{"id":"https://openalex.org/W4289860866","doi":"https://doi.org/10.3390/sym14081610","title":"Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk","display_name":"Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk","publication_year":2022,"publication_date":"2022-08-04","ids":{"openalex":"https://openalex.org/W4289860866","doi":"https://doi.org/10.3390/sym14081610"},"language":"en","primary_location":{"id":"doi:10.3390/sym14081610","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081610","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1610/pdf?version=1661331288","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/8/1610/pdf?version=1661331288","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008525002","display_name":"Ahmed M. Elshenhab","orcid":"https://orcid.org/0000-0003-3574-2939"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed M. Elshenhab","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074973583","display_name":"Osama Moaaz","orcid":"https://orcid.org/0000-0003-3850-1022"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Osama Moaaz","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035637270","display_name":"Ioannis Dassios","orcid":"https://orcid.org/0000-0001-8763-8741"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Ioannis Dassios","raw_affiliation_strings":["FRESLIPS, University College Dublin, Dublin D4, Ireland"],"affiliations":[{"raw_affiliation_string":"FRESLIPS, University College Dublin, Dublin D4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011670471","display_name":"Ayman Elsharkawy","orcid":"https://orcid.org/0000-0003-0288-2548"},"institutions":[{"id":"https://openalex.org/I21376657","display_name":"Tanta University","ror":"https://ror.org/016jp5b92","country_code":"EG","type":"education","lineage":["https://openalex.org/I21376657"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ayman Elsharkawy","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Tanta University, Tanta 31511, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31511, Egypt","institution_ids":["https://openalex.org/I21376657"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035637270"],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.446,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80716414,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"8","first_page":"1610","last_page":"1610"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9767000079154968,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9767000079154968,"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":0.9700999855995178,"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/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.9258999824523926,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/jerk","display_name":"Jerk","score":0.9717862606048584},{"id":"https://openalex.org/keywords/osculating-circle","display_name":"Osculating circle","score":0.870082437992096},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.6975310444831848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5403585433959961},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4813286066055298},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.47332343459129333},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46487191319465637},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.45382535457611084},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4208936095237732},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3945731520652771},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3074083924293518},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.20983079075813293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15669399499893188}],"concepts":[{"id":"https://openalex.org/C181605269","wikidata":"https://www.wikidata.org/wiki/Q497332","display_name":"Jerk","level":3,"score":0.9717862606048584},{"id":"https://openalex.org/C40890689","wikidata":"https://www.wikidata.org/wiki/Q2166240","display_name":"Osculating circle","level":2,"score":0.870082437992096},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.6975310444831848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5403585433959961},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4813286066055298},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.47332343459129333},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46487191319465637},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.45382535457611084},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4208936095237732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3945731520652771},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3074083924293518},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.20983079075813293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15669399499893188},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14081610","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081610","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1610/pdf?version=1661331288","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:80ae9510ea2c4e6a97fbc471dd9343c8","is_oa":true,"landing_page_url":"https://doaj.org/article/80ae9510ea2c4e6a97fbc471dd9343c8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 8, p 1610 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/8/1610/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14081610","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14081610","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081610","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1610/pdf?version=1661331288","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5110325343","display_name":null,"funder_award_id":"RDD/00681","funder_id":"https://openalex.org/F4320320848","funder_display_name":"Sustainable Energy Authority of Ireland"}],"funders":[{"id":"https://openalex.org/F4320320848","display_name":"Sustainable Energy Authority of Ireland","ror":"https://ror.org/015j3sb07"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4289860866.pdf","grobid_xml":"https://content.openalex.org/works/W4289860866.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2030557751","https://openalex.org/W2037061473","https://openalex.org/W2765614848","https://openalex.org/W2800897239","https://openalex.org/W2888952992","https://openalex.org/W2914879571","https://openalex.org/W2998871213","https://openalex.org/W3013077519","https://openalex.org/W3022218374","https://openalex.org/W3090796229","https://openalex.org/W3158881652","https://openalex.org/W3215413450"],"related_works":["https://openalex.org/W2376623953","https://openalex.org/W2352897580","https://openalex.org/W2118664347","https://openalex.org/W2348411017","https://openalex.org/W3049304016","https://openalex.org/W1977630140","https://openalex.org/W2019544916","https://openalex.org/W2093995589","https://openalex.org/W2513330233","https://openalex.org/W2568861134"],"abstract_inverted_index":{"The":[0,82],"resolution":[1,25],"of":[2,8,31,54],"the":[3,17,40,43,46,52,63,68,74,97,109],"acceleration":[4,32,47],"and":[5,26,33,57,65,77],"jerk":[6,34,69,98],"vectors":[7,35],"a":[9,13,87],"particle":[10],"moving":[11],"on":[12,39,86],"space":[14,88],"curve":[15,89],"in":[16,62],"Euclidean":[18],"3-space":[19],"is":[20,49,71,94],"considered.":[21],"By":[22],"applying":[23],"this":[24],"Siacci\u2019s":[27],"theorem,":[28],"alternative":[29],"resolutions":[30],"are":[36,104],"derived":[37],"based":[38],"quasi-frame.":[41],"In":[42,60],"osculating":[44,64],"plane,":[45],"vector":[48,70,99],"resolved":[50,72],"as":[51],"sum":[53],"its":[55],"tangential":[56,75],"radial":[58,80],"components.":[59],"addition,":[61],"rectifying":[66],"planes,":[67],"along":[73],"direction":[76],"two":[78],"special":[79],"directions.":[81],"maximum":[83],"permissible":[84],"speed":[85],"at":[90],"all":[91],"trajectory":[92],"points":[93],"established":[95],"via":[96],"formula.":[100],"Finally,":[101],"some":[102],"examples":[103],"presented":[105],"to":[106],"illustrate":[107],"how":[108],"results":[110],"work.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}