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Mathematical Methods of Analytical Mechanics

Mathematical Methods of Analytical Mechanics
  • Author : Henri Gouin
  • Publisher :Unknown
  • Release Date :2020-11-27
  • Total pages :320
  • ISBN : 9780128229866
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Summary : 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
  • Publisher :Unknown
  • Release Date :2013-04-09
  • Total pages :520
  • ISBN : 9781475720631
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Summary : 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
  • Publisher :Unknown
  • Release Date :2013-11-11
  • Total pages :464
  • ISBN : 9781475716931
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Summary : 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
  • Publisher :Unknown
  • Release Date :2011-08-18
  • Total pages :482
  • ISBN : 0080872697
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Summary : 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
  • Publisher :Unknown
  • Release Date :1997-09-05
  • Total pages :520
  • ISBN : 0387968903
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Summary : 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
  • Publisher :Unknown
  • Release Date :2014-08-26
  • Total pages :456
  • ISBN : 9781482239409
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Summary : 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

Analytical Mechanics

Analytical Mechanics
  • Author : Nivaldo A. Lemos
  • Publisher :Unknown
  • Release Date :2018-08-09
  • Total pages :470
  • ISBN : 9781108416580
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Summary : An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics
  • Author : Frederick W. Byron,Robert W. Fuller
  • Publisher :Unknown
  • Release Date :2012-04-26
  • Total pages :672
  • ISBN : 9780486135069
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Summary : 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.

Mathematical Aspects of Classical and Celestial Mechanics

Mathematical Aspects of Classical and Celestial Mechanics
  • Author : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
  • Publisher :Unknown
  • Release Date :2007-07-05
  • Total pages :505
  • ISBN : 9783540489269
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Summary : 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.

A Student's Guide to Analytical Mechanics

A Student's Guide to Analytical Mechanics
  • Author : John L. Bohn
  • Publisher :Unknown
  • Release Date :2018-09-30
  • Total pages :226
  • ISBN : 9781107145764
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Summary : 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
  • Publisher :Unknown
  • Release Date :2009-09-30
  • Total pages :772
  • ISBN : 9048127645
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Summary : 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.

Analytical Mechanics

Analytical Mechanics
  • Author : Joseph S. Torok
  • Publisher :Unknown
  • Release Date :1999-11-04
  • Total pages :376
  • ISBN : 0471332070
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Summary : 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.

Analytical Mechanics

Analytical Mechanics
  • Author : Louis N. Hand,Janet D. Finch
  • Publisher :Unknown
  • Release Date :1998-11-13
  • Total pages :229
  • ISBN : 9781139643313
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Summary : 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 : John G. Papastavridis
  • Publisher :Unknown
  • Release Date :2014
  • Total pages :1392
  • ISBN : 9814338710
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Summary : 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.

Mathematical Methods in Quantum Mechanics

Mathematical Methods in Quantum Mechanics
  • Author : Gerald Teschl
  • Publisher :Unknown
  • Release Date :2009
  • Total pages :305
  • ISBN : 9780821846605
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Summary : 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 Physics: Classical Mechanics

Mathematical Physics: Classical Mechanics
  • Author : Andreas Knauf
  • Publisher :Unknown
  • Release Date :2018-02-24
  • Total pages :683
  • ISBN : 9783662557747
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Summary : 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.

Classical Mechanics

Classical Mechanics
  • Author : R. Douglas Gregory
  • Publisher :Unknown
  • Release Date :2006-04-13
  • Total pages :229
  • ISBN : 9781139450041
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Summary : 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.

Physics for Mathematicians

Physics for Mathematicians
  • Author : Michael Spivak
  • Publisher :Unknown
  • Release Date :2010
  • Total pages :733
  • ISBN : 0914098322
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Summary :

Classical Mechanics

Classical Mechanics
  • Author : Christopher W. Kulp,Vasilis Pagonis
  • Publisher :Unknown
  • Release Date :2020-11-17
  • Total pages :440
  • ISBN : 9781351024372
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Summary : Classical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation. Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics. It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics. Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms

Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics
  • Author : Oliver Johns
  • Publisher :Unknown
  • Release Date :2011-05-19
  • Total pages :656
  • ISBN : 9780191001628
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Summary : 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.

Advanced Classical Mechanics

Advanced Classical Mechanics
  • Author : Bijan Bagchi
  • Publisher :Unknown
  • Release Date :2017-05-08
  • Total pages :260
  • ISBN : 9781351690430
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Summary : 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.