Geodesic
Approximate form of reachable sets after perturbation of Liouville systems
Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 133
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It is shown that the set of points in Liouville systems of two degrees of freedom, which can be reached from an arbitrarily fixed initial position with a given modulo initial velocity, has the shape of a curvilinear octagon, which lies in the area of possible motion with the corresponding energy. 
@article{TAM_1982_8_1_a15,
     author = {Ya. Tatarinov},
     title = {Approximate form of reachable sets after perturbation of {Liouville} systems},
     journal = {Theoretical and applied mechanics},
     pages = {133 },
     year = {1982},
     volume = {8},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1982_8_1_a15/}
}
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Ya. Tatarinov. Approximate form of reachable sets after perturbation of Liouville systems. Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 133 . http://geodesic.mathdoc.fr/item/TAM_1982_8_1_a15/