Presymplectic form
From HandWiki
In geometric mechanics a presymplectic form is a closed differential 2-form of constant rank on a manifold.[1] However, some authors use different definitions. Recently, Hajduk and Walczak defined a presymplectic form as a closed differential 2-form of maximal rank on a manifold of odd dimension.[2] A symplectic form is a presymplectic form that is also nondegenerate.[3] Lack of nondegeneracy, leading to presymplectic forms, occurs in dynamical systems with singular Lagrangians, Hamiltonian systems with constraints and control theory.[4]
References
- ↑ Vaisman, Izu (1983). "Geometric quantization on presymplectic manifolds" (in en). Monatshefte für Mathematik 96 (4): 293–310. doi:10.1007/BF01471212. ISSN 0026-9255.
- ↑ Boguslaw Hajduk & Rafa Walczak (2009). "Presymplectic manifolds". arXiv:0912.2297 [math.SG].
- ↑ Martınez, Eduardo. "Symplectic, Presymplectic, Poisson, Dirac, ...". http://andres.unizar.es/~wdgmp/EduardoMartinez.pdf. Retrieved 26 July 2013.
- ↑ Alishah, Hassan Najafi. "KAM Theory, Presymplectic Dynamics and Lie algebroids". UNIVERSIDADE TÉCNICA DE LISBOA INSTITUTO SUPERIOR TÉCNICO. http://www.math.illinois.edu/~ruiloja/Estudantes/TeseHNajafi.pdf. Retrieved 26 July 2013.
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