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Hamiltonian structure and conservation laws of two‐dimensional linear elasticity theory
Author(s) -
Medvedev S. B.,
Grebenev V. N.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500090
Subject(s) - poisson bracket , casimir effect , conservation law , hamiltonian (control theory) , mathematics , singularity , poisson manifold , poisson distribution , covariant hamiltonian field theory , mathematical physics , hamiltonian system , classical mechanics , mathematical analysis , physics , pure mathematics , mathematical optimization , statistics , lie algebra
In this study, the existence of Hamiltonian structures for a two‐dimensional, linear‐elastic model is considered. We show that this model admits the so‐called noncanonical singular Poisson bracket. Casimir functionals are found by using the singularity properties of the Poisson bracket obtained. We also demonstrate that these functionals are conserved for an arbitrary choice of Hamiltonian. Excepting the energy functional, we prove that there no exists conservation laws of zero order.