{"id":"https://openalex.org/W2144214034","doi":"https://doi.org/10.1109/robot.2008.4543352","title":"Discrete and continuous mechanics for tree representations of mechanical systems","display_name":"Discrete and continuous mechanics for tree representations of mechanical systems","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2144214034","doi":"https://doi.org/10.1109/robot.2008.4543352","mag":"2144214034"},"language":"en","primary_location":{"id":"doi:10.1109/robot.2008.4543352","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.2008.4543352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5111802656","display_name":"Elliot R. Johnson","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Elliot R. Johnson","raw_affiliation_strings":["Electrical and Computer Engineeringneerin, University of Colorado Boulder, Boulder, CO, USA","Electr. & Comput. Eng., Univ. of Colorado at Boulder, Boulder, CO"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineeringneerin, University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Electr. & Comput. Eng., Univ. of Colorado at Boulder, Boulder, CO","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067725461","display_name":"Todd D. Murphey","orcid":"https://orcid.org/0000-0003-2262-8176"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd D. Murphey","raw_affiliation_strings":["Electrical and Computer Engineeringneerin, University of Colorado Boulder, Boulder, CO, USA","Electr. & Comput. Eng., Univ. of Colorado at Boulder, Boulder, CO"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineeringneerin, University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Electr. & Comput. Eng., Univ. of Colorado at Boulder, Boulder, CO","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111802656"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":null,"apc_paid":null,"fwci":4.4058,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94456133,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1106","last_page":"1111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13286","display_name":"Modeling and Simulation Systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13286","display_name":"Modeling and Simulation Systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/computer-science","display_name":"Computer science","score":0.541001558303833},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.5364440679550171},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5332999229431152},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5322418212890625},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.5290614366531372},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5249174237251282},{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.5222152471542358},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5218719244003296},{"id":"https://openalex.org/keywords/mechanical-system","display_name":"Mechanical system","score":0.5102493762969971},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5028812289237976},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4795265197753906},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4613198935985565},{"id":"https://openalex.org/keywords/rigid-body-dynamics","display_name":"Rigid body dynamics","score":0.45874980092048645},{"id":"https://openalex.org/keywords/lagrangian-mechanics","display_name":"Lagrangian mechanics","score":0.43322494626045227},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3913234770298004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3531762957572937},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.3068872094154358},{"id":"https://openalex.org/keywords/analytical-mechanics","display_name":"Analytical mechanics","score":0.2935486435890198},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2243223488330841},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1807100474834442},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13432303071022034},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13128677010536194}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.541001558303833},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.5364440679550171},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5332999229431152},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5322418212890625},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.5290614366531372},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5249174237251282},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.5222152471542358},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5218719244003296},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.5102493762969971},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5028812289237976},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4795265197753906},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4613198935985565},{"id":"https://openalex.org/C28461519","wikidata":"https://www.wikidata.org/wiki/Q2037529","display_name":"Rigid body dynamics","level":3,"score":0.45874980092048645},{"id":"https://openalex.org/C499771625","wikidata":"https://www.wikidata.org/wiki/Q324669","display_name":"Lagrangian mechanics","level":5,"score":0.43322494626045227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3913234770298004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3531762957572937},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.3068872094154358},{"id":"https://openalex.org/C206183056","wikidata":"https://www.wikidata.org/wiki/Q833065","display_name":"Analytical mechanics","level":4,"score":0.2935486435890198},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2243223488330841},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1807100474834442},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13432303071022034},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13128677010536194},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/robot.2008.4543352","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.2008.4543352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W639693478","https://openalex.org/W1564897360","https://openalex.org/W1991912971","https://openalex.org/W2083334152","https://openalex.org/W2096932164","https://openalex.org/W2098500157","https://openalex.org/W2098917378","https://openalex.org/W2102838235","https://openalex.org/W2105289524","https://openalex.org/W2116156665","https://openalex.org/W2170039048","https://openalex.org/W2295267092","https://openalex.org/W3217246742","https://openalex.org/W4248240275","https://openalex.org/W6674793146","https://openalex.org/W6958751633"],"related_works":["https://openalex.org/W1547662599","https://openalex.org/W4233673530","https://openalex.org/W2329279984","https://openalex.org/W2963433675","https://openalex.org/W2951441175","https://openalex.org/W2159384118","https://openalex.org/W44291963","https://openalex.org/W2183293709","https://openalex.org/W22424866","https://openalex.org/W2013192764"],"abstract_inverted_index":{"We":[0,135,162],"use":[1],"a":[2,18,75,127,152,168,170],"tree-based":[3],"structure":[4],"to":[5,21,39,47,60,78,96,116,138],"represent":[6],"mechanical":[7,80],"systems":[8,41,98],"comprising":[9],"interconnected":[10,148],"rigid":[11,149],"bodies.":[12],"Using":[13],"this":[14,55],"representation,":[15],"we":[16],"derive":[17],"simple":[19],"algorithm":[20,33],"numerically":[22,123],"calculate":[23],"forward":[24],"kinematic":[25],"maps,":[26],"body":[27],"velocities,":[28],"and":[29,37,132],"their":[30],"derivatives.":[31],"The":[32,71],"is":[34,57,69],"computationally":[35,153],"efficient":[36,154],"scales":[38],"large":[40,87],"very":[42],"well":[43],"by":[44],"using":[45,102],"recursion":[46],"take":[48],"advantage":[49],"of":[50,66,110,147,160],"the":[51,67,92,108,117],"tree":[52,72],"structure.":[53],"Moreover,":[54],"method":[56,113],"less":[58],"prone":[59],"modeling":[61],"errors":[62],"because":[63],"each":[64],"element":[65],"graph":[68],"simple.":[70],"representation":[73,93],"provides":[74],"natural":[76],"framework":[77],"simulate":[79,97],"dynamics":[81,104,125],"with":[82,164],"numeric":[83],"computations":[84],"rather":[85],"than":[86],"symbolically-derived":[88],"equations.":[89],"In":[90],"particular,":[91],"allows":[94],"one":[95],"in":[99,126,151],"generalized":[100],"coordinates":[101],"Lagrangian":[103],"without":[105],"symbolically":[106],"finding":[107],"equations":[109,159],"motion.":[111,161],"This":[112],"also":[114],"applies":[115],"relatively":[118],"new":[119],"variational":[120],"integrators":[121],"which":[122],"integrate":[124],"way":[128,155],"that":[129],"preserve":[130],"momentum":[131],"other":[133],"symmetries.":[134],"show":[136],"how":[137],"implement":[139],"both":[140],"integration":[141],"schemes":[142],"for":[143],"an":[144,165],"arbitrary":[145],"system":[146],"bodies":[150],"while":[156],"avoiding":[157],"symbolic":[158],"end":[163],"example":[166],"simulating":[167],"marionette;":[169],"mechanically":[171],"complex,":[172],"high":[173],"degree-of-freedom":[174],"system.":[175]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
