{"id":"https://openalex.org/W331199924","doi":null,"title":"Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions","display_name":"Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions","publication_year":2009,"publication_date":"2009-10-04","ids":{"openalex":"https://openalex.org/W331199924","mag":"331199924"},"language":"en","primary_location":{"id":"mag:331199924","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/ncid/BA91037040","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"book","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103078932","display_name":"Cristina Stoica","orcid":"https://orcid.org/0000-0002-6586-7444","observed_orcids":["https://orcid.org/0000-0002-6586-7444"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cristina Stoica","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6586-7444","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079842507","display_name":"Tanya Schmah","orcid":"https://orcid.org/0000-0002-0404-8824","observed_orcids":["https://orcid.org/0000-0002-0404-8824"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tanya Schmah","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0404-8824","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059930044","display_name":"Darryl D. Holm","orcid":"https://orcid.org/0000-0001-6362-9912","observed_orcids":["https://orcid.org/0000-0001-6362-9912"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Darryl D. Holm","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6362-9912","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0413,"has_fulltext":false,"cited_by_count":177,"citation_normalized_percentile":{"value":0.91739895,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.3634999990463257,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.3634999990463257,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.31049999594688416,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.07980000227689743,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geometric-mechanics","display_name":"geometric mechanics","score":0.9980000257492065},{"id":"https://openalex.org/keywords/lagrangian-mechanics","display_name":"Lagrangian mechanics","score":0.8569999933242798},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":1.0},{"id":"https://openalex.org/keywords/symmetry-lowering","display_name":"symmetry reduction","score":0.7889999747276306},{"id":"https://openalex.org/keywords/moment-maps","display_name":"moment maps","score":0.8109999895095825},{"id":"https://openalex.org/keywords/poisson-reduction","display_name":"Poisson reduction","score":0.8769999742507935},{"id":"https://openalex.org/keywords/lie-group-symmetry","display_name":"Lie group symmetry","score":0.9649999737739563},{"id":"https://openalex.org/keywords/distributed-parameter-systems","display_name":"distributed parameter systems","score":0.7490000128746033},{"id":"https://openalex.org/keywords/euler-poincare-equations","display_name":"Euler-Poincar\u00e9 equations","score":0.9190000295639038},{"id":"https://openalex.org/keywords/ideal-fluid-dynamics","display_name":"ideal fluid dynamics","score":0.6259999871253967},{"id":"https://openalex.org/keywords/volume-preserving-diffeomorphism-group","display_name":"volume-preserving diffeomorphism group","score":0.8090000152587891},{"id":"https://openalex.org/keywords/lie-poisson-structure","display_name":"Lie-Poisson structure","score":0.6990000009536743},{"id":"https://openalex.org/keywords/noether-s-theorem","display_name":"Noether's theorem","score":0.9769999980926514},{"id":"https://openalex.org/keywords/n-particle-systems","display_name":"N-particle systems","score":0.7929999828338623},{"id":"https://openalex.org/keywords/rigid-bodies","display_name":"rigid bodies","score":0.8579999804496765},{"id":"https://openalex.org/keywords/solitons","display_name":"solitons","score":0.7760000228881836},{"id":"https://openalex.org/keywords/computational-anatomy","display_name":"computational anatomy","score":0.7860000133514404},{"id":"https://openalex.org/keywords/image-matching","display_name":"image matching","score":0.9010000228881836},{"id":"https://openalex.org/keywords/geophysical-fluid-dynamics","display_name":"geophysical fluid dynamics","score":0.9779999852180481}],"concepts":[{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.550613284111023},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5271294116973877},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.47851836681365967},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.47223660349845886},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.4657272696495056},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.45339515805244446},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44086018204689026},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4383033514022827},{"id":"https://openalex.org/C188845816","wikidata":"https://www.wikidata.org/wiki/Q1052775","display_name":"Poisson bracket","level":3,"score":0.4137958884239197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41088810563087463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3775826096534729},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.33454573154449463},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3288676142692566},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3256748914718628},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.30279117822647095},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25921154022216797},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.13983377814292908},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13750037550926208},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.10876435041427612}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:331199924","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/ncid/BA91037040","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1495727713","https://openalex.org/W1994246733","https://openalex.org/W2064854048","https://openalex.org/W2126479355","https://openalex.org/W2485149212","https://openalex.org/W2502982738"],"related_works":["https://openalex.org/W4388322878","https://openalex.org/W4388121378","https://openalex.org/W4251509970","https://openalex.org/W1659110421","https://openalex.org/W2758878651","https://openalex.org/W4409906220","https://openalex.org/W4248305210","https://openalex.org/W1975013351","https://openalex.org/W2996764657","https://openalex.org/W2485149212"],"abstract_inverted_index":{",by":[0],"Darryl":[1],"D.":[2],"Holm,":[3],"Tanya":[4],"Schmah":[5],"and":[6,62,103,116,145,173,187,199,259,296],"Cristina":[7],"Stoica,":[8],"Oxford":[9],"University":[10],"Press,Oxford,":[11],"2009,":[12],"xi":[13],"+":[14],"515":[15],"pp.,":[16],"ISBN:":[17],"978-0-19-921290-3The":[18],"purpose":[19],"of":[20,29,37,42,123,126,134,142,155,164,167,169,220,232,249,257,264,282,286],"the":[21,26,34,40,43,57,96,121,124,132,136,143,146,150,165,170,175,203,218,226,240,247,265,280,283,287,289,293],"book":[22,47,58,72],"is":[23,48,158,216,244],"to":[24,56,181,212,268],"provide":[25],"unifying":[27],"viewpoint":[28],"Lagrangian":[30,295],"andHamiltonian":[31],"mechanics":[32],"in":[33,50,149,196,202,246,251],"coordinate-free":[35],"language":[36],"differential":[38],"geometryin":[39],"spirit":[41],"Marsden-Ratiu":[44],"school.":[45],"The":[46,90,128,153,208,235],"similar":[49],"content":[51],"-":[52,55],"althoughless":[53],"formal":[54],"by":[59,73,98],"J.":[60],"Marsden":[61],"T.":[63],"Ratiu":[64],"[7].":[65],"One":[66],"can":[67,84],"also":[68],"mentionthe":[69],"companion":[70],"two-volumes":[71],"Holm":[74],"[4,5]":[75],"written":[76],"at":[77,279],"a":[78,197],"more":[79],"basic":[80],"level,and":[81],"that":[82,119],"one":[83],"recommend":[85],"as":[86,114,160],"an":[87],"introductory":[88],"reading.":[89],"classical":[91],"treatises":[92],"onthe":[93],"subject":[94],"are":[95,107,190,194,277],"books":[97],"Abraham-Marsden":[99],"[1],":[100],"Arnold":[101],"[2]":[102],"Libermann-Marle":[104],"[6].Typical":[105],"applications":[106,263],"N-particle":[108],"systems,":[109,172],"rigid":[110],"bodies,":[111],"continua":[112],"such":[113],"u-ids":[115],"electromagnetic":[117],"systems":[118,215],"illustrate":[120],"powerfulness":[122],"adoptedpoint":[125],"view.":[127],"geometrical":[129],"structure":[130,256],"allows":[131],"covering":[133],"both":[135],"nite-dimensional":[137],"conservative":[138],"case":[139],"(rst":[140],"part":[141,205,210,285],"book)":[144],"innite":[147,213],"dimensionalsituation":[148],"second":[151,209,284],"part.":[152],"notion":[154],"symmetry":[156],"here":[157],"central,":[159],"it":[161],"allowsa":[162],"reduction":[163,186],"number":[166],"dimensions":[168],"mechanical":[171],"furtherexploits":[174],"conserved":[176],"quantities":[177],"(momentum":[178],"map)":[179],"associated":[180],"symmetry.":[182],"Liegroup":[183],"symmetries,":[184],"Poisson":[185],"momentum":[188,260],"maps":[189],"rst":[191,204,290],"discussed.The":[192],"concepts":[193],"introduced":[195],"progressive":[198],"clear":[200],"manner":[201],"ofthe":[206],"book.":[207],"devoted":[211],"dimensional":[214],"motivatedby":[217],"identication":[219],"Euler\u2019s":[221],"ideal":[222],"uid":[223,242],"motion":[224],"with":[225,253],"geodesic":[227],"o":[228],"w":[229],"on":[230],"thegroup":[231],"volume-preserving":[233],"diffeomorphism.":[234],"Euler-PoincarO":[236,266],"(EP)":[237],"variationalprinciple":[238],"for":[239],"Euler":[241],"equations":[243],"exposed":[245],"framework":[248],"geometricmechanics,":[250],"association":[252],"Lie-Poisson":[254],"Hamiltonian":[255],"Noether\u2019stheorem":[258],"maps.":[261],"Original":[262],"equa-tions":[267],"solitons,":[269],"computational":[270],"anatomy,":[271],"image":[272],"matching,":[273],"or":[274],"geophysical":[275],"uiddynamics":[276],"given":[278],"end":[281],"book.Here":[288],"chapter":[291],"recapitulates":[292],"Newtonian,":[294],"Hamiltonian117":[297]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":27},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":11}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}