Integrable Hamiltonian Systems on the Symplectic Realizations of $$\textbf{e}(3)^*$$

  title={Integrable Hamiltonian Systems on the Symplectic Realizations of 
  author={A. Odzijewicz and E. Wawreniuk},
  journal={Russian Journal of Mathematical Physics},
Abstract The phase space of a gyrostat with a fixed point and a heavy top is the Lie–Poisson space $$\textbf{e}(3)^*\cong \mathbb{R}^3\times \mathbb{R}^3$$ dual to the Lie algebra $$\textbf{e}(3)$$ of the Euclidean group $$E(3)$$ . One has three naturally distinguished Poisson submanifolds of $$\textbf{e}(3)^*$$ : (i) the dense open submanifold $$\mathbb{R}^3\times \dot{\mathbb{R}}^3\subset \textbf{e}(3)^*$$ which consists of all $$4$$ -dimensional symplectic leaves ( $$\vec{\Gamma}^2>0… 



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