, mathematics plays an important rôle. Mechanics is the first science of nature which has been expressed in terms of mathematics, by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool. As it was already seen in the first two volumes of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, that is on its five principles, i.e.: the inertia, the forces action, the action and reaction, the independence of the forces action and the initial conditions principle, respectively. Other models, e.g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler’s laws brilliantly verify this model in case of velocities much smaller then the light velocity in vacuum.

Introduction to Asymptotic Methods

Introduction to Asymptotic Methods
Author: David Y. Gao,Vadim A. Krysko
Publsiher: CRC Press
Total Pages: 272
Release: 2006-05-03
ISBN 10: 1420011731
ISBN 13: 9781420011739
Language: EN, FR, DE, ES & NL

Introduction to Asymptotic Methods Book Review:

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m