{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T21:17:21Z","timestamp":1768339041303,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,11,25]],"date-time":"2021-11-25T00:00:00Z","timestamp":1637798400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,25]],"date-time":"2021-11-25T00:00:00Z","timestamp":1637798400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-1824798"],"award-info":[{"award-number":["CMMI-1824798"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s00498-021-00312-z","type":"journal-article","created":{"date-parts":[[2021,11,25]],"date-time":"2021-11-25T12:03:07Z","timestamp":1637841787000},"page":"329-359","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Controlled Lagrangians and stabilization of Euler\u2013Poincar\u00e9 mechanical systems with broken symmetry II: potential shaping"],"prefix":"10.1007","volume":"34","author":[{"given":"C\u00e9sar","family":"Contreras","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9406-132X","authenticated-orcid":false,"given":"Tomoki","family":"Ohsawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,25]]},"reference":[{"issue":"9","key":"312_CR1","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1080\/00207170210135939","volume":"75","author":"G Blankenstein","year":"2002","unstructured":"Blankenstein G, Ortega R, van der Schaft AJ (2002) The matching conditions of controlled Lagrangians and IDA-passivity based control. Int J Control 75(9):645\u2013665","journal-title":"Int J Control"},{"key":"312_CR2","unstructured":"Bloch AM, Leonard NE, Marsden JE (1999) Potential shaping and the method of controlled lagrangians. In: Proceedings of the 38th IEEE conference on decision and control (Cat. No.99CH36304), vol. 2, pp 1652\u20131657"},{"issue":"3","key":"312_CR3","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1002\/rnc.572","volume":"11","author":"AM Bloch","year":"2001","unstructured":"Bloch AM, Leonard NE, Marsden JE (2001) Controlled Lagrangians and the stabilization of Euler\u2013Poincar\u00e9 mechanical systems. Int J Robust Nonlinear Control 11(3):191\u2013214","journal-title":"Int J Robust Nonlinear Control"},{"issue":"12","key":"312_CR4","doi-asserted-by":"publisher","first-page":"2253","DOI":"10.1109\/9.895562","volume":"45","author":"AM Bloch","year":"2000","unstructured":"Bloch AM, Leonard NE, Marsden JE (2000) Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem. IEEE Trans Autom Control 45(12):2253\u20132270","journal-title":"IEEE Trans Autom Control"},{"issue":"10","key":"312_CR5","doi-asserted-by":"publisher","first-page":"1556","DOI":"10.1109\/9.956051","volume":"46","author":"AM Bloch","year":"2001","unstructured":"Bloch AM, Chang DE, Leonard NE, Marsden JE (2001) Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping. IEEE Trans Autom Control 46(10):1556\u20131571","journal-title":"IEEE Trans Autom Control"},{"key":"312_CR6","doi-asserted-by":"crossref","unstructured":"Borum AD, Bretl T (2014) Geometric optimal control for symmetry breaking cost functions. In: 53rd IEEE conference on decision and control, pp 5855\u20135861","DOI":"10.1109\/CDC.2014.7040306"},{"key":"312_CR7","first-page":"3209","volume":"99","author":"AD Borum","year":"2016","unstructured":"Borum AD, Bretl T (2016) Reduction of sufficient conditions for optimal control problems with subgroup symmetry. IEEE Trans Autom Control 99:3209\u20133224 (ISSN 0018-9286)","journal-title":"IEEE Trans Autom Control"},{"key":"312_CR8","doi-asserted-by":"crossref","unstructured":"Bullo F, Lewis AD (2004) Geometric control of mechanical systems, volume\u00a049 of texts in applied mathematics. Springer","DOI":"10.1007\/978-1-4899-7276-7_3"},{"key":"312_CR9","first-page":"1","volume":"186","author":"H Cendra","year":"1998","unstructured":"Cendra H, Holm DD, Marsden JE, Ratiu TS (1998) Lagrangian reduction, the Euler\u2013Poincar\u00e9 equations, and semidirect products. Amer Math Soc Trans 186:1\u201325","journal-title":"Amer Math Soc Trans"},{"issue":"1","key":"312_CR10","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1137\/S0363012902412951","volume":"43","author":"DE Chang","year":"2004","unstructured":"Chang DE, Marsden JE (2004) Reduction of controlled Lagrangian and Hamiltonian systems with symmetry. SIAM J Control Optim 43(1):277\u2013300","journal-title":"SIAM J Control Optim"},{"key":"312_CR11","first-page":"393","volume":"8","author":"DE Chang","year":"2002","unstructured":"Chang DE, Bloch AM, Leonard NE, Marsden JE, Woolsey CA (2002) The equivalence of controlled Lagrangian and controlled Hamiltonian systems. ESAIM: COCV 8:393\u2013422","journal-title":"ESAIM: COCV"},{"key":"312_CR12","doi-asserted-by":"crossref","unstructured":"Chyba M, Haberkorn T, Smith RN, Wilkens GR (2007) Controlling a submerged rigid body: a geometric analysis. In: Bullo F, Fujimoto K (eds), Lagrangian and Hamiltonian methods for nonlinear control 2006. Springer, Berlin, pp 375\u2013385","DOI":"10.1007\/978-3-540-73890-9_30"},{"key":"312_CR13","doi-asserted-by":"crossref","unstructured":"Contreras C, Ohsawa T (2020) Controlled Lagrangians and stabilization of Euler\u2013Poincar\u00e9 mechanical systems with broken symmetry I: Kinetic shaping","DOI":"10.1007\/s00498-021-00312-z"},{"key":"312_CR14","doi-asserted-by":"crossref","unstructured":"Hamberg J (1999) General matching conditions in the theory of controlled Lagrangians. In: Proceedings of the 38th IEEE conference on decision and control, 1999, vol 3, pp 2519\u20132523","DOI":"10.1109\/CDC.1999.831306"},{"key":"312_CR15","doi-asserted-by":"crossref","unstructured":"Hamberg J (2000) Controlled Lagrangians, symmetries and conditions for strong matching. In IFAC Lagrangian and Hamiltonian methods for nonlinear control","DOI":"10.1016\/S1474-6670(17)35547-7"},{"issue":"1","key":"312_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/aima.1998.1721","volume":"137","author":"DD Holm","year":"1998","unstructured":"Holm DD, Marsden JE, Ratiu TS (1998) The Euler\u2013Poincar\u00e9 equations and semidirect products with applications to continuum theories. Adv Math 137(1):1\u201381","journal-title":"Adv Math"},{"key":"312_CR17","doi-asserted-by":"crossref","unstructured":"Holm DD, Schmah T, Stoica C (2009) Geometric mechanics and symmetry: from finite to infinite dimensions. Oxford texts in applied and engineering mathematics. Oxford University Press","DOI":"10.1093\/oso\/9780199212903.001.0001"},{"issue":"3","key":"312_CR18","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/S0005-1098(96)00176-8","volume":"33","author":"NE Leonard","year":"1997","unstructured":"Leonard NE (1997a) Stability of a bottom-heavy underwater vehicle. Automatica 33(3):331\u2013346","journal-title":"Automatica"},{"issue":"1","key":"312_CR19","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/S0167-6911(97)00051-0","volume":"32","author":"NE Leonard","year":"1997","unstructured":"Leonard NE (1997b) Stabilization of underwater vehicle dynamics with symmetry-breaking potentials. Syst Control Lett 32(1):35\u201342","journal-title":"Syst Control Lett"},{"issue":"1\u20133","key":"312_CR20","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/S0167-2789(97)83390-8","volume":"105","author":"NE Leonard","year":"1997","unstructured":"Leonard NE, Marsden JE (1997) Stability and drift of underwater vehicle dynamics: mechanical systems with rigid motion symmetry. Physica D 105(1\u20133):130\u2013162","journal-title":"Physica D"},{"key":"312_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21792-5","volume-title":"Introduction to mechanics and symmetry","author":"JE Marsden","year":"1999","unstructured":"Marsden JE, Ratiu TS (1999) Introduction to mechanics and symmetry. Springer, New York"},{"issue":"1","key":"312_CR22","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1090\/S0002-9947-1984-0719663-1","volume":"281","author":"JE Marsden","year":"1984","unstructured":"Marsden JE, Ratiu TS, Weinstein A (1984a) Semidirect products and reduction in mechanics. Trans Am Math Soc 281(1):147\u2013177","journal-title":"Trans Am Math Soc"},{"key":"312_CR23","doi-asserted-by":"crossref","unstructured":"Marsden JE, Ratiu TS, Weinstein A (1984) Reduction and Hamiltonian structures on duals of semidirect product Lie algebras. In Fluids and plasmas: geometry and dynamics, volume\u00a028 of Contemporary Mathematics. American Mathematical Society","DOI":"10.1090\/conm\/028\/751975"},{"key":"312_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2101-0","volume-title":"Nonlinear dynamical control systems","author":"H Nijmeijer","year":"1990","unstructured":"Nijmeijer H, van der Schaft A (1990) Nonlinear dynamical control systems. Springer, New York"},{"key":"312_CR25","doi-asserted-by":"crossref","unstructured":"Ortega R, Perez J, Nicklasson P, Sira-Ramirez H (1998) Passivity-based Control of Euler\u2013Lagrange systems: mechanical. Electrical and electromechanical applications. Communications and control engineering. Springer, London","DOI":"10.1007\/978-1-4471-3603-3"},{"issue":"2","key":"312_CR26","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/37.915398","volume":"21","author":"R Ortega","year":"2001","unstructured":"Ortega R, van der Schaft AJ, Mareels I, Maschke B (2001) Putting energy back in control. IEEE Control Syst 21(2):18\u201333","journal-title":"IEEE Control Syst"},{"issue":"8","key":"312_CR27","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1109\/TAC.2002.800770","volume":"47","author":"R Ortega","year":"2002","unstructured":"Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Autom Control 47(8):1218\u20131233","journal-title":"IEEE Trans Autom Control"},{"issue":"9","key":"312_CR28","doi-asserted-by":"publisher","first-page":"1641","DOI":"10.1080\/00207170802654410","volume":"82","author":"RN Smith","year":"2009","unstructured":"Smith RN, Chyba M, Wilkens GR, Catone CJ (2009) A geometrical approach to the motion planning problem for a submerged rigid body. Int J Control 82(9):1641\u20131656","journal-title":"Int J Control"},{"issue":"7","key":"312_CR29","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1109\/TAC.2005.851449","volume":"50","author":"MW Spong","year":"2005","unstructured":"Spong MW, Bullo F (2005) Controlled symmetries and passive walking. IEEE Trans Autom Control 50(7):1025\u20131031","journal-title":"IEEE Trans Autom Control"},{"issue":"10","key":"312_CR30","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1016\/0362-546X(86)90086-6","volume":"10","author":"AJ van der Schaft","year":"1986","unstructured":"van der Schaft AJ (1986) Stabilization of Hamiltonian systems. Nonlinear Anal Theory Methods Appl 10(10):1021\u20131035","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"12","key":"312_CR31","doi-asserted-by":"publisher","first-page":"2053","DOI":"10.1016\/S0005-1098(02)00136-X","volume":"38","author":"CA Woolsey","year":"2002","unstructured":"Woolsey CA, Leonard NE (2002) Stabilizing underwater vehicle motion using internal rotors. Automatica 38(12):2053\u20132062","journal-title":"Automatica"},{"issue":"1","key":"312_CR32","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.oceaneng.2008.07.010","volume":"36","author":"CA Woolsey","year":"2009","unstructured":"Woolsey CA, Techy L (2009) Cross-track control of a slender, underactuated AUV using potential shaping. Ocean Eng 36(1):82\u201391","journal-title":"Ocean Eng"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-021-00312-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00498-021-00312-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-021-00312-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T03:27:43Z","timestamp":1699846063000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00498-021-00312-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,25]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["312"],"URL":"https:\/\/doi.org\/10.1007\/s00498-021-00312-z","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,25]]},"assertion":[{"value":"4 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}