{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T19:48:20Z","timestamp":1742932100160,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":50,"publisher":"Springer New York","isbn-type":[{"type":"print","value":"9780387758886"},{"type":"electronic","value":"9780387304403"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-0-387-30440-3_126","type":"book-chapter","created":{"date-parts":[[2009,6,17]],"date-time":"2009-06-17T16:43:47Z","timestamp":1245257027000},"page":"2002-2019","source":"Crossref","is-referenced-by-count":7,"title":["Discrete Control Systems"],"prefix":"10.1007","author":[{"given":"Taeyoung","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Melvin","family":"Leok","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harris","family":"McClamroch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"126_CR1_126","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1002\/(SICI)1097-0312(200003)53:3<354::AID-CPA3>3.0.CO;2-U","volume":"53","author":"D Auckly","year":"2000","unstructured":"Auckly D, Kapitanski L, White W (2000) Control of nonlinear underactuated systems. Commun Pure Appl Math 53:354\u2013369","journal-title":"Commun Pure Appl Math"},{"key":"126_CR2_126","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/BF02188219","volume":"74","author":"G Benettin","year":"1994","unstructured":"Benettin G, Giorgilli A (1994) On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms. J\u00a0Stat Phys 74:1117\u20131143","journal-title":"J Stat Phys"},{"key":"126_CR3_126","volume-title":"Practical Methods for Optimal Control Using Nonlinear Programming","author":"JT Betts","year":"2001","unstructured":"Betts JT (2001) Practical Methods for Optimal Control Using Nonlinear Programming. SIAM, Philadelphia, PA"},{"key":"126_CR4_126","volume-title":"Interdisciplinary Applied Mathematics","author":"AM Bloch","year":"2003","unstructured":"Bloch AM (2003) Nonholonomic Mechanics and Control. In: Interdisciplinary Applied Mathematics, vol\u00a024. Springer, New York"},{"key":"126_CR5_126","unstructured":"Bloch AM, Leonard N, Marsden JE (1997) Matching and stabilization using controlled Lagrangians. In: Proceedings of the IEEE Conference on Decision and Control. Hyatt Regency San Diego, San Diego, CA, 10\u201312 December 1997, pp 2356\u20132361"},{"key":"126_CR6_126","unstructured":"Bloch AM, Leonard N, Marsden JE (1998) Matching and stabilization by the method of controlled Lagrangians. In: Proceedings of the IEEE Conference on Decision and Control. Hyatt Regency Westshore, Tampa, FL, 16\u201318 December 1998, pp 1446\u20131451"},{"key":"126_CR7_126","unstructured":"Bloch AM, Leonard N, Marsden JE (1999) Potential shaping and the method of controlled Lagrangians. In: Proceedings of the IEEE Conference on Decision and Control. Crowne Plaza Hotel and Resort, Phoenix, AZ, 7\u201310 December 1999, pp 1652\u20131657"},{"key":"126_CR8_126","doi-asserted-by":"crossref","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\u00a0I: The first matching theorem. IEEE Trans Syst Control 45:2253\u20132270","journal-title":"IEEE Trans Syst Control"},{"key":"126_CR9_126","doi-asserted-by":"crossref","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 Contr 46:1556\u20131571","journal-title":"IEEE Trans Autom Contr"},{"key":"126_CR10_126","unstructured":"Bloch AM, Leok M, Marsden JE, Zenkov DV (2005) Controlled Lagrangians and stabilization of the discrete cart\u2010pendulum system. In: Proceedings of the IEEE Conference on Decision and Control. Melia Seville, Seville, Spain, 12\u201315 December 2005, pp 6579\u20136584"},{"key":"126_CR11_126","doi-asserted-by":"crossref","unstructured":"Bloch AM, Leok M, Marsden JE, Zenkov DV (2006) Controlled Lagrangians and potential shaping for stabilization of discrete mechanical systems. In: Proceedings of the IEEE Conference on Decision and Control. Manchester Grand Hyatt, San Diego, CA, 13\u201315 December 2006, pp 3333\u20133338","DOI":"10.1109\/CDC.2006.376695"},{"key":"126_CR12_126","volume-title":"Applied Optimal Control","author":"AE Bryson","year":"1975","unstructured":"Bryson AE, Ho Y (1975) Applied Optimal Control. Hemisphere, Washington, D.C."},{"key":"126_CR13_126","doi-asserted-by":"crossref","unstructured":"Chang D-E, Bloch AM, Leonard NE, Marsden JE, Woolsey C (2002) The equivalence of controlled Lagrangian and controlled Hamiltonian systems. Control Calc Var (special issue dedicated to Lions JL) 8:393\u2013422","DOI":"10.1051\/cocv:2002045"},{"key":"126_CR14_126","volume-title":"Geometric Numerical Integration, 2nd edn. Springer Series in Computational Mathematics","author":"E Hairer","year":"2006","unstructured":"Hairer E, Lubich C, Wanner G (2006) Geometric Numerical Integration, 2nd edn. Springer Series in Computational Mathematics, vol\u00a031. Springer, Berlin"},{"key":"126_CR15_126","unstructured":"Hamberg J (1999) General matching conditions in the theory of controlled Lagrangians. In: Proceedings of the IEEE Conference on Decision and Control. Crowne Plaza Hotel and Resort, Phoenix, AZ, 7\u201310 December 1999, pp 2519\u20132523"},{"key":"126_CR16_126","volume-title":"Lagrangian and Hamiltonian Methods for Nonlinear Control","author":"J Hamberg","year":"2000","unstructured":"Hamberg J (2000) Controlled Lagrangians, symmetries and conditions for strong matching. In: Lagrangian and Hamiltonian Methods for Nonlinear Control. Elsevier, Oxford"},{"key":"126_CR17_126","doi-asserted-by":"crossref","unstructured":"Hussein II, Leok M, Sanyal AK, Bloch AM (2006) A\u00a0discrete variational integrator for optimal control problems in SO(3). In: Proceedings of the IEEE Conference on Decision and Control. Manchester Grand Hyatt, San Diego, CA, 13\u201315 December 2006, pp\u00a06636\u20136641","DOI":"10.1109\/CDC.2006.377818"},{"key":"126_CR18_126","doi-asserted-by":"crossref","unstructured":"Iserles A, Munthe-Kaas H, N\u00f8rsett SP, Zanna A (2000) Lie-group methods. In: Acta Numerica, vol\u00a09. Cambridge University Press, Cambridge, pp 215\u2013365","DOI":"10.1017\/S0962492900002154"},{"key":"126_CR19_126","doi-asserted-by":"crossref","unstructured":"Junge D, Marsden JE, Ober-Bl\u00f6baum S (2005) Discrete mechanics and optimal control. In: IFAC Congress, Praha, Prague, 3\u20138 July 2005","DOI":"10.3182\/20050703-6-CZ-1902.00745"},{"issue":"7","key":"126_CR20_126","doi-asserted-by":"crossref","first-page":"3353","DOI":"10.1063\/1.532892","volume":"40","author":"C Kane","year":"1999","unstructured":"Kane C, Marsden JE, Ortiz M (1999) Symplectic\u2010energy\u2010momentum preserving variational integrators. J\u00a0Math Phys 40(7):3353\u20133371","journal-title":"J Math Phys"},{"issue":"10","key":"126_CR21_126","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1002\/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W","volume":"49","author":"C Kane","year":"2000","unstructured":"Kane C, Marsden JE, Ortiz M, West M (2000) Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Int J Numer Meth Eng 49(10):1295\u20131325","journal-title":"Int J Numer Meth Eng"},{"key":"126_CR22_126","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"CT Kelley","year":"1995","unstructured":"Kelley CT (1995) Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia, PA"},{"key":"126_CR23_126","unstructured":"Lee T, Leok M, McClamroch NH (2005) Attitude maneuvers of a\u00a0rigid spacecraft in a\u00a0circular orbit. In: Proceedings of the American Control Conference. Portland Hilton, Portland, OR, 8\u201310 June 2005, pp 1742\u20131747"},{"key":"126_CR24_126","unstructured":"Lee T, Leok M, McClamroch NH (2005) A\u00a0Lie group variational integrator for the attitude dynamics of a\u00a0rigid body with applications to the 3D pendulum. In: Proceedings of the IEEE Conference on Control Applications. Toronto, Canada, 28\u201331 August 2005, pp 962\u2013967"},{"key":"126_CR25_126","doi-asserted-by":"crossref","unstructured":"Lee T, Leok M, McClamroch NH (2006) Optimal control of a\u00a0rigid body using geometrically exact computations on SE(3). In: Proceedings of the IEEE Conference on Decision and Control. Manchester Grand Hyatt, San Diego, CA, 13\u201315 December 2006, pp 2710\u20132715","DOI":"10.1109\/CDC.2006.376687"},{"key":"126_CR26_126","doi-asserted-by":"crossref","first-page":"2907","DOI":"10.1016\/j.cma.2007.01.017","volume":"196","author":"T Lee","year":"2007","unstructured":"Lee T, Leok M, McClamroch NH (2007) Lie group variational integrators for the full body problem. Comput Method Appl Mech Eng 196:2907\u20132924","journal-title":"Comput Method Appl Mech Eng"},{"issue":"2","key":"126_CR27_126","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s10569-007-9073-x","volume":"98","author":"T Lee","year":"2007","unstructured":"Lee T, Leok M, McClamroch NH (2007) Lie group variational integrators for the full body problem in orbital mechanics. Celest Mech Dyn Astron 98(2):121\u2013144","journal-title":"Celest Mech Dyn Astron"},{"key":"126_CR28_126","volume-title":"Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics","author":"B Leimkuhler","year":"2004","unstructured":"Leimkuhler B, Reich S (2004) Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics, vol\u00a014. Cambridge University Press, Cambridge"},{"key":"126_CR29_126","unstructured":"Leok M (2004) Foundations of Computational Geometric Mechanics. Ph\u202fD thesis, California Instittute of Technology"},{"key":"126_CR30_126","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21792-5","volume-title":"Introduction to Mechanics and Symmetry, 2nd edn. Texts in Applied Mathematics","author":"JE Marsden","year":"1999","unstructured":"Marsden JE, Ratiu TS (1999) Introduction to Mechanics and Symmetry, 2nd edn. Texts in Applied Mathematics, vol\u00a017. Springer, New York"},{"key":"126_CR31_126","first-page":"317","volume-title":"Acta Numerica","author":"JE Marsden","year":"2001","unstructured":"Marsden JE, West M (2001) Discrete mechanics and variational integrators. In: Acta Numerica, vol\u00a010. Cambridge University Press, Cambridge, pp 317\u2013514"},{"issue":"6","key":"126_CR32_126","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1088\/0951-7715\/12\/6\/314","volume":"12","author":"JE Marsden","year":"1999","unstructured":"Marsden JE, Pekarsky S, Shkoller S (1999) Discrete Euler\u2013Poincar\u00e9e and Lie\u2013Poisson equations. Nonlinearity 12(6):1647\u20131662","journal-title":"Nonlinearity"},{"key":"126_CR33_126","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1109\/9.871758","volume":"45","author":"B Maschke","year":"2001","unstructured":"Maschke B, Ortega R, van der Schaft A (2001) Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans Autom Contr 45:1498\u20131502","journal-title":"IEEE Trans Autom Contr"},{"key":"126_CR34_126","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF02352494","volume":"139","author":"J Moser","year":"1991","unstructured":"Moser J, Veselov AP (1991) Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun Math Phys 139:217\u2013243","journal-title":"Commun Math Phys"},{"key":"126_CR35_126","doi-asserted-by":"crossref","unstructured":"Ortega R, Spong MW, G\u00f3mez-Estern F, Blankenstein G (2002) Stabilization of a\u00a0class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Autom Contr 47:1218\u20131233","DOI":"10.1109\/TAC.2002.800770"},{"key":"126_CR36_126","first-page":"243","volume-title":"Acta Numerica","author":"JM Sanz-Serna","year":"1992","unstructured":"Sanz-Serna JM (1992) Symplectic integrators for Hamiltonian problems: an overview. In: Acta Numerica, vol\u00a01. Cambridge University Press, Cambridge, pp 243\u2013286"},{"key":"126_CR37_126","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1126\/science.1133599","volume":"314","author":"DJ Scheeres","year":"2006","unstructured":"Scheeres DJ, Fahnestock EG, Ostro SJ, Margot JL, Benner LAM, Broschart SB, Bellerose J, Giorgini JD, Nolan MC, Magri C, Pravec P, Scheirich P, Rose R, Jurgens RF, De Jong EM, Suzuki S (2006) Dynamical configuration of binary near-Earth asteroid (66391) 1999 KW4. Science 314:1280\u20131283","journal-title":"Science"},{"key":"126_CR38_126","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/BF03256503","volume":"54","author":"DJ Scheeres","year":"2006","unstructured":"Scheeres DJ, Hsiao F-Y, Park RS, Villac BF, Maruskin JM (2006) Fundamental limits on spacecraft orbit uncertainty and distribution propagation. J\u00a0Astronaut Sci 54:505\u2013523","journal-title":"J Astronaut Sci"},{"key":"126_CR39_126","first-page":"293","volume":"2","author":"D Xiu","year":"2007","unstructured":"Xiu D (2007) Efficient collocational approach for parametric uncertainty analysis. Comm Comput Phys 2:293\u2013309","journal-title":"Comm Comput Phys"},{"key":"#cr-split#-126_CR40_126.1","unstructured":"Zenkov DV, Bloch AM, Leonard NE, Marsden JE (2000) Matching and stabilization of low\u2010dimensional nonholonomic systems. In: Proceedings of the IEEE Conference on Decision and Control. Sydney Convention and Exhibition Centre, Sydney, NSW Australia"},{"key":"#cr-split#-126_CR40_126.2","unstructured":"12-15 December 2000, pp 1289-1295"},{"key":"126_CR41_126","doi-asserted-by":"crossref","unstructured":"Zenkov DV, Bloch AM, Leonard NE, Marsden JE (2002) Flat nonholonomic matching. In: Proceedings of the American Control Conference. Hilton Anchorage, Anchorage, AK, 8\u201310 May 2002, pp 2812\u20132817","DOI":"10.1109\/ACC.2002.1025215"},{"key":"126_CR42_126","doi-asserted-by":"crossref","unstructured":"Bloch AM (2003) Nonholonomic Mechanics and Control. Interdisciplinary Appl Math, vol\u00a024. Springer","DOI":"10.1007\/b97376"},{"key":"126_CR43_126","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-7276-7","volume-title":"Geometric control of mechanical systems. Texts in Applied Mathematics","author":"F Bullo","year":"2005","unstructured":"Bullo F, Lewis AD (2005) Geometric control of mechanical systems. Texts in Applied Mathematics, vol\u00a049. Springer, New York"},{"key":"126_CR44_126","volume-title":"Geometric Numerical Integration, 2nd edn. Springer Series in Computational Mathematics","author":"E Hairer","year":"2006","unstructured":"Hairer E, Lubich C, Wanner G (2006) Geometric Numerical Integration, 2nd edn. Springer Series in Computational Mathematics, vol\u00a031. Springer, Berlin"},{"key":"126_CR45_126","doi-asserted-by":"crossref","unstructured":"Iserles A, Munthe-Kaas H, N\u00f8rsett SP, Zanna A (2000) Lie-group methods. In: Acta Numerica, vol\u00a09. Cambridge University Press, Cambridge, pp 215\u2013365","DOI":"10.1017\/S0962492900002154"},{"key":"126_CR46_126","volume-title":"Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics","author":"B Leimkuhler","year":"2004","unstructured":"Leimkuhler B, Reich S (2004) Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics, vol\u00a014. Cambridge University Press, Cambridge"},{"key":"126_CR47_126","doi-asserted-by":"crossref","unstructured":"Marsden JE, Ratiu TS (1999) Introduction to Mechanics and Symmetry, 2nd edn. Texts in Applied Mathematics, vol\u00a017. Springer","DOI":"10.1007\/978-0-387-21792-5"},{"key":"126_CR48_126","first-page":"317","volume-title":"Discrete mechanics and variational integrators. In Acta Numerica","author":"JE Marsden","year":"2001","unstructured":"Marsden JE, West M (2001) Discrete mechanics and variational integrators. In Acta Numerica, vol\u00a010. Cambridge University Press, Cambridge, pp 317\u2013514"},{"key":"126_CR49_126","first-page":"243","volume-title":"Acta Numerica","author":"JM Sanz-Serna","year":"1992","unstructured":"Sanz-Serna JM (1992) Symplectic integrators for Hamiltonian problems: an overview. In: Acta Numerica, vol\u00a01. Cambridge University Press, Cambridge, pp 243\u2013286"}],"container-title":["Encyclopedia of Complexity and Systems Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-30440-3_126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T05:55:43Z","timestamp":1739166943000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-30440-3_126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9780387758886","9780387304403"],"references-count":50,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-30440-3_126","relation":{},"subject":[],"published":{"date-parts":[[2009]]}}}