{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T15:50:25Z","timestamp":1742917825232,"version":"3.40.3"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319663197"},{"type":"electronic","value":"9783319663203"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-66320-3_22","type":"book-chapter","created":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T07:34:27Z","timestamp":1503992067000},"page":"301-312","source":"Crossref","is-referenced-by-count":0,"title":["Symbolic-Numeric Integration of the Dynamical Cosserat Equations"],"prefix":"10.1007","author":[{"given":"Dmitry A.","family":"Lyakhov","sequence":"first","affiliation":[]},{"given":"Vladimir P.","family":"Gerdt","sequence":"additional","affiliation":[]},{"given":"Andreas G.","family":"Weber","sequence":"additional","affiliation":[]},{"given":"Dominik L.","family":"Michels","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"22_CR1","series-title":"Applied Mathematical Sciences","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-27649-1","volume-title":"Nonlinear Problems of Elasticity","author":"SS Antman","year":"1995","unstructured":"Antman, S.S.: Nonlinear Problems of Elasticity. Applied Mathematical Sciences, vol. 107. Springer, Heidelberg (1995). doi:\n10.1007\/0-387-27649-1"},{"issue":"4","key":"22_CR2","doi-asserted-by":"crossref","first-page":"041004","DOI":"10.1115\/1.4003625","volume":"6","author":"F Boyer","year":"2011","unstructured":"Boyer, F., De Nayer, G., Leroyer, A., Visonneau, M.: Geometrically exact Kirchhoff beam theory: application to cable dynamics. J. Comput. Nonlinear Dyn. 6(4), 041004 (2011)","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"22_CR3","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.ijsolstr.2007.08.016","volume":"45","author":"DQ Cao","year":"2008","unstructured":"Cao, D.Q., Tucker, R.W.: Nonlinear dynamics of elastic rods using the Cosserat theory: modelling and simulation. Int. J. Solids Struct. 45, 460\u2013477 (2008)","journal-title":"Int. J. Solids Struct."},{"issue":"2","key":"22_CR4","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1115\/1.2900803","volume":"60","author":"J Chung","year":"1993","unstructured":"Chung, J., Hulbert, G.M.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\n            $$\\alpha $$\n           method. J. Appl. Mech. 60(2), 371\u2013375 (1993)","journal-title":"J. Appl. Mech."},{"key":"22_CR5","volume-title":"Th\u00e9orie des corps d\u00e9formables","author":"E Cosserat","year":"1909","unstructured":"Cosserat, E., Cosserat, F.: Th\u00e9orie des corps d\u00e9formables. Hermann, Paris (1909)"},{"key":"22_CR6","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/eqe.4290050306","volume":"5","author":"HM Hilber","year":"1977","unstructured":"Hilber, H.M., Hughes, T.J.R., Taylor, R.L.: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq. Eng. Struct. Dyn. 5, 283\u2013292 (1977)","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"22_CR7","unstructured":"Hilfinger, A.: Dynamics of cilia and flagella. Ph.D. thesis, Technische Universit\u00e4t Dresden (2006)"},{"key":"22_CR8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1017\/S0962492910000048","volume":"19","author":"M Hochbruck","year":"2010","unstructured":"Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numerica 19, 209\u2013286 (2010)","journal-title":"Acta Numerica"},{"key":"22_CR9","doi-asserted-by":"crossref","DOI":"10.1142\/7573","volume-title":"A Practical Course in Differential Equations and Mathematical Modelling. Classical and New Methods. Nonlinear Mathematical Models. Symmetry and Invariance Principles","author":"NH Ibragimov","year":"2009","unstructured":"Ibragimov, N.H.: A Practical Course in Differential Equations and Mathematical Modelling. Classical and New Methods. Nonlinear Mathematical Models. Symmetry and Invariance Principles. Higher Education Press\/World Scientific, Beijing (2009)"},{"key":"22_CR10","series-title":"Berichte des Fraunhofer ITWM","volume-title":"Multibody Dynamics Simulation of Geometrically Exact Cosserat Rods","author":"H Lang","year":"2011","unstructured":"Lang, H., Linn, J., Arnold, M.: Multibody Dynamics Simulation of Geometrically Exact Cosserat Rods. Berichte des Fraunhofer ITWM, vol. 209. Fraunhofer, Munich (2011)"},{"key":"22_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12136-4","volume-title":"Nonlinear Deformable-Body Dynamics","author":"ACJ Luo","year":"2010","unstructured":"Luo, A.C.J.: Nonlinear Deformable-Body Dynamics. Springer, Heidelberg (2010). doi:\n10.1007\/978-3-642-12136-4"},{"key":"22_CR12","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.jcp.2015.10.009","volume":"303","author":"DL Michels","year":"2015","unstructured":"Michels, D.L., Desbrun, M.: A semi-analytical approach to molecular dynamics. J. Comput. Phys. 303, 336\u2013354 (2015)","journal-title":"J. Comput. Phys."},{"key":"22_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/978-3-319-10515-4_23","volume-title":"Computer Algebra in Scientific Computing","author":"DL Michels","year":"2014","unstructured":"Michels, D.L., Lyakhov, D.A., Gerdt, V.P., Sobottka, G.A., Weber, A.G.: Lie symmetry analysis for cosserat rods. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2014. LNCS, vol. 8660, pp. 324\u2013334. Springer, Cham (2014). doi:\n10.1007\/978-3-319-10515-4_23"},{"key":"22_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/978-3-319-45641-6_24","volume-title":"Computer Algebra in Scientific Computing","author":"DL Michels","year":"2016","unstructured":"Michels, D.L., Lyakhov, D.A., Gerdt, V.P., Hossain, Z., Riedel-Kruse, I.H., Weber, A.G.: On the general analytical solution of the Kinematic Cosserat equations. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2016. LNCS, vol. 9890, pp. 367\u2013380. Springer, Cham (2016). doi:\n10.1007\/978-3-319-45641-6_24"},{"key":"22_CR15","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.cag.2015.10.001","volume":"53B","author":"DL Michels","year":"2015","unstructured":"Michels, D.L., Mueller, J.P.T., Sobottka, G.: A physically based approach to the accurate simulation of stiff fibers and stiff fiber meshes. Comput. Graph. 53B, 136\u2013146 (2015)","journal-title":"Comput. Graph."},{"key":"22_CR16","doi-asserted-by":"crossref","first-page":"7:1","DOI":"10.1145\/2508462","volume":"33","author":"DL Michels","year":"2014","unstructured":"Michels, D.L., Sobottka, G.A., Weber, A.G.: Exponential integrators for stiff elastodynamic problems. ACM Trans. Graph. 33, 7:1\u20137:20 (2014)","journal-title":"ACM Trans. Graph."},{"key":"22_CR17","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0274-2","volume-title":"Applications of Lie Groups to Differential Equations","author":"PJ Olver","year":"1993","unstructured":"Olver, P.J.: Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics, vol. 107, 2nd edn. Springer, Heidelberg (1993). doi:\n10.1007\/978-1-4684-0274-2","edition":"2"},{"key":"22_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9379-3","volume-title":"Cosserat Theories: Shells, Rods and Points","author":"MB Rubin","year":"2000","unstructured":"Rubin, M.B.: Cosserat Theories: Shells, Rods and Points. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"22_CR19","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01287-7","volume-title":"Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra","author":"WM Seiler","year":"2010","unstructured":"Seiler, W.M.: Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra. Algorithms and Computation in Mathematics, vol. 24. Springer, Heidelberg (2010). doi:\n10.1007\/978-3-642-01287-7"},{"key":"22_CR20","first-page":"73","volume":"16","author":"GA Sobottka","year":"2008","unstructured":"Sobottka, G.A., Lay, T., Weber, A.G.: Stable integration of the dynamic Cosserat equations with application to hair modeling. J. WSCG 16, 73\u201380 (2008)","journal-title":"J. WSCG"},{"key":"22_CR21","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1002\/nme.1620151011","volume":"15","author":"WL Wood","year":"1981","unstructured":"Wood, W.L., Bossak, M., Zienkiewicz, O.C.: An alpha modification of Newmarks method. Int. J. Numer. Methods Eng. 15, 1562\u20131566 (1981)","journal-title":"Int. J. Numer. Methods Eng."}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-66320-3_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T03:29:20Z","timestamp":1504063760000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-66320-3_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319663197","9783319663203"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-66320-3_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}