{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T11:29:35Z","timestamp":1696591775247},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2008,5,8]],"date-time":"2008-05-08T00:00:00Z","timestamp":1210204800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2008,6]]},"DOI":"10.1007\/s00498-008-0026-z","type":"journal-article","created":{"date-parts":[[2008,5,7]],"date-time":"2008-05-07T08:01:36Z","timestamp":1210147296000},"page":"111-133","source":"Crossref","is-referenced-by-count":5,"title":["Control of mechanical systems on Lie groups based on vertically transverse functions"],"prefix":"10.1007","volume":"20","author":[{"given":"David A.","family":"Liz\u00e1rraga","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Sosa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,5,8]]},"reference":[{"key":"26_CR1","volume-title":"Foundations of mechanics","author":"R Abraham","year":"1985","unstructured":"Abraham R, Marsden JE (1985) Foundations of mechanics, 2nd edn. Addison-Wesley, Reading","edition":"2"},{"key":"26_CR2","doi-asserted-by":"crossref","unstructured":"Bullo F, Lewis AD (2005) Geometric control of mechanical systems. Modeling, analysis, and design for simple mechanical systems. Texts in Applied Mathematics, vol 49. Springer, Heidelberg","DOI":"10.1007\/978-1-4899-7276-7_3"},{"issue":"2","key":"26_CR3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1073\/pnas.8.2.19","volume":"8","author":"LP Eisenhart","year":"1922","unstructured":"Eisenhart LP, Veblen O (1922) The Riemann Geometry and its generalization. Proc Natl Acad Sci USA 8(2): 19\u201323","journal-title":"Proc Natl Acad Sci USA"},{"issue":"1","key":"26_CR4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.5802\/aif.407","volume":"22","author":"J Grifone","year":"1972","unstructured":"Grifone J (1972) Structure presque tangente et connexions I. Ann Instit Fourier 22(1): 287\u2013334","journal-title":"Ann Instit Fourier"},{"key":"26_CR5","doi-asserted-by":"crossref","unstructured":"Helgason S (2001) Differential geometry, Lie groups, and symmetric spaces, Graduate studies in mathematics, vol 34. American Mathematical Society, Providence","DOI":"10.1090\/gsm\/034"},{"key":"26_CR6","doi-asserted-by":"crossref","unstructured":"Imura J, Kobayashi K, Yoshikawa T (1996) Nonholonomic control of 3 link planar manipulator with a free joint. In: IEEE Conference on decision and control (CDC), Kobe, Japan, December, pp 1435\u20131436","DOI":"10.1109\/CDC.1996.572714"},{"key":"26_CR7","volume-title":"Nonlinear systems","author":"HK Khalil","year":"1996","unstructured":"Khalil HK (1996) Nonlinear systems, 2nd edn. Prentice-Hall, Upper Saddle River","edition":"2"},{"key":"26_CR8","volume-title":"Foundations of differential geometry (volume I). Wiley Classics Library","author":"S Kobayashi","year":"1996","unstructured":"Kobayashi S, Nomizu K (1996) Foundations of differential geometry (volume I). Wiley Classics Library. Wiley, London (reprint of the 1963 edition)"},{"key":"26_CR9","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00498-003-0140-x","volume":"16","author":"DA Liz\u00e1rraga","year":"2003","unstructured":"Liz\u00e1rraga DA (2003) Obstructions to the existence of universal stabilizers for smooth control systems. Math Control Signals Syst 16: 255\u2013277","journal-title":"Math Control Signals Syst"},{"key":"26_CR10","doi-asserted-by":"crossref","unstructured":"Liz\u00e1rraga DA, Morin P, Samson C (1999) Non-robustness of continuous homogeneous stabilizers for affine control systems. In: IEEE conference on decision and control (CDC), vol 1, Phoenix, AZ, December, pp 855\u2013860","DOI":"10.1109\/CDC.1999.832897"},{"key":"26_CR11","doi-asserted-by":"crossref","unstructured":"Liz\u00e1rraga DA, Sosa JM (2005) Vertically transverse functions as an extension of the transverse function control approach for second-order systems. In: IEEE conference on decision and control and European control conference ECC. Sevilla, Spain, December, pp 7290\u20137295","DOI":"10.1109\/CDC.2005.1583337"},{"key":"26_CR12","doi-asserted-by":"crossref","unstructured":"Marsden JE, Ratiu TS (1999) Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems, Texts in applied mathematics, vol 17, 2nd edn. Springer, New York","DOI":"10.1007\/978-0-387-21792-5"},{"issue":"4","key":"26_CR13","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1137\/S0363012900366054","volume":"40","author":"P Morin","year":"2001","unstructured":"Morin P, Samson C (2001) A characterization of the Lie algebra rank condition by transverse periodic functions. SIAM J Control Optim 40(4): 1227\u20131249","journal-title":"SIAM J Control Optim"},{"issue":"9","key":"26_CR14","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1109\/TAC.2003.816963","volume":"48","author":"P Morin","year":"2003","unstructured":"Morin P, Samson C (2003) Practical stabilization of driftless systems on Lie groups: the transverse function approach. IEEE Trans Automat Control 48(9): 1496\u20131508","journal-title":"IEEE Trans Automat Control"},{"issue":"1","key":"26_CR15","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1137\/S0363012903421868","volume":"43","author":"P Morin","year":"2004","unstructured":"Morin P, Samson C (2004) Practical and asymptotic stabilization of chained systems by the transverse function control approach. SIAM J Control Optim 43(1): 32\u201357","journal-title":"SIAM J Control Optim"},{"key":"26_CR16","doi-asserted-by":"crossref","unstructured":"Morin P, Samson C (2005) Control of underactuated mechanical systems by the transverse function approach. In: IEEE conference on decision and control and European control conference ECC, Sevilla, Spain, December, pp 7208\u20137213","DOI":"10.1109\/CDC.2005.1583373"},{"key":"26_CR17","doi-asserted-by":"crossref","unstructured":"Morin P, Samson C (2006) Control with transverse functions and a single generator of underactuated mechanical systems. In: IEEE conference on decision and control (CDC), San Diego, CA, December, pp 6110\u20136115","DOI":"10.1109\/CDC.2006.377277"},{"key":"26_CR18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF01661152","volume":"29","author":"BG Schmidt","year":"1973","unstructured":"Schmidt BG (1973) Conditions on a connection to be a metric connection. Commun Math Phys 29: 55\u201359","journal-title":"Commun Math Phys"},{"key":"26_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1799-0","volume-title":"Foundations of differentiable manifolds and lie groups, Graduate texts in mathematics, vol 94","author":"FW Warner","year":"1983","unstructured":"Warner FW (1983) Foundations of differentiable manifolds and lie groups, Graduate texts in mathematics, vol 94. Springer, New York"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-008-0026-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00498-008-0026-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-008-0026-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T09:42:42Z","timestamp":1588671762000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00498-008-0026-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,8]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["26"],"URL":"https:\/\/doi.org\/10.1007\/s00498-008-0026-z","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,8]]}}}