{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T11:06:02Z","timestamp":1783076762583,"version":"3.54.6"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T00:00:00Z","timestamp":1372118400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2014,4]]},"DOI":"10.1007\/s10208-013-9163-y","type":"journal-article","created":{"date-parts":[[2013,6,24]],"date-time":"2013-06-24T16:46:06Z","timestamp":1372092366000},"page":"339-370","source":"Crossref","is-referenced-by-count":23,"title":["Geometric Generalisations of shake and rattle"],"prefix":"10.1007","volume":"14","author":[{"given":"Robert","family":"I McLachlan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Klas","family":"Modin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olivier","family":"Verdier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matt","family":"Wilkins","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,6,25]]},"reference":[{"key":"9163_CR1","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/0021-9991(83)90014-1","volume":"52","author":"H.C. Andersen","year":"1983","unstructured":"H.C. Andersen, Rattle: a \u201cvelocity\u201d version of the shake algorithm for molecular dynamics calculations, J.\u00a0Comput. Phys. 52, 24\u201334 (1983).","journal-title":"J.\u00a0Comput. Phys."},{"key":"9163_CR2","volume-title":"Lectures on Quantum Mechanics","author":"P. Dirac","year":"2001","unstructured":"P. Dirac, Lectures on Quantum Mechanics (Dover Publications, New York, 2001)."},{"key":"9163_CR3","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/0375-9601(88)90773-6","volume":"133","author":"Z. Ge","year":"1988","unstructured":"Z. Ge, J.E. Marsden, Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators, Phys. Lett. A 133, 134\u2013139 (1988).","journal-title":"Phys. Lett. A"},{"key":"9163_CR4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1090\/S0002-9939-1982-0633290-X","volume":"84","author":"M.J. Gotay","year":"1982","unstructured":"M.J. Gotay, On coisotropic imbeddings of presymplectic manifolds, Proc. Am. Math. Soc. 84, 111\u2013114 (1982).","journal-title":"Proc. Am. Math. Soc."},{"key":"9163_CR5","doi-asserted-by":"crossref","first-page":"2388","DOI":"10.1063\/1.523597","volume":"19","author":"M. Gotay","year":"1978","unstructured":"M. Gotay, J. Nester, G. Hinds, Presymplectic manifolds and the Dirac\u2013Bergmann theory of constraints, J.\u00a0Math. Phys. 19, 2388 (1978).","journal-title":"J.\u00a0Math. Phys."},{"key":"9163_CR6","volume-title":"Symplectic Techniques in Physics","author":"V. Guillemin","year":"1990","unstructured":"V. Guillemin, S. Sternberg, Symplectic Techniques in Physics (Cambridge University Press, Cambridge, 1990)."},{"key":"9163_CR7","volume-title":"Solving Ordinary Differential Equations: Nonstiff Problems","author":"E. Hairer","year":"1993","unstructured":"E. Hairer, S. N\u00f8rsett, G. Wanner, Solving Ordinary Differential Equations: Nonstiff Problems (Springer, Berlin, 1993)."},{"key":"9163_CR8","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","author":"E. Hairer","year":"2006","unstructured":"E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer, Berlin, 2006)."},{"key":"9163_CR9","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0733019","volume":"33","author":"L. Jay","year":"1996","unstructured":"L. Jay, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems, SIAM J. Numer. Anal. 33, 368\u2013387 (1996).","journal-title":"SIAM J. Numer. Anal."},{"key":"9163_CR10","volume-title":"Simulating Hamiltonian Dynamics","author":"B. Leimkuhler","year":"2004","unstructured":"B. Leimkuhler, S. Reich, Simulating Hamiltonian Dynamics (Cambridge University Press, Cambridge, 2004)."},{"key":"9163_CR11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1006\/jcph.1994.1085","volume":"112","author":"B. Leimkuhler","year":"1994","unstructured":"B. Leimkuhler, R. Skeel, Symplectic numerical integrators in constrained Hamiltonian systems, J.\u00a0Comput. Phys. 112, 117\u2013125 (1994).","journal-title":"J.\u00a0Comput. Phys."},{"key":"9163_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-3807-6","volume-title":"Symplectic Geometry and Analytical Mechanics","author":"P. Libermann","year":"1987","unstructured":"P. Libermann, C. Marle, Symplectic Geometry and Analytical Mechanics (D. Reidel Publishing Co., Dordrecht, 1987)."},{"key":"9163_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21792-5","volume-title":"Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems","author":"J. Marsden","year":"1999","unstructured":"J. Marsden, T. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems (Springer, New York, 1999)."},{"key":"9163_CR14","unstructured":"R. McLachlan, K. Modin, O. Verdier, M. Wilkins, Symplectic integrators for index one constraints (2012). arXiv:1207.4250 ."},{"key":"9163_CR15","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1137\/0733025","volume":"33","author":"S. Reich","year":"1996","unstructured":"S. Reich, Symplectic integration of constrained Hamiltonian systems by composition methods, SIAM J. Numer. Anal. 33, 475\u2013491 (1996).","journal-title":"SIAM J. Numer. Anal."},{"key":"9163_CR16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0021-9991(77)90098-5","volume":"23","author":"J.-P. Ryckaert","year":"1977","unstructured":"J.-P. Ryckaert, G. Ciccotti, H.J. Berendsen, Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes, J.\u00a0Comput. Phys. 23, 327\u2013341 (1977).","journal-title":"J.\u00a0Comput. Phys."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-013-9163-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-013-9163-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-013-9163-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T11:05:12Z","timestamp":1559127912000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-013-9163-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,25]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,4]]}},"alternative-id":["9163"],"URL":"https:\/\/doi.org\/10.1007\/s10208-013-9163-y","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6,25]]}}}