Integrability and nonintegrability in geometry and mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1988
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
31 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XV, 343 S. |
| ISBN: | 9027728186 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV002768922 | ||
| 003 | DE-604 | ||
| 005 | 20230131 | ||
| 007 | t | ||
| 008 | 900727s1988 |||| 00||| engod | ||
| 020 | |a 9027728186 |9 90-277-2818-6 | ||
| 035 | |a (OCoLC)18383091 | ||
| 035 | |a (DE-599)BVBBV002768922 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h rus | |
| 049 | |a DE-12 |a DE-739 |a DE-355 |a DE-19 |a DE-706 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA614.83 | |
| 082 | 0 | |a 514/.7 |2 19 | |
| 084 | |a SK 350 |0 (DE-625)143233: |2 rvk | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 100 | 1 | |a Fomenko, Anatolij Timofeevič |d 1945- |e Verfasser |0 (DE-588)119092689 |4 aut | |
| 245 | 1 | 0 | |a Integrability and nonintegrability in geometry and mechanics |c A. T. Fomenko |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1988 | |
| 300 | |a XV, 343 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 31 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 7 | |a Equations différentielles |2 ram | |
| 650 | 7 | |a Hamilton, systèmes de |2 ram | |
| 650 | 7 | |a Variétés symplectiques |2 ram | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Symplectic manifolds | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hamiltonsches System |0 (DE-588)4139943-2 |D s |
| 689 | 0 | 1 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 810 | 2 | |a Soviet series |t Mathematics and its applications |v 31 |w (DE-604)BV004708148 |9 31 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001768692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001768692 | ||
Datensatz im Suchindex
| _version_ | 1804117119097372672 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface xiii
Chapter 1. Some Equations of Classical Mechanics and
Their Hamiltonian Properties 1
§1. Classical Equations of Motion of a Three Dimensional
Rigid Body 1
1.1. The Euler Poisson Equations Describing the Motion
of a Heavy Rigid Body around a Fixed Point 1
1.2. Integrable Euler, Lagrange, and Kovalevskaya Cases 6
1.3. General Equations of Motion of a Three Dimensional
Rigid Body 10
§2. Symplectic Manifolds 12
2.1. Symplectic Structure in a Tangent Space to a Manifold 12
2.2. Symplectic Structure on a Manifold 17
2.3. Hamiltonian and Locally Hamiltonian Vector Fields
and the Poisson Bracket 20
2.4. Integrals of Hamiltonian Fields 30
2.5. The Liouville Theorem 32
§3. Hamiltonian Properties of the Equations of Motion of a
Three Dimensional Rigid Body 34
§4. Some Information on Lie Groups and Lie Algebras Necessary
for Hamiltonian Geometry 39
4.1. Adjoint and Coadjoint Representations, Semisimplicity,
the System of Roots and Simple Roots, Orbits, and the
Canonical Symplectic Structure 39
4.2. Model Example: SL(n,C) and sl(n,C) 44
4.3. Real, Compact, and Normal Subalgebras 46
Chapter 2. The Theory of Surgery on Completely
Integrable Hamiltonian Systems of Differential
Equations 55
§1. Classification of Constant Energy Surfaces of Integrable
Systems. Estimation of the Amount of Stable Periodic
Solutions on a Constant Energy Surface. Obstacles in the
Way of Smooth Integrability of Hamiltonian Systems 55
1.1. Formulation of the Results in Four Dimensions 55
viii Table of Contents
1.2. A Short List of the Basic Data from the Classical
Morse Theory 68
1.3. Topological Surgery on Liouville Tori of an Integrable
Hamiltonian System upon Varying Values of a
Second Integral 70
1.4. Separatrix Diagrams Cut out Nontrivial Cycles on
Nonsingular Liouville Tori 73
1.5. The Topology of Hamiltonian Level Surfaces of an
Integrable System and of the Corresponding One
Dimensional Graphs 78
1.6. Proof of the Principal Classification Theorem 2.1.2 91
1.7. Proof of Claim 2.1.1 91
1.8. Proof of Theorem 2.1.1. Lower Estimates on the
Number of Stable Periodic Solutions of a System 92
1.9. Proof of Corollary 2.1.5 97
1.10 Topological Obstacles for Smooth Integrability and
Graphlike Manifolds. Not each Three Dimensional Manifold
Can be Realized as a Constant Energy Manifold of an
Integrable System 98
1.11. Proof of Claim 2.1.4 99
§2. Multidimensional Integrable Systems. Classification of the
Surgery on Liouville Tori in the Neighbourhood of
Bifurcation Diagrams 103
2.1. Bifurcation Diagram of the Momentum Mapping
for an Integrable System. The Surgery of General Position 103
2.2. The Classification Theorem for Liouville Torus Surgery 109
2.3. Toric Handles. A Separatrix Diagram is Always Glued
to a Nonsingular Liouville Torus T
Along a Nontrivial (n 1) Dimensional Cycle T 1 111
2.4. Any Composition of Elementary Bifurcations (of Three
Types) of Liouville Tori Is Realized for a Certain Integrable
System on an Appropriate Symplectic Manifold 116
2.5. Classification of Nonintegrable Critical Submanifolds
of Bott Integrals 123
§3. The Properties of Decomposition of Constant Energy Surfaces
of Integrable Systems into the Sum of Simplest Manifolds 126
3.1. A Fundamental Decomposition Q = ml +pll +gIII
+sIV +rV and the Structure of Singular Fibres 126
3.2. Homological Properties of Constant Energy Surfaces 129
Chapter 3. Some General Principles of Integration of
Hamiltonian Systems of Differential Equations 143
§1. Noncommutative Integration Method 143
1.1. Maximal Linear Commutative Subalgebras in the Algebra
of Functions on Symplectic Manifolds 143
1.2. A Hamiltonian System Is Integrable if Its Hamiltonian
is Included in a Sufficiently Large Lie Algebra of Functions 146
Table of Contents ix
1.3. Proof of the Theorem 149
§2. The General Properties of Invariant Submanifolds of
Hamiltonian Systems 157
2.1. Reduction of a System on One Isolated Level Surface 157
2.2. Further Generalizations of the Noncommutative
Integration Method 160
§3. Systems Completely Integrable in the Noncommutative
Sense Are Often Completely Liouville Integrable in the
Conventional Sense 165
3.1. The Formulation of the General Equivalence Hypothesis
and its Validity for Compact Manifolds 165
3.2. The Properties of Momentum Mapping of a System
Integrable in the Noncommutative Sense 167
3.3. Theorem on the Existence of Maximal Linear
Commutative Algebras of Functions on Orbits in Semisimple
and Reductive Lie Algebras 171
3.4. Proof of the Hypothesis for the Case of Compact Manifolds 173
3.5. Momentum Mapping of Systems Integrable in the
Noncommutative Sense by Means of an Excessive Set
of Integrals 173
3.6. Sufficient Conditions for Compactness of the Lie Algebra
of Integrals of a Hamiltonian System 176
§4. Liouville Integrability on Complex Symplectic Manifolds 178
4.1. Different Notions of Complex Integrability and Their
Interrelation 178
4.2. Integrability on Complex Tori 181
4.3. Integrability on #3 Type Surfaces 182
4.4. Integrability on Beauville Manifolds 184
4.5. Symplectic Structures Integrated without Degeneracies 186
Chapter 4. Integration of Concrete Hamiltonian Systems
in Geometry and Mechanics. Methods and Applications 187
§1. Lie Algebras and Mechanics 187
1.1. Embeddings of Dynamic Systems into Lie Algebras 187
1.2. List of the Discovered Maximal Linear Commutative
Algebras of Polynomials on the Orbits of Coadjoint
Representations of Lie Groups 189
§2. Integrable Multidimensional Analogues of Mechanical Systems
Whose Quadratic Hamiltonians are Contained in the Discovered
Maximal Linear Commutative Algebras of Polynomials
on Orbits of Lie Algebras 207
2.1. The Description of Integrable Quadratic Hamiltonians 207
2.2. Cases of Complete Integrability of Equations of Various
Motions of a Rigid Body 210
2.3. Geometric Properties of Rigid Body Invariant Metrics
on Homogeneous Spaces 216
x Table of Contents
§3. Euler Equations on the Lie Algebra so(4) 220
§4. Duplication of Integrable Analogues of the Euler Equations
by Means of Associative Algebra with Poincare Duality 231
4.1. Algorithm for Constructing Integrable Lie Algebras 231
4.2. Probenius Algebras and Extensions of Lie Algebras 236
4.3. Maximal Linear Commutative Algebras of Functions
on Contractions of Lie Algebras 243
§5. The Orbit Method in Hamiltonian Mechanics and Spin
Dynamics of Superfluid Helium 3 250
Chapter 5. Nonintegrability of Certain Classical
Hamiltonian Systems 256
§1. The Proof of Nonintegrability by the Poincar£ Method 256
1.1. Perturbation Theory and the Study of Systems Close
to Integrable 256
1.2. Nonintegrability of the Equations of Motion of a
Dynamically Nonsymmetric Rigid Body with a Fixed Point 260
1.3. Separatrix Splitting 261
1.4. Nonintegrability in the General Case of the Kirchhoff
Equations of Motion of a Rigid Body in an Ideal Liquid 266
§2. Topological Obstacles for Complete Integrability 267
2.1. Nonintegrability of the Equations of Motion of Natural
Mechanical Systems with Two Degrees of Freedom on
High Genus Surfaces 267
2.2. Nonintegrability of Geodesic Flows on High Genus
Riemann Surfaces with Convex Boundary 272
2.3. Nonintegrability of the Problem of n Gravitating
Centres for n 2 275
2.4. Nonintegrability of Several Gyroscopic Systems 277
§3. Topological Obstacles for Analytic Integrability of Geodesic
Flows on Non Simply Connected Manifolds 281
§4. Integrability and Nonintegrability of Geodesic Flows on
Two Dimensional Surfaces, Spheres, and Tori 287
4.1. The Holomorphic 1 Form of the Integral of a Geodesic
Flow Polynomial in Momenta and the Theorem on
Nonintegrability of Geodesic Flows on Compact Surfaces of
Genus g 1 in the Class of Functions Analytic in Momenta 287
4.2. The Case of a Sphere and a Torus 291
4.3. The Properties of Integrable Geodesic Flows on the
Sphere 294
Table of Contents xi
Chapter 6. A New Topological Invariant of Hamiltonian
Systems of Liouville Integrable Differential Equations.
An Invariant Portrait of Integrable Equations
and Hamiltonians 300
§1. Construction of the Topological Invariant 300
§2. Calculation of Topological Invariants of Certain Classical
Mechanical Systems 311
§3. Morse Type Theory for Hamiltonian Systems Integrated by
Means of Non Bott Integrals 324
References 326
Subject Index 341
|
| any_adam_object | 1 |
| author | Fomenko, Anatolij Timofeevič 1945- |
| author_GND | (DE-588)119092689 |
| author_facet | Fomenko, Anatolij Timofeevič 1945- |
| author_role | aut |
| author_sort | Fomenko, Anatolij Timofeevič 1945- |
| author_variant | a t f at atf |
| building | Verbundindex |
| bvnumber | BV002768922 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.83 |
| callnumber-search | QA614.83 |
| callnumber-sort | QA 3614.83 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 540 SK 520 SK 950 |
| ctrlnum | (OCoLC)18383091 (DE-599)BVBBV002768922 |
| dewey-full | 514/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.7 |
| dewey-search | 514/.7 |
| dewey-sort | 3514 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02048nam a2200517 cb4500</leader><controlfield tag="001">BV002768922</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230131 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900727s1988 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9027728186</subfield><subfield code="9">90-277-2818-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)18383091</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002768922</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA614.83</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514/.7</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 350</subfield><subfield code="0">(DE-625)143233:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Fomenko, Anatolij Timofeevič</subfield><subfield code="d">1945-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119092689</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integrability and nonintegrability in geometry and mechanics</subfield><subfield code="c">A. T. Fomenko</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht u.a.</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1988</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 343 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications / Soviet series</subfield><subfield code="v">31</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus d. Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equations différentielles</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Hamilton, systèmes de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Variétés symplectiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hamiltonian systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symplectic manifolds</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hamiltonsches System</subfield><subfield code="0">(DE-588)4139943-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hamiltonsches System</subfield><subfield code="0">(DE-588)4139943-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Soviet series</subfield><subfield code="t">Mathematics and its applications</subfield><subfield code="v">31</subfield><subfield code="w">(DE-604)BV004708148</subfield><subfield code="9">31</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001768692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001768692</subfield></datafield></record></collection> |
| id | DE-604.BV002768922 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:20Z |
| institution | BVB |
| isbn | 9027728186 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001768692 |
| oclc_num | 18383091 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XV, 343 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Kluwer |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Fomenko, Anatolij Timofeevič 1945- Verfasser (DE-588)119092689 aut Integrability and nonintegrability in geometry and mechanics A. T. Fomenko Dordrecht u.a. Kluwer 1988 XV, 343 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 31 Aus d. Russ. übers. Equations différentielles ram Hamilton, systèmes de ram Variétés symplectiques ram Differential equations Hamiltonian systems Symplectic manifolds Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Differentialgleichung (DE-588)4012249-9 s DE-604 Soviet series Mathematics and its applications 31 (DE-604)BV004708148 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001768692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fomenko, Anatolij Timofeevič 1945- Integrability and nonintegrability in geometry and mechanics Equations différentielles ram Hamilton, systèmes de ram Variétés symplectiques ram Differential equations Hamiltonian systems Symplectic manifolds Differentialgleichung (DE-588)4012249-9 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4139943-2 |
| title | Integrability and nonintegrability in geometry and mechanics |
| title_auth | Integrability and nonintegrability in geometry and mechanics |
| title_exact_search | Integrability and nonintegrability in geometry and mechanics |
| title_full | Integrability and nonintegrability in geometry and mechanics A. T. Fomenko |
| title_fullStr | Integrability and nonintegrability in geometry and mechanics A. T. Fomenko |
| title_full_unstemmed | Integrability and nonintegrability in geometry and mechanics A. T. Fomenko |
| title_short | Integrability and nonintegrability in geometry and mechanics |
| title_sort | integrability and nonintegrability in geometry and mechanics |
| topic | Equations différentielles ram Hamilton, systèmes de ram Variétés symplectiques ram Differential equations Hamiltonian systems Symplectic manifolds Differentialgleichung (DE-588)4012249-9 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Equations différentielles Hamilton, systèmes de Variétés symplectiques Differential equations Hamiltonian systems Symplectic manifolds Differentialgleichung Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001768692&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT fomenkoanatolijtimofeevic integrabilityandnonintegrabilityingeometryandmechanics |