Cardan Motion in Elliptic Geometry

Extract

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 a_i, 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.