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. 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.

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: 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.

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.

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: 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.

Analytical Mechanics

Analytical Mechanics
Author: Antonio Fasano,Stefano Marmi
Publsiher: Oxford University Press
Total Pages: 772
Release: 2006-04-06
ISBN 10: 0198508026
ISBN 13: 9780198508021
Language: EN, FR, DE, ES & NL

Analytical Mechanics Book Review:

Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a pointmass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.

A Primer of Analytical Mechanics

A Primer of Analytical Mechanics
Author: Franco Strocchi
Publsiher: Springer
Total Pages: 114
Release: 2018-03-09
ISBN 10: 3319737619
ISBN 13: 9783319737614
Language: EN, FR, DE, ES & NL

A Primer of Analytical Mechanics Book Review:

This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

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.

Fundamental Principles of Classical Mechanics

Fundamental Principles of Classical Mechanics
Author: Kai S Lam
Publsiher: World Scientific Publishing Company
Total Pages: 592
Release: 2014-07-07
ISBN 10: 9814551503
ISBN 13: 9789814551502
Language: EN, FR, DE, ES & NL

Fundamental Principles of Classical Mechanics Book Review:

This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

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.

Mathematical Methods in Quantum Mechanics

Mathematical Methods in Quantum Mechanics
Author: Gerald Teschl
Publsiher: American Mathematical Soc.
Total Pages: 305
Release: 2009
ISBN 10: 0821846604
ISBN 13: 9780821846605
Language: EN, FR, DE, ES & NL

Mathematical Methods in Quantum Mechanics Book Review:

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Mathematical Aspects of Classical and Celestial Mechanics

Mathematical Aspects of Classical and Celestial Mechanics
Author: Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publsiher: Springer Science & Business Media
Total Pages: 505
Release: 2007-07-05
ISBN 10: 3540489266
ISBN 13: 9783540489269
Language: EN, FR, DE, ES & NL

Mathematical Aspects of Classical and Celestial Mechanics Book Review:

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Advanced Classical Mechanics

Advanced Classical Mechanics
Author: Bijan Bagchi
Publsiher: CRC Press
Total Pages: 260
Release: 2017-05-08
ISBN 10: 1351690426
ISBN 13: 9781351690423
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.

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.

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.

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.

Modern Analytic Mechanics

Modern Analytic Mechanics
Author: Claudio Pellegrini,Richard K. Cooper
Publsiher: Springer Science & Business Media
Total Pages: 341
Release: 2013-04-17
ISBN 10: 1475758677
ISBN 13: 9781475758672
Language: EN, FR, DE, ES & NL

Modern Analytic Mechanics Book Review:

By modern analytic mechanics we mean the classical mechanics of today, that is, the mechanics that has proven particularly useful in understanding the universe as we experience it from the solar system, to particle accelerators, to rocket motion. The mathematical and numerical techniques that are part of this mechanics that we present are those that we have found to be particularly productive in our work in the subject. The balance of topics in this book is somewhat different from previous texts. We emphasize the use of phase space to describe the dynamics of a system and to have a qualitative understanding of nonlinear systems. We incorporate exercises that are to be done using a computer to solve linear and nonlinear problems and to have a graphical representation of the results. While analytic solutions of physics problems are to be prefer. red, it is not always possible to find them for all problems. When that happens, techniques other than analysis must be brought to bear on the problem. In many cases numerical treatments are useful in generating solutions, and with these solutions often come new insights. These insights can sometimes be used for making further analytic progress, and often the process is iterative. Thus the ability to use a computer to solve problems is one of the tools of the modern physicist. Just as analytic problem-solving enhances the student's understanding of physics, so will using the computer enhance his or her appreciation of the subject.