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Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
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
Аннотация:
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.
Ключевые слова:
symplectic reduction, Routh reduction, Lagrangian reduction, reduction by stages.
Поступила: 16 июня 2011 г.; в окончательном варианте 22 ноября 2011 г.; опубликована 29 ноября 2011 г.
Образец цитирования:
Bavo Langerock, Tom Mestdag, Joris Vankerschaver, “Routh Reduction by Stages”, SIGMA, 7 (2011), 109, 31 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma667 https://www.mathnet.ru/rus/sigma/v7/p109
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