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Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this article, the degeneracy distribution of the symplectic form of the coupled Einstein-Maxwell field is given and its connection with the action of the symmetry group is established, based on the multiphase approach to classical field theories.
9 citations
TL;DR: The SR factorization for a given matrix A is a QR-like factorization A=SR, where the matrix S is symplectic and R is J-upper triangular, and the MSGS is the symplectic Gram-Schmidt algorithm implemented via the SGS.
Abstract: The SR factorization for a given matrix A is a QR-like factorization A=SR, where the matrix S is symplectic and R is J-upper triangular. This factorization is fundamental for some important structure-preserving methods in linear algebra and is usually implemented via the symplectic Gram-Schmidt algorithm (SGS).
9 citations
TL;DR: In this paper, it was shown that if a point in the Lie coalgebra is regular, that is, its stabilizer is a maximal torus, then it is possible to desingularize generic symplectic quotients for compact Lie group actions.
Abstract: Symplectic reduction is a technique that can be used to decrease the dimension of Hamiltonian manifolds. Unfortunately, this only works under strong assumptions on the group action, and in general, even for a compact Lie group, the reduction at a coadjoint orbit that is transverse to the moment map will only yield a symplectic orbifold.In this article, we show how to construct resolutions of symplectic orbifolds obtained as quotients of presymplectic manifolds with a torus action. As a corollary, this allows us to desingularize generic symplectic quotients for compact Lie group actions. More precisely, if a point in the Lie coalgebra is regular, that is, its stabilizer is a maximal torus, then we may apply our desingularization result. Regular elements of the Lie coalgebra are generic in the sense that the singular strata have codimension at least three.Additionally, we show that even though the result of a symplectic cut is an orbifold, it can be modified in an arbitrarily small neighborhood of the cut hypersurface to obtain a smooth symplectic manifold. © The Author 2009. Published by Oxford University Press. All rights reserved.
9 citations
TL;DR: In this paper, an explicit symplectic integrator for perturbed elliptic orbits of an arbitrary eccentricity is constructed for the motion of an Earth satellite under the action of the planet's oblateness and of lunar perturbations, and the results confirm the superiority of the method over a classical Wisdom-Holman algorithm in both accuracy and computation time.
Abstract: An explicit symplectic integrator is constructed for perturbed elliptic orbits of an arbitrary eccentricity. The perturbation should be Hamiltonian, but it may depend on time explicitly. The main feature of the integrator is the use of KS variables in the ten-dimensional extended phase space. As an example of its application the motion of an Earth satellite under the action of the planet's oblateness and of lunar perturbations is studied. The results confirm the superiority of the method over a classical Wisdom–Holman algorithm in both accuracy and computation time.
9 citations
9 citations