Geodesic
Cardan Motion in Elliptic Geometry
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 37-43

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Cardan motion in Euclidean geometry may be defined as the motion of a plane Г1 with respect to a coinciding plane Г such that two points A1, A2 of Г1 move along two orthogonal lines ai, a2 of Г1 The properties of this classical motion are well-known: the path of a point of Г1 is in general an ellipse with its center at the intersection o of a1 and a2; there are ∞ l points of Г1 (their locus being the circle C1 with A1, A2 = 2d as diameter) the paths of which are line segments. The moving polhode is the circle Ci, the fixed polhode is the circle (o; 2d). We investigate here Cardan motion-defined in the same way-in the elliptic plane. 
Bottema, Oene. Cardan Motion in Elliptic Geometry. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 37-43. doi: 10.4153/CJM-1975-006-5
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