{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T08:45:14Z","timestamp":1750495514459},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2007,11]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Over the past several decades, a number of <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic>) methods for forward and inverse dynamics computations have been developed in the multibody dynamics and robotics literature. A method was developed by Fixman in 1974 for <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic>) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other of our recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, <jats:italic>SO<\/jats:italic>(3), and the special Euclidean group, <jats:italic>SE<\/jats:italic>(3), and specifically, it requires that one differentiates real-valued functions of Lie-group-valued argument.<\/jats:p>","DOI":"10.1017\/s0263574707003852","type":"journal-article","created":{"date-parts":[[2007,9,28]],"date-time":"2007-09-28T10:03:15Z","timestamp":1190973795000},"page":"739-750","source":"Crossref","is-referenced-by-count":9,"title":["<i>O<\/i>(<i>n<\/i>) mass matrix inversion for serial manipulators and polypeptide chains using Lie derivatives"],"prefix":"10.1017","volume":"25","author":[{"given":"Kiju","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregory S.","family":"Chirikjian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"S0263574707003852_ref30","article-title":"The Flory isolated-pair hypothesis is not valid for polypeptide chains: Implications for protein folding","volume":"97","author":"Pappu","year":"2000","journal-title":"Biophysics"},{"key":"S0263574707003852_ref28","volume-title":"Introduction to Robotics","author":"Craig","year":"1989"},{"key":"S0263574707003852_ref23","unstructured":"23. Lee K. , Chirikjian G. S. , \u201cA New Method for O(n) Inversion of the Mass Matrix,\u201d International Symposium on Multibody Systems and Mechatronics, Uberlandia, Brazil (Mar. 2005)."},{"key":"S0263574707003852_ref15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022566107679"},{"key":"S0263574707003852_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7949(93)90224-2"},{"key":"S0263574707003852_ref29","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500204"},{"key":"S0263574707003852_ref10","doi-asserted-by":"publisher","DOI":"10.2514\/2.4531"},{"key":"S0263574707003852_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(99)00190-9"},{"key":"S0263574707003852_ref7","doi-asserted-by":"publisher","DOI":"10.1109\/70.563652"},{"key":"S0263574707003852_ref31","unstructured":"31. 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S. , \u201cA New Perspective on O(n) Mass-Matrix Inversion for Serial Revolute Manipulators,\u201d IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005)."},{"key":"S0263574707003852_ref3","first-page":"111","volume-title":"Tutorial on Robotics","author":"Hollerbach","year":"1983"},{"key":"S0263574707003852_ref26","volume-title":"Matrix Computations","author":"Golub","year":"1996"},{"key":"S0263574707003852_ref24","doi-asserted-by":"crossref","unstructured":"24. Wang Y. and Chirikjian G. S. , \u201cA New O(n) Method for Inverting the Mass-Matrix for Serial Chains Composed of Rigid Bodies,\u201d Proceedings of IDETC\/CIE, Long Beach, CA, USA (Sep. 2005) DETC 2005-84365.","DOI":"10.1115\/DETC2005-84365"},{"key":"S0263574707003852_ref12","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/PL00007191","article-title":"Parallel Implementation of a Low Order Algorithm for Dynamics of Multibody Systems on a Distributed Memory Computing System","volume":"16","author":"Anderson","year":"2000","journal-title":"J. Eng. Comput."},{"key":"S0263574707003852_ref21","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.71.8.3050"},{"key":"S0263574707003852_ref8","first-page":"116","article-title":"Analytical expression for the inverted inertia matrix of serial robots","volume":"18","author":"Saha","year":"1999","journal-title":"Int. J. 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Naudet J. , Lafeber D. and Terze Z. , \u201cGeneral Formulation of an Efficient Recursive Algorithm based on Canonical Momenta for Forward Dynamics of Open-loop Multibody Systems,\u201d Multibody Dynamics, 2003."}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574707003852","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,6]],"date-time":"2019-04-06T15:27:51Z","timestamp":1554564471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574707003852\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["S0263574707003852"],"URL":"https:\/\/doi.org\/10.1017\/s0263574707003852","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]}}}