Geometric reduction of Hamiltonian systems
2005 (English)In: Reports on mathematical physics, ISSN 0034-4877, Vol. 55, no 3, 325-339 p.Article in journal (Refereed) Published
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.
Constraints, Geometric reduction, Hamiltonian systems, Poisson structures
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-45436DOI: 10.1016/S0034-4877(05)80049-7OAI: oai:DiVA.org:liu-45436DiVA: diva2:266332