Group-Theoretic Methods in Mechanics and Applied Mathematics. (Record no. 14207)
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| fixed length control field | 06212nam a22004453i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5962707 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114018.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2002 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781482265224 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780367446987 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5962707 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5962707 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1125111913 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA171 .K556 2004 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.2 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Klimov, D. M. |
| 245 10 - TITLE STATEMENT | |
| Title | Group-Theoretic Methods in Mechanics and Applied Mathematics. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Milton : |
| Name of producer, publisher, distributor, manufacturer | Taylor & Francis Group, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2002. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2004. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (239 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Foreword -- Authors -- Chapter 1. Basic Notions of Lie Group Theory -- 1.1. Notion of Group -- 1.2. Lie Group. Examples -- 1.3. Group Generator. Lie Algebra -- 1.4. One-Parameter Groups. Uniqueness Theorem -- 1.5. Liouville Equation. Invariants. Eigenfunctions -- 1.6. Linear Partial Differential Equations -- 1. 7. Change of Variables. Canonical Coordinates of a Group -- 1.8. Hausdorff's Formula. Symmetry Groups -- 1.9. Principle of Superposition of Solutions and Separation of Motions in Nonlinear Mechanics -- 1.1 0. Prolongation of Groups. Differential and Integral Invariants -- 1.11. Equations Admitting a Given Group -- 1.12. Symmetries of Partial Differential Equations -- Chapter 2. Group Analysis of Foundations of Classical and Relativistic Mechanics -- 2.1. Axiomatization Problem of Mechanics -- 2.2. Postulates of Classical Mechanics -- 2.3. Projective Symmetries of Newton's First Law -- 2.4. Newton's Second Law. Galilean Symmetries -- 2.5. Postulates of Relativistic Mechanics -- 2.6. Group of Symmetries of Maxwell's Equations -- 2.7. Twice Prolonged Lorentz Group -- 2.8. Differential and Integral Invariants of the Lorentz Group -- 2.9. Relativistic Equations of Motion of a Particle -- 2.1 0. Noninertial Reference Frames -- Chapter 3. Application of Group Methods to Problems of Mechanics -- 3.1. Perturbation Theory for Configuration Manifolds of Resonant Systems -- 3.1.1. Statement of the Problem -- 3.1.2. The Case of Double Natural Frequency -- 3.1.3. The Manifold of Degenerate Forms. Local Evolution Basis -- 3.1.4. Algebra of Local Evolutions -- 3.1.5. Classification of Perturbations -- 3.1.6. The Problem of Stabilization of the Oscillation Shape -- 3.2. Poincare's Equation on Lie Algebras -- 3.3. Kinematics of a Rigid Body. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 3.3.1. Ways of Specifying the Orientation of a Rigid Body -- 3.3.2. Addition of Rotations -- 3.3.3. Topology of the Manifold of Rotations of a Rigid Body (Topology of the S0(3) group -- 3.3.4. Angular Velocity of a Rigid Body -- 3.4. Problems of Mechanics Admitting Similarity Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . I -- 3.4.1. Suslov Problem -- 3.4.2. The Problem of the Follower Trajectory -- 3.4.3. Rolling of a Homogeneous Ball Over a Rough Plane -- 3.5. Problems With Determinable Linear Groups of Symmetries -- 3.5.1. Falling of a Heavy Homogeneous Thread -- 3.5.2. Motion of a Point Particle Under the Action of a Follower Force -- 3.5.3. The Problem of an Optimal Shape of a Body in an Air Flow -- Chapter 4. Finite-Dimensional Hamiltonian Systems -- 4.1. Legendre Transformation -- 4.2. Hamiltonian Systems. Poisson Bracket -- 4.3. Nonautonomous Hamiltonian Systems -- 4.4. Integrals of Hamiltonian Groups. Noether's Theorem -- 4.5. Conservation Laws and Symmetries -- 4.6. Integral Invariants -- 4.6.1. Poincare--Cartan Invariants -- 4.6.2. Liouville's Theorem of the Phase Volume -- 4.7. Canonical Transformations -- 4.8. Hamilton-Jacobi Equation -- 4.1 0. The Angle-Action Variables -- Chapter 5. Asymptotic Methodsof Applied Mathematics -- 5.1. Introduction -- 5.2. Normal Coordinates of Conservative Systems -- 5.3. Single-Frequency Method of Averaging Based onHausdorff's Formula -- 5.4. Poincare Normal Form -- 5.5. The Averaging Principle -- 5.5.1. Averaging of Single-Frequency Systems -- 5.5.2. Multifrequency Systems. Resonance -- 5.6. Asymptotic Integration of Hamiltonian Systems -- 5.6.1. Birkhoff Normal Form -- 5.6.2. Averaging of Hamiltonian Systems in Terms of Lie Series -- 5.6.3. Artificial Hamiltonization -- 5. 7. Method of Tangent Approximations -- 5.8. Classical Examples of Oscillation Theory -- 5.8.1. Van Der Pol's Equation. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 5.8.2. Mathieu's Equation -- 5.8.3. Forced Oscillations of Cuffing's Oscillator -- 5.8.4. Forced Oscillations of Van Der Pol's Oscillator -- Brief Historical Sketch -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Group theory. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Klimov, D. M. |
| Title | Group-Theoretic Methods in Mechanics and Applied Mathematics |
| Place, publisher, and date of publication | Milton : Taylor & Francis Group,c2002 |
| International Standard Book Number | 9780367446987 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5962707">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5962707</a> |
| Public note | Click to View |
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