{"id":157868,"date":"2009-07-01T00:00:00","date_gmt":"2009-07-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/symbolic-lagrangian-multibody-dynamics\/"},"modified":"2018-10-16T20:05:16","modified_gmt":"2018-10-17T03:05:16","slug":"symbolic-lagrangian-multibody-dynamics","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/symbolic-lagrangian-multibody-dynamics\/","title":{"rendered":"Symbolic Lagrangian Multibody Dynamics"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Symbolic Lagrangian formulations of the equations of motion\u00a0of tree-structured constrained mechanical systems have\u00a0the potential to be both more efficient and more numerically\u00a0robust than formulations which use nonlinear kinematic constraint\u00a0equations. We derive a simple recursive factorization\u00a0of the Lagrangian equations of motion which, along with our\u00a0extended implementation of the D* symbolic differentiation\u00a0algorithm, yields empirically measured O(n) inverse dynamics\u00a0and O(n3) forward dynamics. Complex kinematic constraints\u00a0such as point on surface, point on curve, and surface\u00a0on surface are easily handled by the new algorithm. Numerous\u00a0examples demonstrate the wide range of mechanical systems\u00a0the algorithm can be applied to.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Symbolic Lagrangian formulations of the equations of motion\u00a0of tree-structured constrained mechanical systems have\u00a0the potential to be both more efficient and more numerically\u00a0robust than formulations which use nonlinear kinematic constraint\u00a0equations. We derive a simple recursive factorization\u00a0of the Lagrangian equations of motion which, along with our\u00a0extended implementation of the D* symbolic differentiation\u00a0algorithm, yields empirically measured O(n) inverse [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Sung-Hee 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