{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:16:16Z","timestamp":1762521376464,"version":"3.38.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s00332-010-9078-6","type":"journal-article","created":{"date-parts":[[2010,9,24]],"date-time":"2010-09-24T19:25:36Z","timestamp":1285356336000},"page":"3-32","source":"Crossref","is-referenced-by-count":44,"title":["Nonlinear Dynamics of the 3D Pendulum"],"prefix":"10.1007","volume":"21","author":[{"given":"Nalin A.","family":"Chaturvedi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taeyoung","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Melvin","family":"Leok","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. Harris","family":"McClamroch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,9,25]]},"reference":[{"key":"9078_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02535-2","volume-title":"Dynamical Systems III","author":"V.I. Arnold","year":"1988","unstructured":"Arnold, V.I., Kozlov, V.V., Neishtadt, A.I.: Dynamical Systems III. Springer, Berlin (1988)"},{"key":"9078_CR2","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0005-1098(99)00140-5","volume":"36","author":"K.J. Astrom","year":"2000","unstructured":"Astrom, K.J., Furuta, K.: Swinging up a pendulum by energy control. Automatica 36, 287\u2013295 (2000)","journal-title":"Automatica"},{"key":"9078_CR3","doi-asserted-by":"crossref","unstructured":"Bernstein, D.S., McClamroch, N.H., Bloch, A.M.: Development of air spindle and triaxial air bearing testbeds for spacecraft dynamics and control experiments. In: Proceedings of the American Control Conference, pp.\u00a03967\u20133972 (2001)","DOI":"10.1109\/ACC.2001.946287"},{"key":"9078_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/b97376","volume-title":"Nonholonomic Mechanics and Control","author":"A.M. Bloch","year":"2003","unstructured":"Bloch, A.M.: Nonholonomic Mechanics and Control. Springer, Berlin (2003)"},{"key":"9078_CR5","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jappmathmech.2007.06.002","volume":"71","author":"A.D. Bruno","year":"2007","unstructured":"Bruno, A.D.: Analysis of the Euler-Poisson equations by methods of power geometry and normal form. J.\u00a0Appl. Math. Mech. 71, 168\u2013199 (2007)","journal-title":"J.\u00a0Appl. Math. Mech."},{"issue":"722","key":"9078_CR6","first-page":"1","volume":"152","author":"H. Cendra","year":"2001","unstructured":"Cendra, H., Marsden, J.E., Ratiu, T.S.: Lagrangian reduction by stages. Mem. Am. Math. Soc. 152(722), 1\u2013108 (2001)","journal-title":"Mem. Am. Math. Soc."},{"key":"9078_CR7","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1002\/rnc.1178","volume":"17","author":"N.A. Chaturvedi","year":"2007","unstructured":"Chaturvedi, N.A., McClamroch, N.H.: Asymptotic stabilization of the hanging equilibrium manifold of the 3D pendulum. Int. J. Robust Nonlinear Control 17, 1435\u20131454 (2007)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"9078_CR8","unstructured":"Cho, S., Shen, J., McClamroch, N.H., Bernstein, D.S.: Equations of motion of the triaxial attitude control testbed. In: Proceedings of the IEEE Conference on Decision and Control, pp.\u00a03429\u20133434 (2001)"},{"key":"9078_CR9","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1076\/mcmd.9.2.165.16520","volume":"9","author":"S. Cho","year":"2003","unstructured":"Cho, S., Shen, J., McClamroch, N.H.: Mathematical models for the triaxial attitude control testbed. Math. Comput. Model. Dyn. Syst. 9, 165\u2013192 (2003)","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"9078_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8891-2","volume-title":"Global Aspects of Classical Integrable Systems","author":"R.H. Cushman","year":"1997","unstructured":"Cushman, R.H., Bates, L.M.: Global Aspects of Classical Integrable Systems. Birkh\u00e4user, Basel (1997)"},{"key":"9078_CR11","doi-asserted-by":"crossref","unstructured":"Furuta, K.: Control of pendulum: from super mechano-system to human adaptive mechatronics. In: Proceedings of the IEEE Conference on Decision and Control, pp.\u00a01498\u20131507 (2003)","DOI":"10.1109\/CDC.2003.1272824"},{"key":"9078_CR12","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.geomphys.2004.06.007","volume":"53","author":"A. Hern\u00e1ndez-Gardu\u00f1o","year":"2005","unstructured":"Hern\u00e1ndez-Gardu\u00f1o, A., Lawson, J.K., Marsden, J.E.: Relative equilibria for the generalized rigid body. J.\u00a0Geom. Phys. 53, 259\u2013274 (2005)","journal-title":"J.\u00a0Geom. Phys."},{"key":"9078_CR13","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1512\/iumj.1983.32.32023","volume":"32","author":"P.J. Holmes","year":"1983","unstructured":"Holmes, P.J., Marsden, J.E.: Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups. Indiana Univ. Math. J. 32, 962\u2013967 (1983)","journal-title":"Indiana Univ. Math. J."},{"key":"9078_CR14","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.jappmathmech.2006.06.003","volume":"70","author":"A.V. Karapetyan","year":"2006","unstructured":"Karapetyan, A.V.: Invariant sets in the Goryachev-Chaplygin problem: existence, stability, and branching. J. Appl. Math. Mech. 70, 195\u2013198 (2006)","journal-title":"J. Appl. Math. Mech."},{"key":"9078_CR15","unstructured":"Lee, T., Leok, M., McClamroch, N.H.: A Lie group variational integrator for the attitude dynamics of a rigid body with application to the 3D pendulum. In: Proceedings of the IEEE Conference on Decision and Control, pp.\u00a0962\u2013967 (2005)"},{"key":"9078_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0951-7715\/5\/1\/001","volume":"5","author":"D. Lewis","year":"1992","unstructured":"Lewis, D., Ratiu, T.S., Simo, J.C., Marsden, J.E.: The heavy top: a geometric treatment. Nonlinearity 5, 1\u201348 (1992)","journal-title":"Nonlinearity"},{"key":"9078_CR17","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1093\/imamat\/46.1-2.71","volume":"46","author":"J.H. Maddocks","year":"1991","unstructured":"Maddocks, J.H.: Stability of relative equilibria. IMA J. Appl. Math. 46, 71\u201399 (1991)","journal-title":"IMA J. Appl. Math."},{"key":"9078_CR18","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1063\/1.533317","volume":"41","author":"J.E. Marsden","year":"2000","unstructured":"Marsden, J.E., Ratiu, T.S., Scheurle, J.: Reduction theory and the Lagrange-Routh equations. J. Math. Phys. 41, 3379\u20133429 (2000)","journal-title":"J. Math. Phys."},{"key":"9078_CR19","doi-asserted-by":"crossref","unstructured":"Shen, J., Sanyal, A.K., Chaturvedi, N.A., Bernstein, D.S., McClamroch, N.H.: Dynamics and control of a 3D pendulum. In: Proceedings of the IEEE Conference on Decision and Control, pp.\u00a0323\u2013328 (2004)","DOI":"10.1109\/CDC.2004.1428650"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.springerlink.com\/index\/pdf\/10.1007\/s00332-010-9078-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T01:47:14Z","timestamp":1740534434000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00332-010-9078-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,25]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["9078"],"URL":"https:\/\/doi.org\/10.1007\/s00332-010-9078-6","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"type":"print","value":"0938-8974"},{"type":"electronic","value":"1432-1467"}],"subject":[],"published":{"date-parts":[[2010,9,25]]}}}