author={V. Dragovic and B. Gaji{\'c} and B. Jovanovic},
  journal={International Journal of Geometric Methods in Modern Physics},
We start with a review of a class of systems with invariant relations, so called systems of Hess–Appel'rot type that generalizes the classical Hess–Appel'rot rigid body case. The systems of Hess–Appel'rot type have remarkable property: there exists a pair of compatible Poisson structures, such that a system is certain Hamiltonian perturbation of an integrable bi-Hamiltonian system. The invariant relations are Casimir functions of the second structure. The systems of Hess–Appel'rot type carry an… Expand
The rigid body dynamics: classical and algebro-geometric integration
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We construct higher-dimensional generalizations of the classical Hess- Appel’rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of thisExpand
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An L–A pair for the Hess–Apel'rot system and a new integrable case for the Euler–Poisson equations on so(4) × so(4)
  • V. Dragovic, B. Gajić
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2001
We present an L–A pair for the Hess–Apel'rot case of a heavy rigid three-dimensional body. Using it, we give an algebro-geometric integration procedure. Generalizing this L–A pair, we obtain a newExpand
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