{"data":{"id":"10.6084/m9.figshare.c.3849613.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.3849613.v1","prefix":"10.6084","suffix":"m9.figshare.c.3849613.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Orsino, Renato Maia Matarazzo","nameType":"Personal","givenName":"Renato Maia Matarazzo","familyName":"Orsino","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Supplementary material from \"Recursive modular modelling methodology for lumped-parameter dynamic systems\""}],"publisher":"Figshare","container":{},"publicationYear":2017,"subjects":[{"subject":"Mechanical Engineering"},{"subject":"FOS: Mechanical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2017-08-10","dateType":"Created"},{"date":"2017-08-10","dateType":"Updated"},{"date":"2017","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1098/rspa.2016.0891","relatedIdentifierType":"DOI"},{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.c.3849613","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC BY 4.0","rightsUri":"https://creativecommons.org/licenses/by/4.0"}],"descriptions":[{"description":"This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia–Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/collections/Supplementary_material_from_Recursive_modular_modelling_methodology_for_lumped-parameter_dynamic_systems_/3849613/1","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2017-08-10T11:01:08.000Z","registered":"2017-08-10T11:01:09.000Z","published":"2017","updated":"2024-12-19T03:43:24.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},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