Holdings: Generating families in the restricted three-body problem

Generating families in the restricted three-body problem: 2 Quantitative study of bifurcations

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Bibliographic Details
Main Author:	Hénon, Michel 1931-2013 (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2001
Series:	Lecture notes in physics M 65
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 300 S.
ISBN:	3540417338

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MARC


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adam_text	MICHEL HENON GENERATING FAMILIES IN THE RESTRICTED THREE-BODY PROBLEM II. QUANTITATIVE STUDY OF BIFURCATIONS SPRINGER CONTENTS 11. DEFINITIONS AND GENERAL EQUATIONS 1 11.1 INTRODUCTION 1 11.2 THE 0 NOTATION 1 11.2.1 DEFINITIONS 1 11.2.2 COMPUTATION RULES 2 11.3 GENERAL EQUATIONS 4 11.3.1 DEFINITIONS 4 11.3.2 INTERMEDIATE ARCS 6 11.3.3 ORDERS OF MAGNITUDE OF AP T AND AP { 7 11.3.4 MORE ACCURATE ESTIMATE OF AP { 9 11.3.5 MATCHING RELATIONS 11 11.3.6 THE CASE /X = 0 13 11.4 GENERAL METHOD 14 12. QUANTITATIVE STUDY OF TYPE 1 17 12.1 FUNDAMENTAL EQUATIONS 17 12.1.1 ARC RELATIONS 17 12.1.2 ADDITIONAL RELATION FOR TWO ARCS 19 12.1.3 ENCOUNTER RELATIONS 20 12.1.4 RECAPITULATION.... !* 21 12.2 EXCLUSION OF SUCCESSIVE IDENTICAL T-ARCS 23 12.3 THE CASE V = 0 25 12.3.1 FIRST SPECIES ORBIT 25 12.3.2 SECOND SPECIES ORBIT 26 12.4 THE CASE 0 V 1/ 2 27 12.4.1 FIRST SPECIES ORBIT 28 12.4.2 SECOND SPECIES ORBIT 30 12.4.3 SIDES OF PASSAGE 34 12.5 THE CASE V = 1/2 35 12.6 THE CASE V 1/2 36 VIII CONTENTS 13. PARTIAL BIFURCATION OF TYPE 1 39 13.1 PROPERTIES 39 13.1.1 ASYMPTOTIC BRANCHES FOR W - OO 40 13.1.2 VARIATIONAL EQUATIONS FOR W- - OO 41 13.1.3 JACOBIAN 43 13.1.4 RELATION WITH STABILITY 44 13.1.5 ASYMPTOTIC BEHAVIOUR FOR W - OO 47 13.2 SMALL VALUES OF N 47 13.2.1 N = 2 47 13.2.2 N = 3 48 13.2.3 N = 4 50 13.3 POSITIONAL METHOD 51 13.3.1 PRINCIPLE 51 13.3.2 BRANCH ORDER 54 13.3.3 RESULTS 60 14. TOTAL BIFURCATION OF TYPE 1 79 14.1 PROPERTIES 79 14.1.1 JACOBIAN 79 14.1.2 RELATION WITH STABILITY 80 14.1.3 ASYMPTOTIC BEHAVIOUR FOR W - OO 81 14.2 SMALL VALUES OF N 82 14.2.1 N = 2 82 14.2.2 NUMERICAL COMPUTATION: METHOD 83 14.2.3 N = 4 84 14.2.4 N = 6 86 14.3 CONCLUSIONS FOR TYPE 1 87 15. THE NEWTON APPROACH 93 15.1 PARTIAL BIFURCATION OF TYPE 1: VARIABLES AND EQUATIONS 93 15.1.1 ADDITIONAL RELATIONS 95 15.2 METHOD OF SOLUTION 95 15.3 NEWTON POLYHEDRA 98 15.3.1 ENCOUNTER EQUATIONS 98 15.3.2 ARC EQUATIONS: GENERAL CASE 99 15.3.3 ARC EQUATIONS: INITIAL ARC 101 15.3.4 ARC EQUATIONS: FINAL ARC 102 15.3.5 ADDITIONAL RELATIONS: GENERAL CASE 103 15.3.6 ADDITIONAL RELATIONS: FIRST RELATION , 104 15.3.7 ADDITIONAL RELATIONS: LAST RELATION 105 15.3.8 ADDITIONAL RELATIONS: CASE N = 2 105 15.4 INTERSECTIONS WITH THE CONE OF THE PROBLEM 106 15.5 COHERENT BOUNDARY SUBSETS 106 15.5.1 THE MOTZKIN-BURGER ALGORITHM 107 15.5.2 ELIMINATION OF PARASITIC SOLUTIONS 110 CONTENTS IX 15.5.3 PROGRAM. ILL 15.5.4 THE CASE 1P2 ILL 15.6 TRUNCATED SYSTEMS OF EQUATIONS 113 15.6.1 DEGENERACY 113 15.7 POWER TRANSFORMATIONS 114 15.7.1 CASE AAA 115 15.7.2 CASE ACE 117 15.7.3 CASE ABA ; 118 15.7.4 CASE DAD 118 15.7.5 CASE CAA 121 15.7.6 CASE CDA 122 15.7.7 CASE BAB 123 15.7.8 CASE DBD 125 15.7.9 CASE CBA 125 15.7.10 CASE BBB 126 15.8 TOTAL BIFURCATION OF TYPE 1 126 15.8.1 THE CASE 1T2 127 15.9 CONCLUSIONS 129 16. PROVING GENERAL RESULTS 13 1 16.1 VARIABLES AND EQUATIONS 131 16.2 METHOD OF SOLUTION 132 16.3 TWO GENERAL PROPOSITIONS 132 16.4 THE CASE P 2 = PI/2 135 16.5 THE CASE P 2 PI/2 135 16.6 THE CASE P 2 PI/2 136 16.6.1 NO ARCS* 136 16.6.2 ARCS* 138 16.7 CONCLUSIONS 142 16.8 APPENDIX: NO TT NODE* .. . 143 16.8.1 PARTIAL T-SEQUENCEL 143 16.8.2 TOTAL T-SEQUENCE 147 17. QUANTITATIVE STUDY OF TYPE 2 149 17.1 NEW NOTATIONS T F ,T 3 149 17.2 FUNDAMENTAL EQUATIONS 150 17.2.1 ENCOUNTER RELATIONS 151 17.2.2 ARC RELATIONS 151 17.2.3 SEPARATION OF THE CASE N = L 158 17.3 THE CASE V = 0 158 17.3.1 T-ARC 158 17.3.2 5-ARC 159 17.4 THE CASE 0 V 1/3 160 17.5 THE CASE V = 1/3: TRANSITION 2.1 166 17.6 THE CASE 1/3 R/ 1/2 171 X CONTENTS 17.7 THE CASE V = 1/2: TRANSITION 2.2 176 17.8 THE CASE V 1/2 DOES NOT EXIST 179 18. THE CASE 1/3 V 1/2 181 18.1 .R-ARC 181 18.1.1 PROPERTIES 181 18.1.2 NUMBER OF SOLUTIONS 182 18.1.3 STABILITY AND JACOBIAN 183 18.1.4 SMALL VALUES OF N 184 18.2 I?-ORBIT 184 18.2.1 PROPERTIES 185 18.2.2 STABILITY AND JACOBIAN 186 18.2.3 SMALL VALUES OF N 188 18.2.4 SIGN SEQUENCES 191 18.3 STUDY OF THE MAPPING 192 19. PARTIAL TRANSITION 2.1 199 19.1 PROPERTIES 199 19.1.1 ASYMPTOTIC BRANCHES FOR W - OO 201 19.1.2 VARIATIONAL EQUATIONS FOR W -T OO 203 19.1.3 ASYMPTOTIC BRANCHES FOR W -* 0 204 19.1.4 FL-JACOBIAN 207 19.1.5 STABILITY 207 19.2 SMALL VALUES OF N 208 19.2.1 N = 1 208 19.2.2 N = 2 209 19.2.3 N = 3 . * 210 19.2.4 N 3 211 19.3 POSITIONAL METHOD 212 19.3.1 BRANCH ORDER FOR W -»* OO 212 19.3.2 BRANCH ORDER FOR IU : ,-» 0 214 19.3.3 RESULTS 217 19.4 RESULTS FOR BIFURCATIONS OF TYPE 2 221 19.4.1 THE CASE W 0 221 19.4.2 THE CASE W 0 223 20. TOTAL TRANSITION 2.1 225 20.1 PROPERTIES 225 20.1.1 ASYMPTOTIC BRANCHES 226 20.1.2 STABILITY AND JACOBIAN 226 20.2 SMALL VALUES OF N 228 20.2.1 N = 1 228 20.2.2 N = 2 229 20.2.3 N = 3 230 20.2.4 N = 4 232 CONTENTS XI 20.2.5 N 4 236 20.3 RESULTS FOR BIFURCATIONS OF TYPE 2 237 20.3.1 THE CASE W 0 237 20.3.2 THE CASE W 0 237 21. PARTIAL TRANSITION 2.2 239 21.1 PROPERTIES 239 21.1.1 ASYMPTOTIC BRANCHES FOR W - +OO 241 21.1.2 VARIATIONAL EQUATIONS FOR W -»* +00 244 21.1.3 JACOBIAN 246 21.1.4 STABILITY 247 21.1.5 BRANCH NOTATION 247 21.2 SMALL VALUES OF N 248 21.2.1 N = 1 248 21.2.2 N = 2 249 21.2.3 N = 3 251 21.3 POSITIONAL METHOD 252 21.3.1 BRANCH ORDER FOR W - +OO 253 21.3.2 RESULTS 258 21.4 RESULTS FOR BIFURCATIONS OF TYPE 2 265 22. TOTAL TRANSITION 2.2 271 22.1 PROPERTIES 271 22.1.1 STABILITY AND JACOBIAN 272 22.2 SMALL VALUES OF N 272 22.2.1 N = 1 273 22.2.2 N = 2 273 22.2.3 N = 3 276 22.2.4 NUMERICAL COMPUTATION 276 22.3 RESULTS FOR BIFURCATIONS OF TYPE 2 278 23. BIFURCATIONS 2T1 AND 2P1 283 23.1 TOTAL BIFURCATION OF TYPE 2, N = 1 (2T1) 283 23.1.1 THE CASE V = 0 283 23.1.2 THE CASE 0 V 1/2 284 23.1.3 THE CASE V = 1/2 286 23.1.4 THE CASE I/ 1/2 288 23.1.5 RECAPITULATION 288 23.2 PARTIAL BIFURCATION OF TYPE 2, N = 1 (2P1) 290 23.2.1 THE CASE V = 0 290 23.2.2 T-ARCS: THE CASE 0 V 2/3 291 23.2.3 T-ARCS: THE CASE V ^ 2/3 292 23.2.4 5-ARCS: THE CASE 0 V 1 292 23.2.5 5-ARCS: THE CASE V ^ 1 294 23.2.6 RECAPITULATION 294 XII CONTENTS 23.3 CONCLUSIONS FOR TYPE 2 294 23.3.1 THE NEWTON APPROACH 294 23.3.2 PROVING GENERAL RESULTS 295 23.4 TYPE 3 295 INDEX OF DEFINITIONS 297 INDEX OF NOTATIONS 299 REFERENCES 301
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author	Hénon, Michel 1931-2013
author_GND	(DE-588)115737812
author_facet	Hénon, Michel 1931-2013
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author_sort	Hénon, Michel 1931-2013
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spelling	Hénon, Michel 1931-2013 Verfasser (DE-588)115737812 aut Generating families in the restricted three-body problem 2 Quantitative study of bifurcations Michel Hénon Berlin [u.a.] Springer 2001 XII, 300 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics : New series m, monographs 65 Lecture notes in physics : New series m, monographs ... (DE-604)BV025252948 2 Lecture notes in physics M 65 (DE-604)BV021852221 65 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019269994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hénon, Michel 1931-2013 Generating families in the restricted three-body problem Lecture notes in physics M
title	Generating families in the restricted three-body problem
title_auth	Generating families in the restricted three-body problem
title_exact_search	Generating families in the restricted three-body problem
title_full	Generating families in the restricted three-body problem 2 Quantitative study of bifurcations Michel Hénon
title_fullStr	Generating families in the restricted three-body problem 2 Quantitative study of bifurcations Michel Hénon
title_full_unstemmed	Generating families in the restricted three-body problem 2 Quantitative study of bifurcations Michel Hénon
title_short	Generating families in the restricted three-body problem
title_sort	generating families in the restricted three body problem quantitative study of bifurcations
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019269994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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