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Euclidean space motions; trajectories
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.
[1] W. Blaschke: Zur Kinematik. Abh. math. Sem. Univ. Hamburg, 22 (1958), 171 - 175. DOI 10.1007/BF02941949 | MR 0096388 | Zbl 0178.24302
[2] A. Karger: Darboux motions in $E_n$. Czech. Math. Journ. 29 (104) (1979), 303-317. MR 0529518 | Zbl 0405.53004
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