{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T11:11:25Z","timestamp":1772017885421,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,11,11]],"date-time":"2015-11-11T00:00:00Z","timestamp":1447200000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2017,2]]},"DOI":"10.1007\/s10208-015-9287-3","type":"journal-article","created":{"date-parts":[[2015,11,11]],"date-time":"2015-11-11T20:52:20Z","timestamp":1447275140000},"page":"199-257","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Lie Group Spectral Variational Integrators"],"prefix":"10.1007","volume":"17","author":[{"given":"James","family":"Hall","sequence":"first","affiliation":[]},{"given":"Melvin","family":"Leok","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,11]]},"reference":[{"issue":"1","key":"9287_CR1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s002200050642","volume":"204","author":"AI Bobenko","year":"1999","unstructured":"A. I. Bobenko and Y. B. Suris. Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top. Comm. Math. Phys., 204(1):147\u2013188, 1999.","journal-title":"Comm. Math. Phys."},{"key":"9287_CR2","doi-asserted-by":"publisher","unstructured":"G. Bogfjellmo and H. Marthinsen. High-Order Symplectic Partitioned Lie Group Methods. Found. Comput. Math., 2015. doi: 10.1007\/s10208-015-9257-9 .","DOI":"10.1007\/s10208-015-9257-9"},{"issue":"2","key":"9287_CR3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10208-008-9030-4","volume":"9","author":"N Bou-Rabee","year":"2009","unstructured":"N. Bou-Rabee and J. E. Marsden. Hamilton-Pontryagin integrators on Lie groups. I. Introduction and structure-preserving properties. Found. Comput. Math., 9(2):197\u2013219, 2009.","journal-title":"Found. Comput. Math."},{"issue":"2","key":"9287_CR4","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1093\/imanum\/drn018","volume":"29","author":"N Bou-Rabee","year":"2009","unstructured":"N. Bou-Rabee and H. Owhadi. Stochastic variational integrators. IMA J. Numer. Anal., 29(2):421\u2013443, 2009.","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"9287_CR5","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1137\/090758842","volume":"48","author":"N Bou-Rabee","year":"2010","unstructured":"N. Bou-Rabee and H. Owhadi. Long-run accuracy of variational integrators in the stochastic context. SIAM J. Numer. Anal., 48(1):278\u2013297, 2010.","journal-title":"SIAM J. Numer. Anal."},{"key":"9287_CR6","volume-title":"Chebyshev and Fourier spectral methods","author":"JP Boyd","year":"2001","unstructured":"J. P. Boyd. Chebyshev and Fourier spectral methods. Dover Publications Inc., Mineola, NY, second edition, 2001.","edition":"2"},{"key":"9287_CR7","doi-asserted-by":"crossref","unstructured":"C. L. Burnett, D. D. Holm, and D. M. Meier. Inexact trajectory planning and inverse problems in the Hamilton-Pontryagin framework. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 469 (2160):20130249, 24, 2013.","DOI":"10.1098\/rspa.2013.0249"},{"issue":"3\u20134","key":"9287_CR8","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/S0045-7825(02)00520-0","volume":"192","author":"E Celledoni","year":"2003","unstructured":"E. Celledoni and B. Owren. Lie group methods for rigid body dynamics and time integration on manifolds. Comput. Methods Appl. Mech. Engrg., 192 (3-4):421\u2013438, 2003.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"1","key":"9287_CR9","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/0167-2789(91)90081-J","volume":"50","author":"PJ Channell","year":"1991","unstructured":"P. J. Channell and J. C. Scovel. Integrators for Lie-Poisson dynamical systems. Phys. D, 50(1):80\u201388, 1991.","journal-title":"Phys. D"},{"issue":"5","key":"9287_CR10","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1088\/0951-7715\/14\/5\/322","volume":"14","author":"J Cort\u00e9s","year":"2001","unstructured":"J. Cort\u00e9s and S. Mart\u00ednez. Non-holonomic integrators. Nonlinearity, 14(5):1365\u20131392, 2001.","journal-title":"Nonlinearity"},{"issue":"5","key":"9287_CR11","doi-asserted-by":"crossref","first-page":"2211","DOI":"10.1088\/0951-7715\/18\/5\/017","volume":"18","author":"YN Fedorov","year":"2005","unstructured":"Y. N. Fedorov and D. V. Zenkov. Discrete nonholonomic LL systems on Lie groups. Nonlinearity, 18(5):2211\u20132241, 2005.","journal-title":"Nonlinearity"},{"key":"9287_CR12","unstructured":"E. Hairer, C. Lubich, and G. Wanner. Geometric numerical integration, volume\u00a031 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 2006."},{"issue":"4","key":"9287_CR13","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s00211-014-0679-0","volume":"130","author":"J Hall","year":"2015","unstructured":"J. Hall and M. Leok. Spectral Variational Integrators. Numer. Math., 130(4):681\u2013740, 2015.","journal-title":"Numer. Math."},{"key":"9287_CR14","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/S0962492900002154","volume":"9","author":"A Iserles","year":"2000","unstructured":"A. Iserles, H. Z. Munthe-Kaas, S. P. N\u00f8rsett, and A. Zanna. Lie-group methods. Acta Numer., 9:215\u2013365, 2000.","journal-title":"Acta Numer."},{"issue":"19","key":"9287_CR15","doi-asserted-by":"crossref","first-page":"5521","DOI":"10.1088\/0305-4470\/39\/19\/S12","volume":"39","author":"SM Jalnapurkar","year":"2006","unstructured":"S. M. Jalnapurkar, M. Leok, J. E. Marsden, and M. West. Discrete Routh reduction. J. Phys. A, 39(19):5521\u20135544, 2006.","journal-title":"J. Phys. A"},{"issue":"1","key":"9287_CR16","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0733019","volume":"33","author":"LO Jay","year":"1996","unstructured":"L. O. Jay. Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems. SIAM J. Numer. Anal., 33(1):368\u2013387, 1996.","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9287_CR17","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1137\/S1064827595293223","volume":"20","author":"LO Jay","year":"1998","unstructured":"L. O Jay. Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods. SIAM J. Sci. Comput., 20(2):416\u2013446, 1998.","journal-title":"SIAM J. Sci. Comput."},{"key":"9287_CR18","doi-asserted-by":"crossref","unstructured":"M. Kobilarov, J. E. Marsden, and G. S. Sukhatme. Geometric discretization of nonholonomic systems with symmetries. Discrete Contin. Dyn. Syst. Ser. S, 3(1): 61\u201384, 2010. ISSN 1937-1632.","DOI":"10.3934\/dcdss.2010.3.61"},{"issue":"19","key":"9287_CR19","doi-asserted-by":"crossref","first-page":"5509","DOI":"10.1088\/0305-4470\/39\/19\/S11","volume":"39","author":"S Lall","year":"2006","unstructured":"S. Lall and M. West. Discrete variational Hamiltonian mechanics. J. Phys. A, 39(19):5509\u20135519, 2006.","journal-title":"J. Phys. A"},{"key":"9287_CR20","doi-asserted-by":"publisher","unstructured":"T. Lee, N. H. McClamroch, and M. Leok. A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum. Proc. IEEE Conf. on Control Applications, pages 962\u2013967, 2005. doi: 10.1109\/CCA.2005.1507254 .","DOI":"10.1109\/CCA.2005.1507254"},{"issue":"29\u201330","key":"9287_CR21","doi-asserted-by":"crossref","first-page":"2907","DOI":"10.1016\/j.cma.2007.01.017","volume":"196","author":"T Lee","year":"2007","unstructured":"T. Lee, M. Leok, and N. H. McClamroch. Lie group variational integrators for the full body problem. Comput. Methods Appl. Mech. Engrg., 196 (29-30):2907\u20132924, 2007.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"9","key":"9287_CR22","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1002\/nme.2603","volume":"79","author":"T Lee","year":"2009","unstructured":"T. Lee, M. Leok, and N. H. McClamroch. Lagrangian mechanics and variational integrators on two-spheres. Internat. J. Numer. Methods Engrg., 79(9): 1147\u20131174, 2009.","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"9287_CR23","unstructured":"M. Leok. Foundations of Computational Geometric Mechanics. PhD thesis, California Institute of Technology, 2004. URL http:\/\/resolver.caltech.edu\/CaltechETD:etd-03022004-000251 ."},{"issue":"2","key":"9287_CR24","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s11464-012-0190-9","volume":"7","author":"M Leok","year":"2012","unstructured":"M. Leok and T. Shingel. General techniques for constructing variational integrators. Front. Math. China, 7(2):273\u2013303, 2012.","journal-title":"Front. Math. China"},{"issue":"4","key":"9287_CR25","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.1093\/imanum\/drq027","volume":"31","author":"M Leok","year":"2011","unstructured":"M. Leok and J. Zhang. Discrete Hamiltonian variational integrators. IMA J. Numer. Anal., 31(4):1497\u20131532, 2011.","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"9287_CR26","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00205-002-0212-y","volume":"167","author":"A Lew","year":"2003","unstructured":"A. Lew, J. E. Marsden, M. Ortiz, and M. West. Asynchronous variational integrators. Arch. Ration. Mech. Anal., 167(2):85\u2013146, 2003.","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9287_CR27","doi-asserted-by":"crossref","unstructured":"J. E. Marsden and T. S. Ratiu. Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, volume\u00a017 of Texts in Applied Mathematics. Springer-Verlag, New York, second edition, 1999.","DOI":"10.1007\/978-0-387-21792-5"},{"key":"9287_CR28","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1017\/S096249290100006X","volume":"10","author":"JE Marsden","year":"2001","unstructured":"J. E. Marsden and M. West. Discrete mechanics and variational integrators. Acta Numer., 10:357\u2013514, 2001.","journal-title":"Acta Numer."},{"issue":"2","key":"9287_CR29","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s002200050505","volume":"199","author":"JE Marsden","year":"1998","unstructured":"J. E. Marsden, G. W. Patrick, and S. Shkoller. Multisymplectic geometry, variational integrators, and nonlinear PDEs. Comm. Math. Phys., 199(2):351\u2013395, 1998.","journal-title":"Comm. Math. Phys."},{"issue":"6","key":"9287_CR30","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1088\/0951-7715\/12\/6\/314","volume":"12","author":"JE Marsden","year":"1999","unstructured":"J. E. Marsden, S. Pekarsky, and S. Shkoller. Discrete Euler-Poincar\u00e9 and Lie-Poisson equations. Nonlinearity, 12(6):1647, 1999.","journal-title":"Nonlinearity"},{"issue":"1\u20132","key":"9287_CR31","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/S0393-0440(00)00018-8","volume":"36","author":"JE Marsden","year":"2000","unstructured":"J. E. Marsden, S. Pekarsky, and S. Shkoller. Symmetry reduction of discrete Lagrangian mechanics on Lie groups. J. Geom. Phys., 36(1-2):140\u2013151, 2000.","journal-title":"J. Geom. Phys."},{"issue":"4","key":"9287_CR32","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s00332-005-0698-1","volume":"16","author":"R McLachlan","year":"2006","unstructured":"R. McLachlan and M. Perlmutter. Integrators for nonholonomic mechanical systems. J. Nonlinear Sci., 16(4):283\u2013328, 2006.","journal-title":"J. Nonlinear Sci."},{"issue":"3","key":"9287_CR33","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/BF01212956","volume":"5","author":"RI McLachlan","year":"1995","unstructured":"R. I. McLachlan and C. Scovel. Equivariant constrained symplectic integration. J. Nonlinear Sci., 5(3):233\u2013256, 1995.","journal-title":"J. Nonlinear Sci."},{"issue":"2","key":"9287_CR34","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1093\/imanum\/dru013","volume":"35","author":"RI McLachlan","year":"2015","unstructured":"R. I. McLachlan, K. Modin, and O. Verdier. Collective Lie-Poisson integrators on $${\\mathbb{R}}^3$$ R 3 . IMA J. Numer. Anal., 35(2):546\u2013560, 2015.","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"9287_CR35","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF02352494","volume":"139","author":"J Moser","year":"1991","unstructured":"J. Moser and A.P. Veselov. Discrete versions of some classical integrable systems and factorization of matrix polynomials. Comm. Math. Phys., 139(2):217\u2013243, 1991.","journal-title":"Comm. Math. Phys."},{"issue":"4","key":"9287_CR36","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1137\/090776822","volume":"49","author":"T Ohsawa","year":"2011","unstructured":"T. Ohsawa, A.M. Bloch, and M. Leok. Discrete Hamilton\u2013Jacobi theory. SIAM J. Control Optim., 49(4):1829\u20131856, 2011.","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"9287_CR37","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s00211-009-0245-3","volume":"113","author":"GW Patrick","year":"2009","unstructured":"G. W. Patrick and C. Cuell. Error analysis of variational integrators of unconstrained Lagrangian systems. Numer. Math., 113(2):243\u2013264, 2009.","journal-title":"Numer. Math."},{"key":"9287_CR38","doi-asserted-by":"crossref","unstructured":"L. N. Trefethen. Spectral methods in MATLAB, volume\u00a010 of Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.","DOI":"10.1137\/1.9780898719598"},{"key":"9287_CR39","doi-asserted-by":"crossref","unstructured":"J. Vankerschaver, C. Liao, and M. Leok. Generating functionals and Lagrangian partial differential equations. J. Math. Phys., 54(8):082901, 22, 2013.","DOI":"10.1063\/1.4817391"},{"issue":"3","key":"9287_CR40","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/0375-9601(88)90773-6","volume":"133","author":"G Zhong","year":"1988","unstructured":"G. Zhong and J. E. Marsden. Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators. Phys. Lett. A, 133(3):134\u2013139, 1988.","journal-title":"Phys. Lett. A"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9287-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-015-9287-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9287-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9287-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T13:00:52Z","timestamp":1567342852000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-015-9287-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,11]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["9287"],"URL":"https:\/\/doi.org\/10.1007\/s10208-015-9287-3","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,11]]}}}