Routh Reduction for Singular Lagrangians
| dc.contributor.author | Langerock, Bavo | |
| dc.contributor.author | Castrillón López, Marco | |
| dc.date.accessioned | 2023-06-20T03:32:53Z | |
| dc.date.available | 2023-06-20T03:32:53Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map JL are required apart from the momentum being a regular value of JL. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler-Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler-Lagrange equa-tions for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21388 | |
| dc.identifier.doi | 10.1142/S0219887810004907 | |
| dc.identifier.issn | 0219-8878 | |
| dc.identifier.officialurl | http://www.worldscinet.com/ijgmmp/ijgmmp.shtml | |
| dc.identifier.relatedurl | http://www.worldscientific.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43824 | |
| dc.issue.number | 8 | |
| dc.journal.title | Int. J. Geom. Methods Mod. Phys | |
| dc.language.iso | eng | |
| dc.page.final | 1489 | |
| dc.page.initial | 1451 | |
| dc.publisher | Springer-Verlag | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514.85 | |
| dc.subject.keyword | constrained Lagrangian systems | |
| dc.subject.keyword | momentum map | |
| dc.subject.keyword | reduction | |
| dc.subject.keyword | Routhian | |
| dc.subject.keyword | singular Lagrangians | |
| dc.subject.keyword | symmetry | |
| dc.subject.keyword | symplectic form | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | Routh Reduction for Singular Lagrangians | |
| dc.type | journal article | |
| dc.volume.number | 7 | |
| dcterms.references | V.I. Arnold. Dynamical Systems III, volume Encyclopaedia ofMathematics. Springer-Verlag,1988. H. Cendra, J.E. Marsden, and T.S. Ratiu. Lagrangian Reduction by Stages, volume 152 of Memoirs of the American Mathematical Society. 2001. M.C. Ciocci and B. Langerock. Dynamics of the Tippe Top via Routhian Reduction. Regul. and Chaotic Dyn., 12:602–614, 2007. M. Crampin and T. Mestdag. Routh’s procedure for non-Abelian symmetry groups. J. Math. Phys., 49, 2008. H. Goldstein. Classical Mechanics. Addison-Wesley Series in Physics. Addison-Wesley Publishing Co., Reading Mass., second edition, 1980. M.J. Gotay and J.M. Nester. Presymplectic Lagrangian systems I: the constraint algorithm and the euivalence problem. Ann. Inst. Henri Poincar´e, 30(2):129–142, 1979. M.J. Gotay and J.M. Nester. Presymplectic Lagrangian systems II: the second-order equation problem. Ann. Inst. Henri Poincaré, 32(1):1–13, 1980. M.J. Gotay, J.M. Nester, and G. Hinds. Presymplectic manifold and the Dirac-Bergmann theory of constraints. J. Math. Phys., 19(11):2388–2399, 1978.33 S.M. Jalnapurkar and J.E. Marsden. Reduction of Hamiltons variational principle. Dynam-ics and Stability of Systems, 15(3):287–318, 2000. S. Kobayashi and K. Nomizu. Foundations of differential geometry, volume I and II. Intersience Publishers, 1963. D. Kramer, H. Stephani, E. Herlt, and M. MacCallum. Exact solutions of Einsteins field equations. Number 6 in Cambridge monographs on mathematical physics. Cambridge University Press, 1980. B. Langerock, F. Cantrijn, and J. Vankerschaver. Routhian reduction for quasi-invariant Lagrangians. J. Math. Phys., 51(2), 2010. math.DG/09120863. D. Lewis. Lagrangian block diagonalization. J. Dynamics and diff. Equations, 4(1), 1992. M. Castrillón López and T.S. Ratiu. Reduction in principal bundles: Covariant Lagrange-Poincaré equations. Comm. Math. Phys., 236:223–250, 2003. J.E. Marsden, T.S. Ratiu, and J. Scheurle. Reduction theory and the Lagrange-Routh equations. Journal of Mathematical Physics, 41(6):3379–3429, 2000. Kenneth R. Meyer. Symmetries and integrals in mechanics. In Dynamical systems (Proc.Sympos., Univ. Bahia, Salvador, 1971), pages 259–272. Academic Press, New York, 1973. L.A. Pars. A Treatise on Analytical Dynamics. Heinemann Educational Books, 1965. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
Download
Original bundle
1 - 1 of 1