3D-Darboux motions in 4-dimensional Euclidean space.
Karger, Adolf (1995)
Mathematica Pannonica
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3D-Darboux motions in 4-dimensional Euclidean space.
Kinematic geometry in -dimensional Euclidean and spherical space
Adolf Karger (1972)
Czechoslovak Mathematical Journal
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The Euclidean plane kinematics
El Said El Shinnawy (1979)
Aplikace matematiky
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Restricting his considerations to the Euclidean plane, the author shows a method leading to the solution of the equivalence problem for all Lie groups of motions. Further, he presents all transitive one-parametric system of motions in the Euclidean plane.
The Darboux theorem on plane trajectories of two-parametric space motions
Adolf Karger (1988)
Aplikace matematiky
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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.