Sparse hierarchies of K coupled gyrostats (M=2K+1 modes, no linear feedback) possess exactly (M+1)/2 quadratic invariants recoverable as Casimirs of a constructible non-canonical Poisson structure.
Gluhovsky (2008), Gyrostatic extensions of the Howard-Krishnamurti model of thermal convection with shear
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Quadratic invariants and Hamiltonian structure in coupled gyrostat low-order model hierarchies
Sparse hierarchies of K coupled gyrostats (M=2K+1 modes, no linear feedback) possess exactly (M+1)/2 quadratic invariants recoverable as Casimirs of a constructible non-canonical Poisson structure.