{"id":"https://openalex.org/W2060623772","doi":"https://doi.org/10.1109/cdc.2009.5400369","title":"Multiple Instantaneous Collisions in a Variational Framework","display_name":"Multiple Instantaneous Collisions in a Variational Framework","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2060623772","doi":"https://doi.org/10.1109/cdc.2009.5400369","mag":"2060623772"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5082550252","display_name":"Vlad Seghete","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vlad Seghete","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA","institution_ids":["https://openalex.org/I111979921"]}]},{"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/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd D. Murphey","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"5015","last_page":"5020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9983000159263611,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9983000159263611,"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/T11416","display_name":"Numerical methods for differential equations","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.7725456953048706},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.7683020830154419},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7393168807029724},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6566262245178223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4956897497177124},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48114120960235596},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.4552227258682251},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4183673560619354},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4118242561817169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3545823395252228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21500948071479797},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10050985217094421}],"concepts":[{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.7725456953048706},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.7683020830154419},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7393168807029724},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6566262245178223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4956897497177124},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48114120960235596},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.4552227258682251},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4183673560619354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4118242561817169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3545823395252228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21500948071479797},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10050985217094421},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2009.5400369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W31862767","https://openalex.org/W70650894","https://openalex.org/W1514487078","https://openalex.org/W1709064880","https://openalex.org/W2029294123","https://openalex.org/W2046156462","https://openalex.org/W2062388571","https://openalex.org/W2075921599","https://openalex.org/W2085897137","https://openalex.org/W2098500157","https://openalex.org/W2124486569","https://openalex.org/W2144214034","https://openalex.org/W2157731667","https://openalex.org/W4206840271","https://openalex.org/W6637539608","https://openalex.org/W6666150991"],"related_works":["https://openalex.org/W2537694785","https://openalex.org/W2006096639","https://openalex.org/W2961659155","https://openalex.org/W2005694504","https://openalex.org/W3011672241","https://openalex.org/W1989699225","https://openalex.org/W2029535240","https://openalex.org/W3099195500","https://openalex.org/W2593289484","https://openalex.org/W4214897045"],"abstract_inverted_index":{"Variational":[0],"integrators":[1],"have":[2,16],"become":[3],"of":[4,22,41,56],"interest":[5],"to":[6,29],"the":[7,20,42,75],"controls":[8],"community,":[9],"particularly":[10],"since":[11],"in":[12,19,33,74],"recent":[13],"years":[14],"they":[15],"been":[17],"used":[18],"context":[21],"optimal":[23],"control.":[24],"This":[25],"paper":[26],"discusses":[27],"how":[28,49],"resolve":[30],"simultaneous":[31,57],"impacts":[32,58,67],"a":[34],"variational":[35],"context,":[36],"assuming":[37],"that":[38],"all":[39],"boundaries":[40],"impacting":[43],"bodies":[44],"are":[45],"differentiable.":[46],"We":[47,69],"demonstrate":[48],"this":[50],"analysis":[51],"works":[52],"for":[53,64],"arbitrary":[54],"numbers":[55],"and":[59,77],"derive":[60],"discrete":[61,78],"time":[62],"algorithms":[63],"resolving":[65],"these":[66],"numerically.":[68],"illustrate":[70],"our":[71],"results,":[72],"both":[73],"continuous":[76],"domain,":[79],"using":[80],"Newton's":[81],"cradle":[82],"as":[83],"an":[84],"example.":[85]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}