Geodesic
Euclidean space motions with affinely equivalent trajectories
Applications of Mathematics, Tome 28 (1983) no. 1, pp. 32-43

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The author studies the Euclidean space motions with the property that the trajectory of every point is an affine image of a given space curve. Such motions split into plane motions and translations and their trajectories are cylindrical curves. They are characterized as motions with the following property: Not all trajectories are plane curves and if any trajectory has a planar point, it lies in a plane. Motions with infinitely many straight trajectories form a special subclass of those motions.
DOI : 10.21136/AM.1983.104000
Classification : 51N20
Keywords: Euclidean space motions; trajectories 
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Karger, Adolf. Euclidean space motions with affinely equivalent trajectories. Applications of Mathematics, Tome 28 (1983) no. 1, pp. 32-43. doi: 10.21136/AM.1983.104000

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