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two parametric space motions; Darboux-theorem; kinematics geometry
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.
[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 0119471 | Zbl 0098.34701
[3] A. Karger: Two-parametric motions in $E_3$. Apl. mat. 32 (1987), 96-119. MR 0885757
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