FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2132849333> ?p ?o ?g. }

• W2132849333 abstract "This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler{Poincare reduction (for the case in which the conguration space is a Lie group) as well as Euler-Poincare reductionfor semidirect products.The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange{Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory.We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange{Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory.In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of Marsden, Ratiu and Scheurle [2000], which studies the Lagrange-Routh equations." @default.
• W2132849333 created "2016-06-24" @default.
• W2132849333 creator A5018631946 @default.
• W2132849333 creator A5058692396 @default.
• W2132849333 creator A5090498729 @default.
• W2132849333 date "2001-07-01" @default.
• W2132849333 modified "2023-10-02" @default.
• W2132849333 title "Lagrangian Reduction by Stages" @default.
• W2132849333 cites W1517510250 @default.
• W2132849333 cites W1524590822 @default.
• W2132849333 cites W1534305016 @default.
• W2132849333 cites W1541587142 @default.
• W2132849333 cites W1559305177 @default.
• W2132849333 cites W1575346238 @default.
• W2132849333 cites W1575757764 @default.
• W2132849333 cites W1588860486 @default.
• W2132849333 cites W1601110984 @default.
• W2132849333 cites W1661681931 @default.
• W2132849333 cites W1681099931 @default.
• W2132849333 cites W1719066964 @default.
• W2132849333 cites W1751949721 @default.
• W2132849333 cites W1762147622 @default.
• W2132849333 cites W1810841586 @default.
• W2132849333 cites W1820493214 @default.
• W2132849333 cites W1825591403 @default.
• W2132849333 cites W1899717397 @default.
• W2132849333 cites W1968369152 @default.
• W2132849333 cites W1976074773 @default.
• W2132849333 cites W1977250608 @default.
• W2132849333 cites W1979251648 @default.
• W2132849333 cites W1979806876 @default.
• W2132849333 cites W1982779826 @default.
• W2132849333 cites W1988630735 @default.
• W2132849333 cites W1988827374 @default.
• W2132849333 cites W1994246733 @default.
• W2132849333 cites W1996250140 @default.
• W2132849333 cites W1999111109 @default.
• W2132849333 cites W2000008197 @default.
• W2132849333 cites W2003161517 @default.
• W2132849333 cites W2004850935 @default.
• W2132849333 cites W2009035354 @default.
• W2132849333 cites W2009082840 @default.
• W2132849333 cites W2012322577 @default.
• W2132849333 cites W2013291269 @default.
• W2132849333 cites W2013325119 @default.
• W2132849333 cites W2013563090 @default.
• W2132849333 cites W2014613771 @default.
• W2132849333 cites W2023969170 @default.
• W2132849333 cites W2025365558 @default.
• W2132849333 cites W2025637651 @default.
• W2132849333 cites W2030045047 @default.
• W2132849333 cites W2039078443 @default.
• W2132849333 cites W2042038080 @default.
• W2132849333 cites W2046669744 @default.
• W2132849333 cites W2046988039 @default.
• W2132849333 cites W2047062138 @default.
• W2132849333 cites W2054908020 @default.
• W2132849333 cites W2055315817 @default.
• W2132849333 cites W2058008825 @default.
• W2132849333 cites W2060119452 @default.
• W2132849333 cites W2064854048 @default.
• W2132849333 cites W2067980435 @default.
• W2132849333 cites W2072397974 @default.
• W2132849333 cites W2080904103 @default.
• W2132849333 cites W2082280760 @default.
• W2132849333 cites W2084386115 @default.
• W2132849333 cites W2084884762 @default.
• W2132849333 cites W2086607193 @default.
• W2132849333 cites W2094997310 @default.
• W2132849333 cites W2102263452 @default.
• W2132849333 cites W2113055611 @default.
• W2132849333 cites W2123850162 @default.
• W2132849333 cites W2124969394 @default.
• W2132849333 cites W2125929512 @default.
• W2132849333 cites W2130006697 @default.
• W2132849333 cites W2140796472 @default.
• W2132849333 cites W2148271773 @default.
• W2132849333 cites W2149297753 @default.
• W2132849333 cites W2162550557 @default.
• W2132849333 cites W2162621498 @default.
• W2132849333 cites W2171421055 @default.
• W2132849333 cites W2171658097 @default.
• W2132849333 cites W2236204289 @default.
• W2132849333 cites W1871030895 @default.
• W2132849333 hasPublicationYear "2001" @default.
• W2132849333 type Work @default.
• W2132849333 sameAs 2132849333 @default.
• W2132849333 citedByCount "106" @default.
• W2132849333 countsByYear W21328493332012 @default.
• W2132849333 countsByYear W21328493332013 @default.
• W2132849333 countsByYear W21328493332014 @default.
• W2132849333 countsByYear W21328493332015 @default.
• W2132849333 countsByYear W21328493332016 @default.
• W2132849333 countsByYear W21328493332017 @default.
• W2132849333 countsByYear W21328493332018 @default.
• W2132849333 countsByYear W21328493332019 @default.
• W2132849333 countsByYear W21328493332021 @default.
• W2132849333 crossrefType "book" @default.
• W2132849333 hasAuthorship W2132849333A5018631946 @default.
• W2132849333 hasAuthorship W2132849333A5058692396 @default.

• next