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- W3147514561 abstract "Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson struc-ture, 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 decompo-sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela-tion 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 di-rectly 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." @default.
- W3147514561 created "2021-04-13" @default.
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- W3147514561 date "2009-01-01" @default.
- W3147514561 modified "2023-09-23" @default.
- W3147514561 title "Decomposition of almost Poisson structure of non-self-adjoint dynamical systems" @default.
- W3147514561 hasPublicationYear "2009" @default.
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