Geodesic
The Darboux theorem on plane trajectories of two-parametric space motions
Applications of Mathematics, Tome 33 (1988) no. 6, pp. 417-442
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The paper contains the proof of the classification theorem for two-parametric space motions with at least 5 points with plane trajectories. The proof is based on [1] and on the cannonical form of a certain tensor of order 3. The second part of the paper deals with the problem of plane trajectories from the differential-geometrical point of view. Some applications are given.
The paper contains the proof of the classification theorem for two-parametric space motions with at least 5 points with plane trajectories. The proof is based on [1] and on the cannonical form of a certain tensor of order 3. The second part of the paper deals with the problem of plane trajectories from the differential-geometrical point of view. Some applications are given.
DOI : 10.21136/AM.1988.104322
Classification : 53A17
Keywords: two parametric space motions; Darboux-theorem; kinematics geometry 
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Karger, Adolf. The Darboux theorem on plane trajectories of two-parametric space motions. Applications of Mathematics, Tome 33 (1988) no. 6, pp. 417-442. doi: 10.21136/AM.1988.104322

[1] G. Koenigs: Leçons de Cinématique. Paris 1897, Note III by G. Darboux: Sur les mouvements algébriques.

[2] W. Blaschke: Kinematik und Quaternionen. Berlin 1960. | MR | Zbl

[3] A. Karger: Two-parametric motions in $E_3$. Apl. mat. 32 (1987), 96-119. | MR

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