{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:35:26Z","timestamp":1787337326410,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>This article investigates the use of the computation of the exact free rigid body motion as a component of splitting methods for rigid bodies subject to external forces. We review various matrix and quaternion representations of the solution of the free rigid body equation which involve Jacobi ellipic functions and elliptic integrals and are amenable to numerical computations. We consider implementations which are exact (i.e., computed to machine precision) and semiexact (i.e., approximated via quadrature formulas). We perform a set of extensive numerical comparisons with state-of-the-art geometrical integrators for rigid bodies, such as the preprocessed discrete Moser\u2013Veselov method. Our numerical simulations indicate that these techniques, combined with splitting methods, can be favorably applied to the numerical integration of torqued rigid bodies.<\/jats:p>","DOI":"10.1137\/070704393","type":"journal-article","created":{"date-parts":[[2008,5,14]],"date-time":"2008-05-14T18:05:51Z","timestamp":1210788351000},"page":"2084-2112","source":"Crossref","is-referenced-by-count":19,"title":["The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods"],"prefix":"10.1137","volume":"30","author":[{"given":"E.","family":"Celledoni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F.","family":"Fass\u00f2","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.","family":"S\u00e4fstr\u00f6m","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Zanna","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,5,14]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. A. Stegun,\n                      Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables\n                      , National Bureau of Standards Appl. Math. Ser. 55 (reprint of the 1972 edition) Dover, New York, 1992."},{"key":"R2","unstructured":"P. E. Appell,\n                      Trait\u00e9 de M\u00e9canique Rationnelle\n                      , Vol. 2, Gauthier\u2013Villars, Paris, 1924\/26."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500381720"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00492-7"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. F. Byrd and M. D. Friedman,\n                      Handbook of Elliptic Integrals for Engineers and Scientists\n                      , Grundlehren Math. Wiss. 67, 2nd ed., Springer-Verlag, New York, 1971.","DOI":"10.1007\/978-3-642-65138-0"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/19\/S08"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1063\/1.474310"},{"key":"R8","unstructured":"K. Efstathiou and D. Sadovskii,\n                      No Polar Coordinates. Based on Lectures by R. Cushman\n                      , London Math. Soc. Lecture Note Ser. 306, Geometric Mechanics and Symmetry, Cambridge University Press, Cambridge, 2005."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00232-8"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-005-1139-8"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"E. Hairer, C. Lubich, and G. Wanner,\n                      Geometric Numerical Integration\n                      , Springer Ser. Comput. Math. 31, Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-3-662-05018-7"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/42\/003"},{"key":"R13","first-page":"293","volume":"39","author":"Jacobi C. G. J.","year":"1949","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01586859"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8928(98)00025-2"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"D. F. Lawden,\n                      Elliptic Functions and Applications\n                      , Appl. Math. Sci. 80, Springer-Verlag, New York, 1989.","DOI":"10.1007\/978-1-4757-3980-0"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"B. Leimkuhler and S. Reich,\n                      Simulating Hamiltonian Dynamics\n                      , Cambridge Monogr. Appl. Comput. Math. 14, 1st ed., Cambridge University Press, London, 2004.","DOI":"10.1017\/CBO9780511614118"},{"key":"R18","unstructured":"M. Leok, T. Lee, and N. H. McClamroch,\n                      Attitude maneuvers of a rigid spacecraft in a circular orbit\n                      , in Proceedings of the IEEE American Control Conference, 2006, pp. 1742\u20131747."},{"key":"R19","doi-asserted-by":"crossref","unstructured":"J. E. Marsden and T. S. Ratiu,\n                      Introduction to mechanics and symmetry, texts a basic exposition of classical mechanical systems\n                      , in Appl. Math. 17, 2nd ed., Springer-Verlag, New York, 1999.","DOI":"10.1007\/978-0-387-21792-5"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.71.3043"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492902000053"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-004-0118-6"},{"key":"R23","unstructured":"J. Wm. Mitchell,\n                      A Simplified Variation of Parameters Solution for the Motion of an Arbirarily Torqued Mass Asymmetric Rigid Body\n                      , Ph.D. thesis, University of Cincinnati, 2000."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02352494"},{"key":"R25","unstructured":"W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,\n                      Numerical Recipes in Fortran $77$ and Fortran $90$, The Art of Scientific and Parallel Computing\n                      , 2nd ed., Cambridge University Press, Cambridge, 1996."},{"key":"R26","first-page":"181","volume":"10","author":"Reich S.","year":"1996","journal-title":"Fields Inst. Commun.","ISSN":"https:\/\/id.crossref.org\/issn\/1069-5265","issn-type":"print"},{"key":"R27","unstructured":"A. J. Stone, A. Dullweber, M. P. Hodges, P. L. A. Popelier, and D. J. Wales,\n                      ORIENT Version\n                      3.2:\n                      A Program for Studying Interaction between Molecules\n                      , Cambridge University, London, 1995."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1086\/116931"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.11.019"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.75.056701"},{"key":"R31","unstructured":"E. T. Whittaker,\n                      A Treatise on the Analytical Dynamics of Particles and Rigid Bodies\n                      , 4th ed., Cambridge University Press, London, 1937."},{"key":"R32","doi-asserted-by":"crossref","unstructured":"H. Yoshida,\n                      Construction of higher order symplectic integrators\n                      , Phys. Lett. A, 150 (1990). pp. 262\u2013268.","DOI":"10.1016\/0375-9601(90)90092-3"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070704393","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:58:03Z","timestamp":1787335083000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070704393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070704393"],"URL":"https:\/\/doi.org\/10.1137\/070704393","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}