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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T05:23:05Z","timestamp":1672377785965},"reference-count":31,"publisher":"Association for Computing Machinery (ACM)","issue":"2","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2010,4]]},"abstract":"\n We present two algorithms and their corresponding Fortran routines for the exact computation of free rigid body motions. The methods use the same description of the angular momentum part\n \n m<\/jats:italic>\n <\/jats:bold>\n by Jacobi elliptic functions, and suitably chosen frames for the attitude matrix\/quaternion\n Q<\/jats:italic>\n \/\n q<\/jats:italic>\n , respectively. The frame transformation requires the computation of elliptic integrals of the third kind. Implementation and usage of the routines are described, and some examples of drivers are included. Accuracy and performance are also tested to provide reliable numerical results.\n <\/jats:p>","DOI":"10.1145\/1731022.1731033","type":"journal-article","created":{"date-parts":[[2010,5,6]],"date-time":"2010-05-06T17:41:18Z","timestamp":1273167678000},"page":"1-24","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Algorithm 903"],"prefix":"10.1145","volume":"37","author":[{"given":"Elena","family":"Celledoni","sequence":"first","affiliation":[{"name":"Norwegian University of Science and Technology, Trondheim, Norway"}]},{"given":"Antonella","family":"Zanna","sequence":"additional","affiliation":[{"name":"University of Bergen, Bergen, Norway"}]}],"member":"320","published-online":{"date-parts":[[2010,4,23]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"National Bureau of Standards Applied Mathematics Series","volume":"55","author":"Abramowitz M.","unstructured":"Abramowitz , M. and Stegun , I. A . 1992. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Reprint of the 1972 edition . National Bureau of Standards Applied Mathematics Series , vol. 55 . Dover Publications, Inc., New York. Abramowitz, M. and Stegun, I. A. 1992. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Reprint of the 1972 edition. National Bureau of Standards Applied Mathematics Series, vol. 55. Dover Publications, Inc., New York."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.12988\/imf.2007.07190"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500381720"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00492-7"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397975"},{"key":"e_1_2_2_6_1","unstructured":"Byrd P. and Friedman M. 1971. Handbook of Elliptic Integrals for Engineers and Scientists. 2nd ed. Die Grundlehren der Mathematischen Wissenschaften Band 67. Springer-Verlag Berlin Germany. Byrd P. and Friedman M. 1971. Handbook of Elliptic Integrals for Engineers and Scientists. 2nd ed. Die Grundlehren der Mathematischen Wissenschaften Band 67. Springer-Verlag Berlin Germany."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/355958.355970"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/070704393"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/19\/S08"},{"key":"e_1_2_2_10_1","volume-title":"Geometric Mechanics and Symmetry. The Peyresq Lectures","author":"Cushman R.","unstructured":"Cushman , R. 2005. No polar coordinates . In J. Montaldi and T. Ratiu, Eds., Geometric Mechanics and Symmetry. The Peyresq Lectures . London Mathematical Society Lecture Note Series 306. Cambridge University Press , Cambridge, UK. Cushman, R. 2005. No polar coordinates. In J. Montaldi and T. 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Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic. Celest. Mech. Dynam. Astron. 105, 1--3, 245--260.","journal-title":"Celest. Mech. Dynam. Astron."},{"key":"e_1_2_2_14_1","volume-title":"Geometric Numerical Integration. Springer Series in Computational Mathematics","volume":"31","author":"Hairer E.","unstructured":"Hairer , E. , Lubich , C. , and Wanner , G . 2002 . Geometric Numerical Integration. Springer Series in Computational Mathematics , vol. 31 . Springer, Berlin, Germany. Hairer, E., Lubich, C., and Wanner, G. 2002. Geometric Numerical Integration. Springer Series in Computational Mathematics, vol. 31. 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Wolfram Research, Champaign, IL."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1731022.1731033","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T09:35:53Z","timestamp":1672306553000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1731022.1731033"}},"subtitle":["FRB--Fortran routines for the exact computation of free rigid body motions"],"short-title":[],"issued":{"date-parts":[[2010,4]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["10.1145\/1731022.1731033"],"URL":"https:\/\/doi.org\/10.1145\/1731022.1731033","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4]]},"assertion":[{"value":"2008-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-04-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}