NDLI: Decomposition of almost Poisson structure of non-self-adjoint dynamical systems

Content Provider	Springer Nature Link
Author	Guo, YongXin Liu, Chang Liu, ShiXing Chang, Peng
Copyright Year	2009
Abstract	Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decomposition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding relation between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost “Lie-Poisson” one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket directly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.
Starting Page	761
Ending Page	770
Page Count	10
File Format	PDF
ISSN	10069321
Journal	Science in China Series E: Technological Sciences
Volume Number	52
Issue Number	3
e-ISSN	1862281X
Language	English
Publisher	SP Science in China Press
Publisher Date	2009-02-24
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	almost-Poisson structure non-self-adjointness nonholonomic systems symplectic form Jacobi identity torsion Engineering
Content Type	Text
Resource Type	Article
Subject	Engineering Materials Science

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