Verfügbarkeit: Introduction to mechanics and symmetry

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Bibliographische Detailangaben
Beteiligte Personen:	Marsden, Jerrold E. 1942-2010 (VerfasserIn), Ratiu, Tudor S. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York ; Berlin [u.a.] Springer 1994
Schriftenreihe:	Texts in applied mathematics 17
Schlagwörter:	Mechanica Mécanique analytique Symmetrie Symétrie (Physique) Mechanics, Analytic Symmetry (Physics) Mechanik Theoretische Mechanik Hamiltonsches System
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIV, 500 S. graph. Darst.
ISBN:	3540972757 0387972757 3540943471 0387943471

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Datensatz im Suchindex

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adam_text	JERROL D E . MARSDE N TUDO R S . RATI U INTRODUCTIO N T O MECHANIC S AN D SYMMETR Y A BASI C EXPOSITIO N OF CLASSICA L MECHANICA L SYSTEM S RNVTFTU YY:/- :YY- WIT H 43 ILLUSTRATIONS SPRINGER-VERLAG NEW YORK BERLIN HEIDELBER G LONDO N PARI S TOKYO HON G KON G BARCELONA BUDAPEST CONTENT S PREFAC E I X 1 INTRODUCTIO N AN D OVERVIE W 1 1.1 LAGRANGIA N AN D HAMILTONIA N FORMALISM S 1 1.2 TH E RIGID BOD Y 5 1.3 LIE-POISSON BRACKETS , POISSON MANIFOLDS, MOMENTU M MAP S 8 1.4 INCOMPRESSIBL E FLUID S 14 1.5 TH E MAXWELL-VLASOV SYSTE M 17 1.6 TH E MAXWELL AN D POISSON-VLASOV BRACKET S 19 1.7 TH E POISSON-VLASOV T O FLUI D MA P 21 1.8 TH E MAXWELL-VLASOV BRACKE T 22 1.9 TH E HEAVY TO P 23 1.10 NONLINEA R STABILIT Y 25 1.11 BIFURCATION 36 1.12 TH E POINCARE-MELNIKOV METHO D AN D CHAO S 39 1.13 RESONANCES , GEOMETRI C PHASES , AN D CONTRO L 42 2 HAMILTONIA N SYSTEM S O N LINEA R SYMPIECTI C SPACE S 5 3 2.1 INTRODUCTIO N 53 2.2 SYMPIECTIC FORM S ON VECTOR SPACES 57 2.3 EXAMPLE S 58 2.4 CANONICA L TRANSFORMATION S OR SYMPIECTIC MAP S 60 2.5 TH E ABSTRAC T HAMILTO N EQUATION S 64 2.6 TH E CLASSICAL HAMILTO N EQUATION S 65 XII CONTENTS 2.7 WHE N AR E EQUATION S HAMILTONIAN ? 67 2.8 HAMILTONIA N FLOWS 70 2.9 POISSON BRACKET S 72 2.10 A PARTICL E IN A ROTATIN G HOO P 76 2.11 TH E POINCARE-MELNIKOV METHO D AN D CHAO S 82 3 A N INTRODUCTIO N T O INFINITE-DIMENSIONA L SYSTEM S 9 3 3.1 LAGRANGE S AN D HAMILTON S EQUATION S FOR FIELD THEOR Y .. . 93 3.2 EXAMPLES : HAMILTON S EQUATION S 95 3.3 EXAMPLES : POISSON BRACKET S AN D CONSERVED QUANTITIE S . . . 103 4 INTERLUDE : MANIFOLDS , VECTO R FIELDS , DIFFERENTIA L FORM S 10 9 4.1 MANIFOLDS 109 4.2 DIFFERENTIAL FORM S 113 4.3 TH E LIE DERIVATIV E 120 4.4 STOKES THEORE M 124 5 HAMILTONIA N SYSTEM S O N SYMPLECTI C MANIFOLD S 13 1 5.1 SYMPLECTIC MANIFOLDS 131 5.2 SYMPLECTI C TRANSFORMATION S 134 5.3 COMPLE X STRUCTURE S AN D KAHLE R MANIFOLDS 135 5.4 HAMILTONIA N SYSTEM S 140 5.5 POISSON BRACKET S ON SYMPLECTIC MANIFOLDS 142 6 COTANGEN T BUNDLE S 14 7 6.1 TH E LINEA R CAS E 147 6.2 TH E NONLINEA R CASE 149 6.3 COTANGEN T LIFTS 152 6.4 LIFTS OF ACTION S 155 6.5 GENERATIN G FUNCTION S 156 6.6 FIBE R TRANSLATION S AN D MAGNETI C TERM S 158 6.7 A PARTICL E I N A MAGNETI C FIEL D 160 6.8 LINEARIZATIO N OF HAMILTONIA N SYSTEM S 161 7 LAGRANGIA N MECHANIC S 16 7 7.1 TH E PRINCIPL E OF CRITICA L ACTIO N 167 7.2 TH E LEGENDRE TRANSFORM 169 7.3 LAGRANGE S EQUATION S 171 7.4 HYPERREGULA R LAGRANGIAN S AN D HAMILTONIAN S 173 7.5 GEODESIES 178 7.6 TH E KALUZA-KLEI N APPROAC H T O CHARGE D PARTICLE S 181 7.7 MOTIO N IN A POTENTIA L FIELD 183 7.8 TH E LAGRANGE-D ALEMBER T PRINCIPL E 186 7.9 TH E HAMILTON-JACOB I EQUATIO N 191 7.10 TH E CLASSICAL LIMIT AN D TH E MASLOV INDE X 197 CONTENTS YY YY 8 VARIATIONA L PRINCIPLES , CONSTRAINTS , ROTATIN G SYSTEM S 21 1 8.1 A RETUR N T O VARIATIONA L PRINCIPLE S 211 8.2 TH E LAGRANG E MULTIPLIE R THEORE M 219 8.3 HOLONOMIC CONSTRAINT S 221 8.4 CONSTRAINE D MOTIO N IN A POTENTIA L FIELD 223 8.5 DIRA C CONSTRAINT S 226 8.6 CENTRIFUGAL AN D CORIOLIS FORCES 231 8.7 TH E GEOMETRI C PHAS E FOR A PARTICL E IN A HOO P 235 8.8 TH E GENERA L THEOR Y OF MOVING SYSTEM S 238 9 A N INTRODUCTIO N T O LI E GROUP S 24 1 9.1 BASIC DEFINITIONS AN D PROPERTIE S 243 9.2 SOME CLASSICAL LIE GROUP S 256 9.3 ACTION S OF LIE GROUP S 267 1 0 POISSO N MANIFOLD S 28 5 10.1 TH E DEFINITION OF POISSON MANIFOLDS 285 10.2 EXAMPLE S 286 10.3 HAMILTONIA N VECTOR FIELD S AN D CASIMI R FUNCTION S 291 10.4 EXAMPLE S 295 10.5 PROPERTIE S OF HAMILTONIA N FLOWS 296 10.6 TH E POISSON TENSOR 298 10.7 QUOTIENT S OF POISSON MANIFOLDS 308 10.8 TH E SCHOUTE N BRACKE T 311 10.9 GENERALITIE S ON LIE-POISSON STRUCTURE S 318 1 1 MOMENTU M MAP S 32 3 11.1 CANONICA L ACTION S AN D THEI R INFINITESIMAL GENERATOR S . . . 323 11.2 MOMENTU M MAP S 325 11.3 A N ALGEBRAI C DEFINITION OF TH E MOMENTU M MA P 328 11.4 CONSERVATIO N OF MOMENTU M MAP S 329 11.5 EXAMPLE S 330 11.6 EQUIVARIANC E OF MOMENTU M MAP S 336 1 2 COMPUTATIO N AN D PROPERTIE S O F MOMENTU M MAP S 33 9 12.1 MOMENTU M MAP S ON COTANGEN T BUNDLE S 339 12.2 MOMENTU M MAP S ON TANGEN T BUNDLE S 344 12.3 EXAMPLE S 345 12.4 EQUIVARIANC E AN D INFINITESIMAL EQUIVARIANC E 351 12.5 EQUIVARIAN T MOMENTU M MAP S AR E POISSON 357 12.6 MORE EXAMPLE S 360 12.7 POISSON AUTOMORPHISM S 365 12.8 MOMENTU M MAP S AN D CASIMI R FUNCTION S 366 XIV CONTENTS 1 3 EULER-POINCAR E AN D LIE-POISSO N REDUCTIO N 36 9 13.1 TH E LIE-POISSON REDUCTIO N THEORE M 369 13.2 PROOF OF TH E LIE-POISSON REDUCTIO N THEORE M FOR GL{N) . . 372 13.3 PROO F OF TH E LIE-POISSON REDUCTIO N THEORE M FOR DIFF VO I(-M) 373 13.4 PROOF OF TH E LIE-POISSON REDUCTIO N THEORE M FOR DIFF CA N(F ) 375 13.5 LIE-POISSON REDUCTIO N USING MOMENTU M FUNCTION S 377 13.6 REDUCTIO N AN D RECONSTRUCTIO N OF DYNAMIC S 379 13.7 TH E LINEARIZED LIE-POISSON BRACKE T 383 13.8 TH E EULER-POINCAR E EQUATION S 388 13.9 TH E REDUCE D EULER-LAGRANG E EQUATION S 396 1 4 COADJOIN T ORBIT S 39 9 14.1 EXAMPLE S OF COADJOINT ORBIT S 400 14.2 TANGEN T VECTORS T O COADJOINT ORBIT S 406 14.3 EXAMPLE S OF TANGEN T VECTORS 407 14.4 TH E SYMPLECTI C STRUCTUR E ON COADJOINT ORBIT S 408 14.5 EXAMPLE S OF SYMPLECTIC STRUCTURE S ON ORBIT S 412 14.6 TH E ORBI T BRACKE T VI A RESTRICTIO N 413 14.7 TH E SPECIAL LINEA R GROU P ON TH E PLAN E 420 14.8 TH E EUCLIDEA N GROU P OF TH E PLAN E 421 14.9 TH E EUCLIDEA N GROU P OF THREE-SPAC E 424 1 5 TH E FRE E RIGI D BOD Y 43 1 15.1 MATERIAL , SPATIAL , AN D BOD Y COORDINATE S 431 15.2 TH E LAGRANGIA N OF TH E FREE RIGID BOD Y 432 15.3 TH E LAGRANGIA N AN D HAMILTONIA N FOR TH E RIGID BOD Y IN BOD Y REPRESENTATIO N 434 15.4 KINEMATIC S ON LIE GROUP S 438 15.5 POINSOT S THEORE M 439 15.6 EULE R ANGLES 440 15.7 TH E HAMILTONIA N OF TH E FREE RIGID BOD Y IN TH E MATERIA L DESCRIPTIO N VI A EULE R ANGLES 442 15.8 TH E ANALYTICA L SOLUTION OF TH E FREE RIGID BOD Y PROBLE M . . 444 15.9 RIGID BOD Y STABILIT Y 449 15.10HEAVY TO P STABILIT Y 453 15.11THE RIGID BOD Y AN D TH E PENDULU M 458 REFERENCE S 46 5 INDE X 49 3
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spellingShingle	Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Texts in applied mathematics Mechanica gtt Mécanique analytique ram Symmetrie gtt Symétrie (Physique) ram Mechanics, Analytic Symmetry (Physics) Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Symmetrie (DE-588)4058724-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd
subject_GND	(DE-588)4038168-7 (DE-588)4185100-6 (DE-588)4058724-1 (DE-588)4139943-2
title	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_auth	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_exact_search	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_full	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_fullStr	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_full_unstemmed	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_short	Introduction to mechanics and symmetry
title_sort	introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_sub	a basic exposition of classical mechanical systems
topic	Mechanica gtt Mécanique analytique ram Symmetrie gtt Symétrie (Physique) ram Mechanics, Analytic Symmetry (Physics) Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Symmetrie (DE-588)4058724-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd
topic_facet	Mechanica Mécanique analytique Symmetrie Symétrie (Physique) Mechanics, Analytic Symmetry (Physics) Mechanik Theoretische Mechanik Hamiltonsches System
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002476038
work_keys_str_mv	AT marsdenjerrolde introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems AT ratiutudors introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems

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