{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:23:53Z","timestamp":1762917833208,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T00:00:00Z","timestamp":1514332800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s00332-017-9434-x","type":"journal-article","created":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T02:11:33Z","timestamp":1514340693000},"page":"943-983","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Reduced Dynamics of the Non-holonomic Whipple Bicycle"],"prefix":"10.1007","volume":"28","author":[{"given":"Fr\u00e9d\u00e9ric","family":"Boyer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mathieu","family":"Porez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4596-1801","authenticated-orcid":false,"given":"Johan","family":"Mauny","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,27]]},"reference":[{"key":"9434_CR1","volume-title":"Trait\u00e9 de m\u00e9canique rationnelle","author":"P Appell","year":"1931","unstructured":"Appell, P.: Trait\u00e9 de m\u00e9canique rationnelle. Gauthier-Villars et Cie, Paris (1931)"},{"issue":"4","key":"9434_CR2","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MCS.2005.1499389","volume":"25","author":"KJ Astrom","year":"2005","unstructured":"Astrom, K.J., Klein, R.E., Lennartsson, A.: Bicycle dynamics and control: adapted bicycles for education and research. IEEE Control Syst. 25(4), 26\u201347 (2005)","journal-title":"IEEE Control Syst."},{"key":"9434_CR3","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4gdk","volume-title":"Feedback Systems: An Introduction for Scientists and Engineers","author":"KJ Astr\u00f6m","year":"2010","unstructured":"Astr\u00f6m, K.J., Murray, R.M.: Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press, Cambridge (2010)"},{"issue":"2084","key":"9434_CR4","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1098\/rspa.2007.1849","volume":"463","author":"P Basu-Mandal","year":"2007","unstructured":"Basu-Mandal, P., Chatterjee, A., Papadopoulos, J.: Hands-free circular motions of a benchmark bicycle. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 463(2084), 1983\u20132003 (2007)","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"9434_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4939-3017-3","volume-title":"Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics","author":"AM Bloch","year":"2015","unstructured":"Bloch, A.M.: Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics, vol. 24. Springer, New York (2015)"},{"issue":"1","key":"9434_CR6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02199365","volume":"136","author":"AM Bloch","year":"1996","unstructured":"Bloch, A.M., Krishnaprasad, P.S., Marsden, J.E., Murray, R.M.: Nonholonomic mechanical systems with symmetry. Arch. Ration. Mech. Anal. 136(1), 21\u201399 (1996)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9434_CR7","doi-asserted-by":"crossref","first-page":"76","DOI":"10.24033\/bsmf.597","volume":"27","author":"C Bourlet","year":"1899","unstructured":"Bourlet, C.: \u00c9tude th\u00e9orique sur la bicyclette. Bull. Soc. Math. Fr. 27, 76\u201396 (1899)","journal-title":"Bull. Soc. Math. Fr."},{"key":"9434_CR8","first-page":"117","volume":"5","author":"J Boussinesq","year":"1899","unstructured":"Boussinesq, J.: Aper\u00e7u sur la th\u00e9orie de la bicyclette. J. Math. Pures Appl. 5, 117\u2013136 (1899)","journal-title":"J. Math. Pures Appl."},{"issue":"3","key":"9434_CR9","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1109\/TRO.2013.2294733","volume":"30","author":"F Boyer","year":"2014","unstructured":"Boyer, F., Belkhiri, A.: Reduced locomotion dynamics with passive internal dofs: application to nonholonomic and soft robotics. IEEE Trans. Rob. 30(3), 578\u2013592 (2014)","journal-title":"IEEE Trans. Rob."},{"issue":"3","key":"9434_CR10","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1109\/TRO.2015.2411411","volume":"31","author":"F Boyer","year":"2015","unstructured":"Boyer, F., Belkhiri, A.: Erratum to \u201cReduced locomotion dynamics with passive internal dofs: application to nonholonomic and soft robotics\u201d [Jun 14 578\u2013592]. IEEE Trans. Rob. 31(3), 805\u2013805 (2015)","journal-title":"IEEE Trans. Rob."},{"issue":"2","key":"9434_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/1748-3190\/10\/2\/025007","volume":"10","author":"F Boyer","year":"2015","unstructured":"Boyer, F., Porez, M.: Multibody system dynamics for bio-inspired locomotion: from geometric structures to computational aspects. Bioinspir. Biomim. 10(2), 1\u201321 (2015)","journal-title":"Bioinspir. Biomim."},{"key":"9434_CR12","unstructured":"Boyer, F., Primault, D.: The Poincar\u00e9\u2013Chetayev equations and flexible multibody systems. J. Appl. Math. Mech. 69(6), 925\u2013942 (2005). http:\/\/hal.archives-ouvertes.fr\/hal-00672477"},{"issue":"1","key":"9434_CR13","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/70.481750","volume":"12","author":"G Campion","year":"1996","unstructured":"Campion, G., Bastin, G., D\u2019Andr\u00e9a-Novel, B.: Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Trans. Robot. Autom. 12(1), 47\u201362 (1996)","journal-title":"IEEE Trans. Robot. Autom."},{"key":"9434_CR14","first-page":"1","volume":"6","author":"E Carvallo","year":"1901","unstructured":"Carvallo, E.: Th\u00e9orie du movement du monocycle part 2: Th\u00e9orie de la bicyclette. J. l\u2019\u00c9cole Polytech. 6, 1\u2013118 (1901)","journal-title":"J. l\u2019\u00c9cole Polytech."},{"key":"9434_CR15","doi-asserted-by":"crossref","unstructured":"Cendra, H., Marsden, J.E., Ratiu, T.S.: Geometric mechanics, lagrangian reduction, and nonholonomic systems. In: Engquist, B., Schmid, W. (eds.) Mathematics Unlimited\u20142001 and Beyond, pp. 221\u2013273. Springer, Beriln (2001)","DOI":"10.1007\/978-3-642-56478-9_10"},{"issue":"4","key":"9434_CR16","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1134\/S1560354708040102","volume":"13","author":"S Chaplygin","year":"2008","unstructured":"Chaplygin, S.: On the theory of motion of nonholonomic systems. The reducing-multiplier theorem. Regul. Chaotic Dyn. 13(4), 369\u2013376 (2008)","journal-title":"Regul. Chaotic Dyn."},{"key":"9434_CR17","doi-asserted-by":"crossref","unstructured":"Chitta, S., Cheng, P., Frazzoli, E., Kumar, V.: Robotrikke: a novel undulatory locomotion system. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation (ICRA), pp. 1597\u20131602 (2005)","DOI":"10.1109\/ROBOT.2005.1570342"},{"issue":"9","key":"9434_CR18","doi-asserted-by":"crossref","first-page":"2831","DOI":"10.1016\/j.automatica.2013.05.021","volume":"49","author":"L Consolini","year":"2013","unstructured":"Consolini, L., Maggiore, M.: Control of a bicycle using virtual holonomic constraints. Automatica 49(9), 2831\u20132839 (2013)","journal-title":"Automatica"},{"key":"9434_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-7560-7","volume-title":"Rigid Body Dynamics Algorithms","author":"R Featherstone","year":"2008","unstructured":"Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, Berlin (2008)"},{"issue":"2","key":"9434_CR20","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1088\/0143-0807\/11\/2\/010","volume":"11","author":"G Franke","year":"1990","unstructured":"Franke, G., Suhr, W., Riess, F.: An advanced model of bicycle dynamics. Eur. J. Phys. 11(2), 116\u2013121 (1990)","journal-title":"Eur. J. Phys."},{"key":"9434_CR21","doi-asserted-by":"crossref","unstructured":"Getz, N.H., Marsden, J.E.: Control for an autonomous bicycle. In: Proceedings of 1995 IEEE International Conference on Robotics and Automation, vol.\u00a02, pp. 1397\u20131402 (1995)","DOI":"10.1109\/ROBOT.1995.525473"},{"key":"9434_CR22","unstructured":"Hertz, H.: Die Prinzipen der Mechanik in neuem Zusammenhange dargestellt. Gesamelte Werke, Band III. Leipzig (1894)"},{"issue":"6","key":"9434_CR23","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1119\/1.1990413","volume":"10","author":"AT Jones","year":"1942","unstructured":"Jones, A.T.: Physics and bicycles. Am. J. Phys. 10(6), 332\u2013333 (1942)","journal-title":"Am. J. Phys."},{"issue":"6","key":"9434_CR24","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1002\/rob.4620120607","volume":"12","author":"SD Kelly","year":"1995","unstructured":"Kelly, S.D., Murray, R.M.: Geometric phases and robotic locomotion. J. Robot. Syst. 12(6), 417\u2013431 (1995)","journal-title":"J. Robot. Syst."},{"key":"9434_CR25","unstructured":"Klein, F., Sommerfeld, A.: \u00dcber die theorie des kreisels. \u00dcber die Theorie des Kreisels, by Klein, Felix; Sommerfeld, Arnold. New York: Johnson Reprint Corp., 1965. Bibliotheca mathematica Teubneriana; Bd. 1 4 (1965)"},{"issue":"6027","key":"9434_CR26","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1126\/science.1201959","volume":"332","author":"JDG Kooijman","year":"2011","unstructured":"Kooijman, J.D.G., Meijaard, J.P., Papadopoulos, J.M., Ruina, A., Schwab, A.L.: A bicycle can be self-stable without gyroscopic or caster effects. Science 332(6027), 339\u2013342 (2011)","journal-title":"Science"},{"issue":"3","key":"9434_CR27","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1088\/0143-0807\/8\/3\/013","volume":"8","author":"Y H\u00e9naff Le","year":"1987","unstructured":"Le H\u00e9naff, Y.: Dynamical stability of the bicycle. Eur. J. Phys. 8(3), 207\u2013210 (1987)","journal-title":"Eur. J. Phys."},{"issue":"4","key":"9434_CR28","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1016\/0021-8928(59)90029-2","volume":"23","author":"A Letov","year":"1959","unstructured":"Letov, A.: Stability of an automatically controlled bicycle moving on a horizontal plane. J. Appl. Math. Mech. 23(4), 934\u2013942 (1959)","journal-title":"J. Appl. Math. Mech."},{"key":"9434_CR29","unstructured":"Lobry, C., Sari, T.: Singular perturbation methods in control theory. Contrle Non Linaire et Applications. Cours du CIMPA, Collection Travaux en Cours, pp. 155\u2013182. Hermann, Paris (2005)"},{"issue":"2084","key":"9434_CR30","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1098\/rspa.2007.1857","volume":"463","author":"J Meijaard","year":"2007","unstructured":"Meijaard, J., Papadopoulos, J.M., Ruina, A., Schwab, A.: Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 463(2084), 1955\u20131982 (2007)","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"issue":"5","key":"9434_CR31","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/TRO.2009.2014123","volume":"25","author":"P Morin","year":"2009","unstructured":"Morin, P., Samson, C.: Control of nonholonomic mobile robots based on the transverse function approach. IEEE Trans. Robot. 25(5), 1058\u20131073 (2009)","journal-title":"IEEE Trans. Robot."},{"issue":"7","key":"9434_CR32","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1177\/027836499801700701","volume":"17","author":"J Ostrowski","year":"1998","unstructured":"Ostrowski, J., Burdick, J.: The geometric mechanics of undulatory robotic locomotion. Int. J. Robot. Res. (IJRR) 17(7), 683\u2013701 (1998)","journal-title":"Int. J. Robot. Res. (IJRR)"},{"key":"9434_CR33","doi-asserted-by":"crossref","unstructured":"Ostrowski, J., Burdick, J., Lewis, A.D., Murray, R.M.: The mechanics of undulatory locomotion: the mixed kinematic and dynamic case. In: Proceedings of 1995 IEEE International Conference on Robotics and Automation (ICRA), vol.\u00a02, pp. 1945\u20131951 (1995)","DOI":"10.1109\/ROBOT.1995.525549"},{"key":"9434_CR34","doi-asserted-by":"crossref","unstructured":"Ostrowski, J., Lewis, A., Murray, R., Burdick, J.: Nonholonomic mechanics and locomotion: the snakeboard example. In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation (ICRA), vol. 3, pp. 2391\u20132397 (1994)","DOI":"10.1109\/ROBOT.1994.351153"},{"issue":"1","key":"9434_CR35","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1109\/70.744607","volume":"15","author":"JP Ostrowski","year":"1999","unstructured":"Ostrowski, J.P.: Computing reduced equations for robotic systems with constraints and symmetries. IEEE Trans. Robot. Autom. 15(1), 111\u2013123 (1999)","journal-title":"IEEE Trans. Robot. Autom."},{"key":"9434_CR36","unstructured":"Psiaki, M.: Bicycle stability: a mathematical and numerical analysis. Undergradute thesis. Physics Dept., Princeton University, Princeton (1979)"},{"issue":"79","key":"9434_CR37","first-page":"129","volume":"28","author":"WJM Rankine","year":"1869","unstructured":"Rankine, W.J.M.: On the dynamical principles of the motion of velocipedes. The Engineer 28(79), 129 (1869)","journal-title":"The Engineer"},{"key":"9434_CR38","volume-title":"Advanced Dynamics","author":"SP Timoshenko","year":"1948","unstructured":"Timoshenko, S.P., Young, D.H.: Advanced Dynamics. McGraw-Hill, London (1948)"},{"issue":"120","key":"9434_CR39","first-page":"312","volume":"30","author":"FJ Whipple","year":"1899","unstructured":"Whipple, F.J.: The stability of the motion of a bicycle. Quarterly Journal of Pure and Applied Mathematics 30(120), 312\u2013348 (1899)","journal-title":"Quarterly Journal of Pure and Applied Mathematics"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00332-017-9434-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9434-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-017-9434-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,8]],"date-time":"2019-10-08T14:47:30Z","timestamp":1570546050000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-017-9434-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,27]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["9434"],"URL":"https:\/\/doi.org\/10.1007\/s00332-017-9434-x","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"type":"print","value":"0938-8974"},{"type":"electronic","value":"1432-1467"}],"subject":[],"published":{"date-parts":[[2017,12,27]]}}}