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Karger, Adolf
Similarity motions in $E_3$ with plane trajectories. (English). Aplikace matematiky, vol. 26 (1981), issue 3, pp. 194-201
MSC: 51N05, 53A17 | MR 0615606 | Zbl 0474.53008 | DOI: 10.21136/AM.1981.103911
Keywords:
Darboux motions; kinematics; similarity motions
Summary:
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).
References:
[1] W. Blaschke: Zur Kinematik. Abh. math. Sem. Univ. Hamburg 22 (1958), str. 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), str. 303-317. MR 0529518 | Zbl 0405.53004
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