Geodesic
Focus-focus singularities in classical mechanics
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 101-112

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In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of a focus-focus singularity with given complexity is found. It is shown that only simple focus-focus singularities can appear in a typical mechanical system. Model examples of mechanical systems with complicated focus-focus singularity are given.
Keywords: integrable hamiltonian systems, focus-focus singularities, obstruction to the existence of singularities. 
@article{ND_2014_10_1_a6,
     author = {Gleb E. Smirnov},
     title = {Focus-focus singularities in classical mechanics},
     journal = {Russian journal of nonlinear dynamics},
     pages = {101--112},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_1_a6/}
}
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Gleb E. Smirnov. Focus-focus singularities in classical mechanics. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/ND_2014_10_1_a6/