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Geometric reduction of Hamiltonian systems
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
Blaszak, M., Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznán, Poland.
2005 (English)In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 55, no 3, 325-339 p.Article in journal (Refereed) Published
Abstract [en]

Given a foliation S of a manifold M, a distribution Z in M transversal to S and a Poisson bivector ? on M, we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical ideas of Dirac (Dirac reduction) and more modern theory of J. Marsden and T. Ratiu, but our method leads to formulae that allow for an explicit calculation of the reduced Poisson bracket. Moreover, we analyse the reduction of Hamiltonian systems corresponding to the bivector ?.

Place, publisher, year, edition, pages
2005. Vol. 55, no 3, 325-339 p.
Keyword [en]
Constraints, Geometric reduction, Hamiltonian systems, Poisson structures
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-45436DOI: 10.1016/S0034-4877(05)80049-7OAI: oai:DiVA.org:liu-45436DiVA: diva2:266332
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Marciniak, Krzysztof

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