Mathematical Methods Of Analytical Mechanics

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 52,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475720631

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Mathematical Methods of Classical Mechanics by V.I. Arnol'd Pdf

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.

Author : Henri Gouin
Publisher : Elsevier
Page : 322 pages
File Size : 55,7 Mb
Release : 2020-11-27
Category : Mathematics
ISBN : 9780128229866

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Mathematical Methods of Analytical Mechanics by Henri Gouin Pdf

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

Author : V. I. Arnold
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 51,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475716931

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Mathematical Methods of Classical Mechanics by V. I. Arnold Pdf

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.

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 55,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846605

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Mathematical Methods in Quantum Mechanics by Gerald Teschl Pdf

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).

Author : Grant R. Fowles,George L. Cassiday
Publisher : Unknown
Page : 584 pages
File Size : 45,8 Mb
Release : 2005
Category : Mechanics, Analytic
ISBN : UCSD:31822033266271

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Analytical Mechanics by Grant R. Fowles,George L. Cassiday Pdf

With the direct, accessible, and pragmatic approach of Fowles and Cassiday's ANALYTICAL MECHANICS, Seventh Edition, thoroughly revised for clarity and concision, students will grasp challenging concepts in introductory mechanics. A complete exposition of the fundamentals of classical mechanics, this proven and enduring introductory text is a standard for the undergraduate Mechanics course. Numerical worked examples increased students' problem-solving skills, while textual discussions aid in student understanding of theoretical material through the use of specific cases.

Author : Giovanni Gallavotti
Publisher : Springer Science & Business Media
Page : 586 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662007310

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The Elements of Mechanics by Giovanni Gallavotti Pdf

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.

Author : Carl S. Helrich
Publisher : Springer
Page : 349 pages
File Size : 52,9 Mb
Release : 2016-10-01
Category : Science
ISBN : 9783319444918

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Analytical Mechanics by Carl S. Helrich Pdf

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.

Author : Martin Kružík,Tomáš Roubíček
Publisher : Springer
Page : 617 pages
File Size : 48,5 Mb
Release : 2019-03-02
Category : Science
ISBN : 9783030020651

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Mathematical Methods in Continuum Mechanics of Solids by Martin Kružík,Tomáš Roubíček Pdf

This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

Author : Oliver Johns
Publisher : OUP Oxford
Page : 653 pages
File Size : 41,8 Mb
Release : 2011-05-19
Category : Science
ISBN : 9780191001628

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Analytical Mechanics for Relativity and Quantum Mechanics by Oliver Johns Pdf

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.

Author : Louis N. Hand,Janet D. Finch
Publisher : Cambridge University Press
Page : 569 pages
File Size : 53,5 Mb
Release : 1998-11-13
Category : Science
ISBN : 9781139643313

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Analytical Mechanics by Louis N. Hand,Janet D. Finch Pdf

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.

Author : Vladimir Igor'evič Arnol'd
Publisher : Unknown
Page : 462 pages
File Size : 43,8 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:1014637231

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Mathematical methods of classical mechanics by Vladimir Igor'evič Arnol'd Pdf

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 55,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846308

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Quantum Mechanics for Mathematicians by Leon Armenovich Takhtadzhi͡an Pdf

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including 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.

Author : Vladimir Igorevich Arnolʹd
Publisher : Unknown
Page : 516 pages
File Size : 53,9 Mb
Release : 1997
Category : Mechanics, Analytic
ISBN : OCLC:1319420616

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Mathematical Methods of Classical Mechanics by Vladimir Igorevich Arnolʹd Pdf

Author : Frederick W. Byron,Robert W. Fuller
Publisher : Courier Corporation
Page : 674 pages
File Size : 49,8 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486135069

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Mathematics of Classical and Quantum Physics by Frederick W. Byron,Robert W. Fuller Pdf

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.

Author : P. Libermann,Charles-Michel Marle
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400938076

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Symplectic Geometry and Analytical Mechanics by P. Libermann,Charles-Michel Marle Pdf

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.