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SIGMA, 2011, Volume 7, 109, 31 pages (Mi sigma667)  

This article is cited in 4 scientific papers (total in 4 papers)

Routh Reduction by Stages

Bavo Langerockabc, Tom Mestdaga, Joris Vankerschaverad

a Department of Mathematics, Ghent University, Krijgslaan 281, S22, B9000 Ghent, Belgium
b Belgian Institute for Space Aeronomy, Ringlaan 3, B1180 Brussels, Belgium
c Department of Mathematics, K.U. Leuven, Celestijnenlaan 200 B, B3001 Leuven, Belgium
d Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, San Diego CA 92093-0112, USA

Abstract: This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the magnetic Lagrangian system obtained after Routh reduction w.r.t. to the full symmetry group.

Keywords: symplectic reduction, Routh reduction, Lagrangian reduction, reduction by stages.

DOI: https://doi.org/10.3842/SIGMA.2011.109

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Full text: http://emis.mi.ras.ru/.../109
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Bibliographic databases:

ArXiv: 1106.2950
Document Type: Article
MSC: 37J05; 37J15; 52D20
Received: June 16, 2011; in final form November 22, 2011; Published online November 29, 2011
Language: English

Citation: Bavo Langerock, Tom Mestdag, Joris Vankerschaver, “Routh Reduction by Stages”, SIGMA, 7 (2011), 109, 31 pp.

Citation in format AMSBIB
\Bibitem{LanMesVan11}
\by Bavo Langerock, Tom Mestdag, Joris Vankerschaver
\paper Routh Reduction by Stages
\jour SIGMA
\yr 2011
\vol 7
\papernumber 109
\totalpages 31
\mathnet{http://mi.mathnet.ru/sigma667}
\crossref{https://doi.org/10.3842/SIGMA.2011.109}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857180485}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Langerock B., Andres E.G.-T., Cantrijn F., “Routh Reduction and the Class of Magnetic Lagrangian Systems”, J. Math. Phys., 53:6 (2012), 062902  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Andres E.G.-T., Guzman E., Marrero J.C., Mestdag T., “Reduced Dynamics and Lagrangian Submanifolds of Symplectic Manifolds”, J. Phys. A-Math. Theor., 47:22 (2014), 225203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Andres E.G.-T., Langerock B., Cantrijn F., “Aspects of Reduction and Transformation of Lagrangian Systems with Symmetry”, J. Geom. Mech., 6:1 (2014), 1–23  crossref  mathscinet  zmath  isi  scopus
    4. Balseiro P., Fernandez O.E., “Reduction of Nonholonomic Systems in Two Stages and Hamiltonization”, Nonlinearity, 28:8 (2015), 2873–2912  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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