Geodesic
The geometry of Poisson brackets and methods for integration, in the sense of Liouville, of systems on symmetric spaces
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 29 (1986), pp. 3-108.

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A survey is given of various methods of integrating Hamiltonian systems on symmetric spaces and Lie algebras, and an analysis is also presented of applications of the technique developed to some mechanical problems. Some questions of nonintegrability of Hamiltonian systems on symplectic manifolds are considered, and, in particular, the Morse theory of completely integrable Hamiltonian systems is expounded. 
@article{INTD_1986_29_a0,
     author = {V. V. Trofimov and A. T. Fomenko},
     title = {The geometry of {Poisson} brackets and methods for integration, in the sense of {Liouville,} of systems on symmetric spaces},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {3--108},
     publisher = {mathdoc},
     volume = {29},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1986_29_a0/}
}
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V. V. Trofimov; A. T. Fomenko. The geometry of Poisson brackets and methods for integration, in the sense of Liouville, of systems on symmetric spaces. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 29 (1986), pp. 3-108. http://geodesic.mathdoc.fr/item/INTD_1986_29_a0/