Abstract
Poisson brackets are constructed by the same mathematical procedure for three physical theories: ideal magnetohydrodynamics, multifluid plasmas, and elasticity. Each of these brackets is given a simple Lie-algebraic interpretation. Moreover, each bracket is induced to physical space by use of a canonical Poisson bracket in the space of Clebsch potentials, which are constructed for each physical theory by the standard procedure of constrained Lagrangians.
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