Geodesic
The geodesic flow of a~sub-Riemannian metric on a~solvable lie group
Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 120-128

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We consider the sub-Riemannian problem on the three-dimensional solvable Lie group $\mathrm{SOLV}^+$. The problem is based on constructing a Hamiltonian structure for a given metric by the Pontryagin Maximum Principle. 
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     author = {A. D. Mazhitova},
     title = {The geodesic flow of {a~sub-Riemannian} metric  on a~solvable lie group},
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A. D. Mazhitova. The geodesic flow of a~sub-Riemannian metric  on a~solvable lie group. Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 120-128. http://geodesic.mathdoc.fr/item/MT_2012_15_1_a6/