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. 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.

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. 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

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.

Analytical Mechanics

Analytical Mechanics
Author: Grant R. Fowles,George L. Cassiday
Publsiher: Brooks/Cole Publishing Company
Total Pages: 514
Release: 2005
ISBN 10: 9780534494926
ISBN 13: 0534494927
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

Master introductory mechanics with ANALYTICAL MECHANICS! Direct and practical, this physics text is designed to help you grasp the challenging concepts of physics. Specific cases are included to help you master theoretical material. Numerous worked examples found throughout increase your problem-solving skills and prepare you to succeed on tests.

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.

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.

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: 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.

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.

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.

Geometric Formulation of Classical and Quantum Mechanics

Geometric Formulation of Classical and Quantum Mechanics
Author: G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili
Publsiher: World Scientific
Total Pages: 392
Release: 2011
ISBN 10: 9814313726
ISBN 13: 9789814313728
Language: EN, FR, DE, ES & NL

Geometric Formulation of Classical and Quantum Mechanics Book Review:

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Elementary Mechanics Using Matlab

Elementary Mechanics Using Matlab
Author: Anders Malthe-Sørenssen
Publsiher: Springer
Total Pages: 590
Release: 2015-06-01
ISBN 10: 3319195875
ISBN 13: 9783319195872
Language: EN, FR, DE, ES & NL

Elementary Mechanics Using Matlab Book Review:

This book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks. Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts. While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Matlab, and a chapter devoted to the basics of scientific programming with Matlab is included. A parallel edition using Python instead of Matlab is also available. Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.

Modern Methods of Analytical Mechanics and their Applications

Modern Methods of Analytical Mechanics and their Applications
Author: Valentin V. Rumyantsev,Alexander V. Karapetyan
Publsiher: Springer
Total Pages: 344
Release: 2014-05-04
ISBN 10: 3709125200
ISBN 13: 9783709125205
Language: EN, FR, DE, ES & NL

Modern Methods of Analytical Mechanics and their Applications Book Review:

The volume aims at giving a comprehensive and up-to-date view of modern methods of analytical mechanics (general equations, invariant objects, stability and bifurcations) and their applications (rigid body dynamics, celestial mechanics, multibody systems etc.). The course is at an advanced level. It is designed for postgraduate students, research engineers and academics that are familiar with basic concepts of analytical dynamics and stability theory. Although the course deals with mechanical problems, most of the concepts and methods involved are equally applicated to general dynamical systems.

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics
Author: Frederick W. Byron,Robert W. Fuller
Publsiher: Courier Corporation
Total Pages: 672
Release: 2012-04-26
ISBN 10: 0486135063
ISBN 13: 9780486135069
Language: EN, FR, DE, ES & NL

Mathematics of Classical and Quantum Physics Book Review:

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

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.

Mathematical Methods for Geophysics and Space Physics

Mathematical Methods for Geophysics and Space Physics
Author: William I. Newman
Publsiher: Princeton University Press
Total Pages: 272
Release: 2016-05-03
ISBN 10: 0691170606
ISBN 13: 9780691170602
Language: EN, FR, DE, ES & NL

Mathematical Methods for Geophysics and Space Physics Book Review:

An essential textbook on the mathematical methods used in geophysics and space physics Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
Author: E. T. Whittaker
Publsiher: Cambridge University Press
Total Pages: 456
Release: 1988-12-15
ISBN 10: 9780521358835
ISBN 13: 0521358833
Language: EN, FR, DE, ES & NL

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies Book Review:

There can be few books on mathematical mechanics as famous as this, a work that forms a comprehensive account of all the classical results of analytical dynamics.