# Derivation of reduced two-dimensional fluid models via Diracâ€™s theory of constrained Hamiltonian systems

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A classification of compatible Lie-Poisson brackets on e*(3) is constructed. The corresponding bi-Hamiltonian systems are the classical integrable cases of the Euler-Poisson and Kirchhoff equations which describe the motion of a solid body. Bibliography: 12 titles.

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Hamiltonian n-dimensional Lotkaâ€“Volterra systems are introduced that have n-1 conserved quantities. The explicit integrability in quadratures is demonstrated.

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We consider the dynamics of biaxial nematics following the Hamiltonian approach. The hydrodynamic parameters related to the broken symmetry are introduced in terms of the distortion tensor. The densities and flows of additive integrals of motion are represented in terms of the thermodynamic...