Group-theoretic methods in mechanics and applied mathematics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Taylor & Francis
2002
|
| Edition: | 1. publ. |
| Series: | Differential and integral equations and their applications
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 230 S. graph. Darst. |
| ISBN: | 0415298636 |
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MARC
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| 245 | 1 | 0 | |a Group-theoretic methods in mechanics and applied mathematics |c D. M. Klimov and V. Ph. Zhuravlev |
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Record in the Search Index
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|---|---|
| adam_text | GROUP-THEORETIC METHODS IN MECHANICS AND APPLIED MATHEMATICS D. M.
KLIMOV AND V. PH. ZHURAVLEV INSTITUTE FOR PROBLEMS IN MECHANICS RUSSIAN
ACADEMY OF SCIENCE MOSCOW, RUSSIA LONDON AND NEW YORK CONTENTS FOREWORD
VII AUTHORS X 1. BASIC NOTIONS OF LIE GROUP THEORY 1 1.1. NOTION OF
GROUP 1 1.2. LIE GROUP. EXAMPLES 3 1.3. GROUP GENERATOR. LIE ALGEBRA 5
1.4. ONE-PARAMETER GROUPS. UNIQUENESS THEOREM 11 1.5. LIOUVILLE
EQUATION. INVARIANTS. EIGENFUNCTIONS 13 1.6. LINEAR PARTIAL DIFFERENTIAL
EQUATIONS 17 1.7. CHANGE OF VARIABLES. CANONICAL COORDINATES OF A GROUP
18 1.8. HAUSDORFF S FORMULA. SYMMETRY GROUPS 20 1.9. PRINCIPLE OF
SUPERPOSITION OF SOLUTIONS AND SEPARATION OF MOTIONS IN NONLINEAR
MECHANICS 29 1.10. PROLONGATION OF GROUPS. DIFFERENTIAL AND INTEGRAL
INVARIANTS 31 1.11. EQUATIONS ADMITTING A GIVEN GROUP 36 1.12.
SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS 42 2. GROUP ANALYSIS OF
FOUNDATIONS OF CLASSICAL AND RELATIVISTIC MECHANICS 47 2.1.
AXIOMATIZATION PROBLEM OF MECHANICS 47 2.2. POSTULATES OF CLASSICAL
MECHANICS 48 2.3. PROJECTIVE SYMMETRIES OF NEWTON S FIRST LAW 50 2.4.
NEWTON S SECOND LAW. GALILEAN SYMMETRIES 51 2.5. POSTULATES OF
RELATIVISTIC MECHANICS 54 2.6. GROUP OF SYMMETRIES OF MAXWELL S
EQUATIONS 54 2.7. TWICE PROLONGED LORENTZ GROUP 56 2.8. DIFFERENTIAL AND
INTEGRAL INVARIANTS OF THE LORENTZ GROUP 60 2.9. RELATIVISTIC EQUATIONS
OF MOTION OF A PARTICLE 62 2.10. NONINERTIAL REFERENCE FRAMES 63 3.
APPLICATION OF GROUP METHODS TO PROBLEMS OF MECHANICS 65 3.1.
PERTURBATION THEORY FOR CONFIGURATION MANIFOLDS OF RESONANT SYSTEMS 65
3.1.1. STATEMENT OF THE PROBLEM 65 3.1.2. THE CASE OF DOUBLE NATURAL
FREQUENCY 66 3.1.3. THE MANIFOLD OF DEGENERATE FORMS. LOCAL EVOLUTION
BASIS 67 3.1.4. ALGEBRA OF LOCAL EVOLUTIONS 69 3.1.5. CLASSIFICATION OF
PERTURBATIONS 70 3.1.6. THE PROBLEM OF STABILIZATION OF THE OSCILLATION
SHAPE 71 3.2. POINCARE S EQUATION ON LIE ALGEBRAS 73 VI CONTENTS 3.3.
KINEMATICS OF A RIGID BODY 76 3.3.1. WAYS OF SPECIFYING THE ORIENTATION
OF A RIGID BODY 76 3.3.2. ADDITION OF ROTATIONS 90 3.3.3. TOPOLOGY,OF
THE MANIFOLD OF ROTATIONS OF A RIGID BODY (TOPOLOGY OF THE SO(3) GROUP)
96 3.3.4. ANGULAR VELOCITY OF A RIGID BODY 97 3.4. PROBLEMS OF MECHANICS
ADMITTING SIMILARITY GROUPS 104 3.4.1. SUSLOV PROBLEM 104 3.4.2. THE
PROBLEM OF THE FOLLOWER TRAJECTORY 107 3.4.3. ROLLING OF A HOMOGENEOUS
BALL OVER A ROUGH PLANE 109 3.5. PROBLEMS WITH DETERMINABLE LINEAR
GROUPS OF SYMMETRIES 112 3.5.1. FALLING OF A HEAVY HOMOGENEOUS THREAD
112 3.5.2. MOTION OF A POINT PARTICLE UNDER THE ACTION OF A FOLLOWER
FORCE 115 3.5.3. THE PROBLEM OF AN OPTIMAL SHAPE OF A BODY IN AN AIR
FLOW 120 4. FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS 125 4.1. LEGENDRE
TRANSFORMATION 125 4.2. HAMILTONIAN SYSTEMS. POISSON BRACKET 126 4.3.
NONAUTONOMOUS HAMILTONIAN SYSTEMS 128 4.4. INTEGRALS OF HAMILTONIAN
GROUPS. NOETHER S THEOREM 129 4.5. CONSERVATION LAWS AND SYMMETRIES 132
4.6. INTEGRAL INVARIANTS 133 4.6.1. POINCARE-CARTAN INVARIANTS 134
4.6.2. LIOUVILLE S THEOREM OF THE PHASE VOLUME 138 4.7. CANONICAL
TRANSFORMATIONS 139 4.8. HAMILTON-JACOBI EQUATION 145 4.9. LIOUVILLE S
THEOREM OF INTEGRABLE SYSTEMS 147 4.10. THE ANGLE-ACTION VARIABLES 148
5. ASYMPTOTIC METHODS OF APPLIED MATHEMATICS 151 5.1. INTRODUCTION 151
5.2. NORMAL COORDINATES OF CONSERVATIVE SYSTEMS 153 5.3.
SINGLE-FREQUENCY METHOD OF AVERAGING BASED ON HAUSDORFF S FORMULA 158
5.4. POINCARE NORMAL FORM 160 5.5. THE AVERAGING PRINCIPLE 170 5.5.1.
AVERAGING OF SINGLE-FREQUENCY SYSTEMS 175 5.5.2. MULTIFREQUENCY SYSTEMS.
RESONANCE 183 5.6. ASYMPTOTIC INTEGRATION OF HAMILTONIAN SYSTEMS 189
5.6.1. BIRKHOFF NORMAL FORM 189 5.6.2. AVERAGING OF HAMILTONIAN SYSTEMS
IN TERMS OF LIE SERIES 200 5.6.3. ARTIFICIAL HAMILTONIZATION 201 5.7.
METHOD OF TANGENT APPROXIMATIONS 204 5.8. CLASSICAL EXAMPLES OF
OSCILLATION THEORY 208 5.8.1. VAN DER POL S EQUATION 208 5.8.2.
MATHIEU S EQUATION : 209 5.8.3. FORCED OSCILLATIONS OF DUFFING S
OSCILLATOR 212 5.8.4. FORCED OSCILLATIONS OF VAN DER POL S OSCILLATOR
215 BRIEF HISTORICAL SKETCH 219 INDEX 225
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| bvnumber | BV014412733 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014412733 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:28Z |
| institution | BVB |
| isbn | 0415298636 |
| language | English |
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| physical | IX, 230 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Taylor & Francis |
| record_format | marc |
| series | Differential and integral equations and their applications |
| series2 | Differential and integral equations and their applications |
| spelling | Klimov, Dmitrij M. Verfasser aut Group-theoretic methods in mechanics and applied mathematics D. M. Klimov and V. Ph. Zhuravlev 1. publ. London [u.a.] Taylor & Francis 2002 IX, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential and integral equations and their applications 2 Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Mechanik (DE-588)4038168-7 s Angewandte Mathematik (DE-588)4142443-8 s DE-604 Žuravlev, Viktor P. Verfasser aut Differential and integral equations and their applications 2 (DE-604)BV014412675 2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009857317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klimov, Dmitrij M. Žuravlev, Viktor P. Group-theoretic methods in mechanics and applied mathematics Differential and integral equations and their applications Angewandte Mathematik (DE-588)4142443-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4072157-7 (DE-588)4038168-7 |
| title | Group-theoretic methods in mechanics and applied mathematics |
| title_auth | Group-theoretic methods in mechanics and applied mathematics |
| title_exact_search | Group-theoretic methods in mechanics and applied mathematics |
| title_full | Group-theoretic methods in mechanics and applied mathematics D. M. Klimov and V. Ph. Zhuravlev |
| title_fullStr | Group-theoretic methods in mechanics and applied mathematics D. M. Klimov and V. Ph. Zhuravlev |
| title_full_unstemmed | Group-theoretic methods in mechanics and applied mathematics D. M. Klimov and V. Ph. Zhuravlev |
| title_short | Group-theoretic methods in mechanics and applied mathematics |
| title_sort | group theoretic methods in mechanics and applied mathematics |
| topic | Angewandte Mathematik (DE-588)4142443-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Angewandte Mathematik Gruppentheorie Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009857317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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