Geodesic
Two-Parametric Motions in the Lobatchevski Plane
Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 027-036.

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We classify two-parametric motions in the Lobatchevski plane L2. These motions are surfaces on the Lie group SO(2, 1). In the first part the basic properties of motions in L2 are derived and it turns out that the kinematical space belonging to these motions is locally the space SO(2, 2) / SO(2, 1) realized as the unit quadric with signature (2, 2) in the vector space R4. The remaining part contains explicit expressions and graphic representations of surfaces induced by motions with constant invariants. We also present some special cases - developable surfaces. 
@article{JGG_2002_6_1_a2,
     author = {M. Hlavova},
     title = {Two-Parametric {Motions} in the {Lobatchevski} {Plane}},
     journal = {Journal for geometry and graphics},
     pages = {027--036},
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     volume = {6},
     number = {1},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a2/}
}
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M. Hlavova. Two-Parametric Motions in the Lobatchevski Plane. Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 027-036. http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a2/