{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T04:42:45Z","timestamp":1768365765642,"version":"3.49.0"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2012,7,1]],"date-time":"2012-07-01T00:00:00Z","timestamp":1341100800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2012,8,5]]},"abstract":"<jats:p>We show that the motion of rigid bodies under water can be realistically simulated by replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This allows us to model fluid-body interaction without simulating the surrounding fluid at all. We explain some of the phenomena that arise and compare our results against real experiments. It turns out that many real scenarios (sinking bodies, balloons) can be matched using a single, hand-tuned scaling parameter. We describe how to integrate our method into an existing physics engine, which makes underwater rigid body dynamics run in real time.<\/jats:p>","DOI":"10.1145\/2185520.2185600","type":"journal-article","created":{"date-parts":[[2012,8,6]],"date-time":"2012-08-06T18:11:37Z","timestamp":1344276697000},"page":"1-7","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["Underwater rigid body dynamics"],"prefix":"10.1145","volume":"31","author":[{"given":"Steffen","family":"Wei\u00dfmann","sequence":"first","affiliation":[{"name":"TU Berlin"}]},{"given":"Ulrich","family":"Pinkall","sequence":"additional","affiliation":[{"name":"TU Berlin"}]}],"member":"320","published-online":{"date-parts":[[2012,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Anderson Jr J. D. 2005. Ludwig Prandtl's Boundary Layer. Physics Today December. Anderson Jr J. D. 2005. Ludwig Prandtl's Boundary Layer. Physics Today December.","DOI":"10.1063\/1.2169443"},{"key":"e_1_2_2_2_1","unstructured":"Baraff D. 1993. Non-penetrating rigid body simulation. In State of the Art Reports Eurographics. Baraff D. 1993. Non-penetrating rigid body simulation. In State of the Art Reports Eurographics."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.107"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015733"},{"key":"e_1_2_2_6_1","doi-asserted-by":"crossref","unstructured":"Field S. Klaus M. and Moore M. 1997. Chaotic dynamics of falling disks. Nature 388 July. Field S. Klaus M. and Moore M. 1997. Chaotic dynamics of falling disks. Nature 388 July.","DOI":"10.1038\/40817"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00032-3"},{"key":"e_1_2_2_8_1","doi-asserted-by":"crossref","unstructured":"Kallay M. 2006. Computing the moment of inertia of a solid defined by a triangle mesh. journal of graphics gpu and game tools 11 2. Kallay M. 2006. Computing the moment of inertia of a solid defined by a triangle mesh. journal of graphics gpu and game tools 11 2.","DOI":"10.1080\/2151237X.2006.10129220"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-004-0650-9"},{"key":"e_1_2_2_10_1","article-title":"{On the motion of a solid of revolution in a fluid}","author":"Kirchhoff G. R.","year":"1870","unstructured":"Kirchhoff , G. R. 1870 . {On the motion of a solid of revolution in a fluid} . Journal f\u00fcr die Reine und Angewandte Mathematik 71. (in German). Kirchhoff, G. R. 1870. {On the motion of a solid of revolution in a fluid}. Journal f\u00fcr die Reine und Angewandte Mathematik 71. (in German).","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik 71. (in German)."},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1516522.1516527"},{"key":"e_1_2_2_12_1","doi-asserted-by":"crossref","unstructured":"Lamb H. 1895. Hydrodynamics. Cambridge Univ Pr. Lamb H. 1895. Hydrodynamics . Cambridge Univ Pr.","DOI":"10.5962\/bhl.title.18729"},{"key":"e_1_2_2_13_1","volume-title":"Proc. ACC","author":"Lee T.","year":"2009","unstructured":"Lee , T. , Leok , M. , and Mcclamroch , N. H . 2009. Dynamics of connected rigid bodies in a perfect fluid . In Proc. ACC 2009 , {Online}. Available : http:\/\/arxiv.org\/abs\/0809.1488. Lee, T., Leok, M., and Mcclamroch, N. H. 2009. Dynamics of connected rigid bodies in a perfect fluid. In Proc. ACC 2009, {Online}. Available: http:\/\/arxiv.org\/abs\/0809.1488."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211200700849X"},{"key":"e_1_2_2_15_1","volume-title":"Marine hydrodynamics","author":"Newman J. N.","unstructured":"Newman , J. N. 1977. Marine hydrodynamics . MIT Press . Newman, J. N. 1977. Marine hydrodynamics. MIT Press."},{"key":"e_1_2_2_16_1","volume-title":"Proc. IEEE CDC.","author":"Nordkvist N.","unstructured":"Nordkvist , N. , and Sanyal , A. K . 2010. A Lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics . In Proc. IEEE CDC. Nordkvist, N., and Sanyal, A. K. 2010. A Lie group variational integrator for rigid body motion in SE(3) with applications to underwater vehicle dynamics. In Proc. IEEE CDC."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1805964.1805967"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.144501"},{"key":"e_1_2_2_19_1","volume-title":"Vortex Dynamics","author":"Saffman P. G.","unstructured":"Saffman , P. G. 1992. Vortex Dynamics . Cambridge Univ Pr . Saffman, P. G. 1992. Vortex Dynamics. Cambridge Univ Pr."},{"key":"e_1_2_2_20_1","doi-asserted-by":"crossref","unstructured":"Shashikanth B. N. Sheshmani A. David S. and Jerrold K. 2008. Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape. 37--64. Shashikanth B. N. Sheshmani A. David S. and Jerrold K. 2008. Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape. 37--64.","DOI":"10.1007\/s00162-007-0065-y"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1179352.1141962"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.1983.325207"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.3934\/jgm.2009.1.223"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1631272.1631457"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.3541844"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2185520.2185600","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2185520.2185600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:48:45Z","timestamp":1750236525000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2185520.2185600"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7]]},"references-count":24,"aliases":["10.1145\/2185520.2335455"],"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8,5]]}},"alternative-id":["10.1145\/2185520.2185600"],"URL":"https:\/\/doi.org\/10.1145\/2185520.2185600","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7]]},"assertion":[{"value":"2012-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}