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

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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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
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. Balseiro P., Fernandez O.E., “Reduction of Nonholonomic Systems in Two Stages and Hamiltonization”, Nonlinearity, 28:8 (2015), 2873–2912
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