Hamiltonian structure and conservation laws of two‐dimensional linear elasticity theory

Abstract

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.