Abstract
A Hamiltonian formulation for elasticity and thermoelasticity is proposed and its relation with the corresponding configurational setting is examined. Firstly, a variational principle, concerning the 'inverse motion' mapping, is formulated and the corresponding Euler–Lagrange equations are explored. Next, this Lagrangian formulation is used to define the Hamiltonian density function. The equations of Hamilton are derived in a form which is very similar to the one of the corresponding equations in particle mechanics (finite-dimensional case). From the Hamiltonian formulation it follows that the canonical momentum is identified with the pseudomomentum. Furthermore, a meaning for the Poisson bracket is defined and the entailed relations with the canonical variables as well as the balance laws are examined.
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