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In this paper, we propose a deformation model for inextensible elastic rods. The method of Lagrange multipliers is employed to enforce the inextensibility of the rod, and to couple the material frames with the centerline. The resulting system is banded, allowing for an efficient linear time solution. We also propose a manifold projection method to incorporate the non\u2010penetration constraints resulting from contact handling into our constrained Lagrangian mechanics (CLM) problem. We further augment the contact model by treating torsional friction. This allows to reproduce friction effects such as dynamic rolling and twisting of rods. Various examples underline the benefits and applicability of our model. Copyright \u00a9 2010 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/cav.362","type":"journal-article","created":{"date-parts":[[2010,11,26]],"date-time":"2010-11-26T23:32:59Z","timestamp":1290814379000},"page":"561-572","source":"Crossref","is-referenced-by-count":16,"title":["Inextensible elastic rods with torsional friction based on Lagrange multipliers"],"prefix":"10.1002","volume":"21","author":[{"given":"Jonas","family":"Spillmann","sequence":"first","affiliation":[]},{"given":"Matthias","family":"Harders","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,11,26]]},"reference":[{"key":"e_1_2_29_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360662"},{"key":"e_1_2_29_3_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01381.x"},{"key":"e_1_2_29_4_2","doi-asserted-by":"crossref","unstructured":"ChentanezN AlterovitzR RitchieD et al.Interactive simulation of surgical needle insertion and steering. 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