{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:19:09Z","timestamp":1743005949473,"version":"3.40.3"},"publisher-location":"Cham","reference-count":33,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319919072"},{"type":"electronic","value":"9783319919089"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-319-91908-9_16","type":"book-chapter","created":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T05:05:00Z","timestamp":1570165500000},"page":"283-310","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multi-Mode DAE Models - Challenges, Theory and Implementation"],"prefix":"10.1007","author":[{"given":"Albert","family":"Benveniste","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beno\u00eet","family":"Caillaud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hilding","family":"Elmqvist","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalil","family":"Ghorbal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Otter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Pouzet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,5]]},"reference":[{"key":"16_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/3-540-57318-6_30","volume-title":"Hybrid Systems","author":"R Alur","year":"1993","unstructured":"Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991-1992. LNCS, vol. 736, pp. 209\u2013229. Springer, Heidelberg (1993). \n                      https:\/\/doi.org\/10.1007\/3-540-57318-6_30"},{"key":"16_CR2","unstructured":"Barela, M.: A complementarity approach to modeling dynamic electric circuits. Ph.D. thesis, University of Iowa (2016)"},{"key":"16_CR3","doi-asserted-by":"crossref","unstructured":"Benveniste, A., Caillaud, B., Elmqvist, H., Ghorbal, K., Otter, M., Pouzet, M.: Structural analysis of multi-mode DAE systems. In: HSCC, pp. 253\u2013263. ACM (2017)","DOI":"10.1145\/3049797.3049806"},{"issue":"1","key":"16_CR4","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1006\/inco.2000.9999","volume":"163","author":"A Benveniste","year":"2000","unstructured":"Benveniste, A., Caillaud, B., Guernic, P.L.: Compositionality in dataflow synchronous languages: specification and distributed code generation. Inf. Comput. 163(1), 125\u2013171 (2000)","journal-title":"Inf. Comput."},{"key":"16_CR5","doi-asserted-by":"crossref","unstructured":"Benveniste,A., Caillaud, B., Pouzet, M., Elmqvist, H., Otter, M.: Structural analysis of multi-mode DAE systems. Research report RR-8933, Inria, July 2016","DOI":"10.1145\/3049797.3049806"},{"issue":"1","key":"16_CR6","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/JPROC.2002.805826","volume":"91","author":"A Benveniste","year":"2003","unstructured":"Benveniste, A., Caspi, P., Edwards, S.A., Halbwachs, N., Guernic, P.L., de Simone, R.: The synchronous languages 12 years later. Proc. IEEE 91(1), 64\u201383 (2003)","journal-title":"Proc. IEEE"},{"key":"16_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BFb0014318","volume-title":"Algebraic Methodology and Software Technology","author":"G Berry","year":"1996","unstructured":"Berry, G.: Constructive semantics of Esterel: from theory to practice (abstract). In: Wirsing, M., Nivat, M. (eds.) AMAST 1996. LNCS, vol. 1101, p. 225. Springer, Heidelberg (1996). \n                      https:\/\/doi.org\/10.1007\/BFb0014318"},{"issue":"1","key":"16_CR8","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65\u201398 (2017)","journal-title":"SIAM Rev."},{"key":"16_CR9","doi-asserted-by":"crossref","unstructured":"Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial Value Problems in Differential-Algebraic Equations. SIAM (1996)","DOI":"10.1137\/1.9781611971224"},{"key":"16_CR10","unstructured":"Dunford, N., Schwartz, J.: Linear Operators, Part I, General Theory. Wiley-Interscience (1958)"},{"key":"16_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1007\/978-3-319-47169-3_15","volume-title":"Leveraging Applications of Formal Methods, Verification and Validation: Discussion, Dissemination, Applications","author":"H Elmqvist","year":"2016","unstructured":"Elmqvist, H., Henningsson, T., Otter, M.: Systems modeling and programming in a unified environment based on Julia. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9953, pp. 198\u2013217. Springer, Cham (2016). \n                      https:\/\/doi.org\/10.1007\/978-3-319-47169-3_15"},{"key":"16_CR12","doi-asserted-by":"crossref","unstructured":"Elmqvist, H., Henningsson, T., Otter, M.: Innovations for future Modelica. In: Jiri Kofranek, F.C. (ed.) Proceedings of the 12th International Modelica Conference, May 2017. \n                      http:\/\/www.ep.liu.se\/ecp\/132\/076\/ecp17132693.pdf","DOI":"10.3384\/ecp17132693"},{"key":"16_CR13","doi-asserted-by":"crossref","unstructured":"Elmqvist, H., Mattsson, S.-E., Otter, M.: Modelica extensions for multi-mode DAE systems. In: Tummescheit, H., Arz\u00e8n, K.-E. (eds.) Proceedings of the 10th International Modelica Conference, Lund, Sweden. Modelica Association, September 2014. \n                      http:\/\/www.ep.liu.se\/ecp\/096\/019\/ecp14096019.pdf","DOI":"10.3384\/ecp14096183"},{"issue":"1","key":"16_CR14","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1137\/0909004","volume":"9","author":"CW Gear","year":"1988","unstructured":"Gear, C.W.: Differential-algebraic equation index transformations. SIAM J. Sci. Stat. Comput. 9(1), 39\u201347 (1988)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"16_CR15","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0377-0427(85)90008-1","volume":"12","author":"CW Gear","year":"1985","unstructured":"Gear, C.W., Leimkuhler, B., Gupta, G.K.: Automatic integration of euler-lagrange equations with constraints. J. Comput. Appl. Math. 12, 77\u201390 (1985)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"16_CR16","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1109\/81.989165","volume":"49","author":"WPMH Heemels","year":"2002","unstructured":"Heemels, W.P.M.H., Camlibel, M.K., Schumacher, J.M.: On the dynamic analysis of piecewise-linear networks. IEEE Trans. Circ. Syst. I: Fundam. Theory Appl. 49(3), 315\u2013327 (2002)","journal-title":"IEEE Trans. Circ. Syst. I: Fundam. Theory Appl."},{"key":"16_CR17","volume-title":"System Dynamics: A Unified Approach","author":"D Karnopp","year":"1990","unstructured":"Karnopp, D., Margolis, D., Rosenberg, R.: System Dynamics: A Unified Approach. Wiley, Hoboken (1990)"},{"key":"16_CR18","first-page":"1","volume-title":"Nonstandard Analysis and its Applications","author":"T Lindstr\u00f8m","year":"1988","unstructured":"Lindstr\u00f8m, T.: An invitation to nonstandard analysis. In: Cutland, N. (ed.) Nonstandard Analysis and its Applications, pp. 1\u2013105. Cambridge University Press, Cambridge (1988)"},{"key":"16_CR19","doi-asserted-by":"crossref","unstructured":"Mattsson, S.-E., Otter, M., Elmqvist, H.: Multi-mode DAE systems with varying index. In: Elmqvist, H., Fritzson, P. (eds.) Proceedings of the 11th International Modelica Conference, Versailles, France. Modelica Association, September 2015. \n                      http:\/\/www.ep.liu.se\/ecp\/118\/009\/ecp1511889.pdf","DOI":"10.3384\/ecp1511889"},{"issue":"8","key":"16_CR20","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1016\/j.jprocont.2009.05.002","volume":"19","author":"V Mehrmann","year":"2009","unstructured":"Mehrmann, V., Wunderlich, L.: Hybrid systems of differential-algebraic equations - analysis and numerical solution. J. Process Control 19(8), 1218\u20131228 (2009). Special Section on Hybrid Systems: Modeling, Simulation and Optimization","journal-title":"J. Process Control"},{"key":"16_CR21","unstructured":"Modelica: A unified object-oriented language for systems modeling. Language Specification, Version 3.4. Technical report, Modelica Association, April 2017. \n                      https:\/\/www.modelica.org\/documents\/ModelicaSpec34.pdf"},{"key":"16_CR22","doi-asserted-by":"crossref","unstructured":"Otter, M., Elmqvist, H.: Transformation of differential algebraic array equations to index one form. In: Kofranek, J., Casella, F. (eds.) Proceedings of the 12th International Modelica Conference, May 2017. \n                      http:\/\/www.ep.liu.se\/ecp\/132\/064\/ecp17132565.pdf","DOI":"10.3384\/ecp17132565"},{"issue":"2","key":"16_CR23","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1137\/0909014","volume":"9","author":"C Pantelides","year":"1988","unstructured":"Pantelides, C.: The consistent initialization of differential-algebraic systems. SIAM J. Sci. Stat. Comput. 9(2), 213\u2013231 (1988)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"16_CR24","unstructured":"Pepper, P., Mehlhase, A., H\u00f6ger, C., Scholz, L.: A compositional semantics for Modelica-style variable-structure modeling. In: 4th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools (2011). \n                      http:\/\/www.ep.liu.se\/ecp\/056\/006\/ecp1105606.pdf"},{"issue":"2","key":"16_CR25","first-page":"147","volume":"226","author":"Friedrich Pfeiffer","year":"2012","unstructured":"Pfeiffer, F.: On non-smooth multibody dynamics. Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn. 226(2), 147\u2013177 (2012). \n                      http:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1464419312438487","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics"},{"key":"16_CR26","volume-title":"Multibody Dynamics with Unilateral Contacts","author":"F Pfeiffer","year":"2008","unstructured":"Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, Hoboken (2008)"},{"issue":"2","key":"16_CR27","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1023\/A:1021998624799","volume":"41","author":"JD Pryce","year":"2001","unstructured":"Pryce, J.D.: A simple structural analysis method for DAEs. BIT 41(2), 364\u2013394 (2001)","journal-title":"BIT"},{"key":"16_CR28","unstructured":"Robinson, A.: Nonstandard Analysis. Princeton Landmarks in Mathematics (1996). ISBN 0-691-04490-2"},{"key":"16_CR29","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s11044-013-9370-y","volume":"31","author":"S Schoeder","year":"2013","unstructured":"Schoeder, S., Ulbrich, H., Schindler, T.: Discussion of the Gear-Gupta-Leimkuhler method for impacting mechanical systems. Multibody Sys. Dyn. 31, 477\u2013495 (2013)","journal-title":"Multibody Sys. Dyn."},{"key":"16_CR30","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s002110050165","volume":"72","author":"SL Campbell","year":"1995","unstructured":"Campbell, S.L., Gear, C.W.: The index of general nonlinear DAEs. Numer. Math. 72, 173\u2013196 (1995)","journal-title":"Numer. Math."},{"key":"16_CR31","unstructured":"Thoma, J.: Introduction to Bond Graphs and Their Applications. Pergamon International Library of Science, Technology, Engineering and Social Studies. Pergamon Press (1975)"},{"key":"16_CR32","unstructured":"Trenn, S.: Distributional differential algebraic equations. Ph.D. thesis, Technischen Universit\u00e4t Ilmenau (2009). \n                      https:\/\/www.db-thueringen.de\/servlets\/MCRFileNodeServlet\/dbt_derivate_00018071\/ilm1-2009000207.pdf"},{"key":"16_CR33","unstructured":"Zimmer, D.: Equation-based modeling of variable-structure systems. Ph.D. thesis, ETH Z\u00fcrich, no. 18924 (2010). \n                      http:\/\/www.inf.ethz.ch\/personal\/fcellier\/PhD\/zimmer_phd.pdf"}],"container-title":["Lecture Notes in Computer Science","Computing and Software Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-91908-9_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,5]],"date-time":"2019-10-05T20:06:33Z","timestamp":1570305993000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-91908-9_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783319919072","9783319919089"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-91908-9_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"5 October 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}