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Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
  • Author : V.I. Arnol'd
  • Publsiher : Springer Science & Business Media
  • Release : 09 April 2013
  • ISBN : 1475720637
  • Pages : 520 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKMathematical Methods of Classical Mechanics

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. Arnol'd
  • Publisher : Springer Science & Business Media
  • Release : 09 April 2013
GET THIS BOOKMathematical Methods of Classical Mechanics

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.

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Methods of Differential Geometry in Analytical Mechanics

Methods of Differential Geometry in Analytical Mechanics
  • Author : M. de León,P.R. Rodrigues
  • Publisher : Elsevier
  • Release : 18 August 2011
GET THIS BOOKMethods of Differential Geometry in Analytical Mechanics

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

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The Elements of Mechanics

The Elements of Mechanics
  • Author : Giovanni Gallavotti
  • Publisher : Springer Science & Business Media
  • Release : 17 April 2013
GET THIS BOOKThe Elements of Mechanics

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

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Mathematical Methods of Analytical Mechanics

Mathematical Methods of Analytical Mechanics
  • Author : Henri Gouin
  • Publisher : Elsevier
  • Release : 27 November 2020
GET THIS BOOKMathematical Methods of Analytical Mechanics

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

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Classical Mechanics with Calculus of Variations and Optimal Control

Classical Mechanics with Calculus of Variations and Optimal Control
  • Author : Mark Levi
  • Publisher : American Mathematical Soc.
  • Release : 07 March 2014
GET THIS BOOKClassical Mechanics with Calculus of Variations and Optimal Control

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

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Analytical Mechanics

Analytical Mechanics
  • Author : John G. Papastavridis
  • Publisher : World Scientific Publishing Company Incorporated
  • Release : 12 August 2022
GET THIS BOOKAnalytical Mechanics

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

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Quantum Mechanics for Mathematicians

Quantum Mechanics for Mathematicians
  • Author : Leon Armenovich Takhtadzhi͡an
  • Publisher : American Mathematical Soc.
  • Release : 12 August 2022
GET THIS BOOKQuantum Mechanics for Mathematicians

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

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The Analytical Foundations of Celestial Mechanics

The Analytical Foundations of Celestial Mechanics
  • Author : Aurel Wintner
  • Publisher : Courier Corporation
  • Release : 18 June 2014
GET THIS BOOKThe Analytical Foundations of Celestial Mechanics

With this 1941 monograph, Aurel Wintner joined Poincaré, Birkhoff, and others in placing celestial mechanics on a sound mathematical basis. The product of many years of work by the author, it remains an extremely valuable contribution to the literature of this field. Starting with a review of dynamical operations, the treatment advances to local and non-local questions, dynamical systems, the problem of two bodies and the problem of several bodies, and an introduction to the restricted problem. Suitable for advanced undergraduates

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Analytical Mechanics

Analytical Mechanics
  • Author : Carl S. Helrich
  • Publisher : Springer
  • Release : 01 October 2016
GET THIS BOOKAnalytical Mechanics

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

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Analytical Mechanics

Analytical Mechanics
  • Author : Louis N. Hand,Janet D. Finch
  • Publisher : Cambridge University Press
  • Release : 13 November 1998
GET THIS BOOKAnalytical Mechanics

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,

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Analytical Techniques of Celestial Mechanics

Analytical Techniques of Celestial Mechanics
  • Author : Victor A. Brumberg
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKAnalytical Techniques of Celestial Mechanics

The aim of this book is to describe contemporary analytical and semi analytical techniques for solving typical celestial-mechanics problems. The word "techniques" is used here as a term intermediate between "methods" and "recipes". One often conceives some method of solution of a problem as a general mathematical tool, while not taking much care with its computa tional realization. On the other hand, the word "recipes" may nowadays be understood in the sense of the well-known book Numerical Recipes (Press et

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Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
  • Author : V. I. Arnold
  • Publisher : Springer Science & Business Media
  • Release : 11 November 2013
GET THIS BOOKMathematical Methods of Classical Mechanics

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

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Classical Mechanics

Classical Mechanics
  • Author : Matthew J. Benacquista,Joseph D. Romano
  • Publisher : Springer
  • Release : 27 February 2018
GET THIS BOOKClassical Mechanics

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.

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