Geodesic
Similarity motions in $E_3$ with plane trajectories
Applications of Mathematics, Tome 26 (1981) no. 3, pp. 194-201
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In this paper the author finds and describes all similarity space motions, which have only plane trajectories of points. All such motions are explicitly expressed. They are of 5 types, all of them cylindrical. Trajectories are conic sections (3 types) or arbitrary plane curves (2 types).
In this paper the author finds and describes all similarity space motions, which have only plane trajectories of points. All such motions are explicitly expressed. They are of 5 types, all of them cylindrical. Trajectories are conic sections (3 types) or arbitrary plane curves (2 types).
DOI : 10.21136/AM.1981.103911
Classification : 51N05, 53A17
Keywords: Darboux motions; kinematics; similarity motions 
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Karger, Adolf. Similarity motions in $E_3$ with plane trajectories. Applications of Mathematics, Tome 26 (1981) no. 3, pp. 194-201. doi: 10.21136/AM.1981.103911

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

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

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