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.
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

[1] W. Blaschke: Zur Kinematik. Abh. math. Sem. Univ. Hamburg, 22 (1958), 171 - 175. | DOI | MR | Zbl

[2] A. Karger: Darboux motions in $E_n$. Czech. Math. Journ. 29 (104) (1979), 303-317. | MR | Zbl

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