Displaying similar documents to “Properties of space motions with two straight trajectories”

Euclidean space motions with affinely equivalent trajectories

Adolf Karger (1983)

Aplikace matematiky

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The author studies the Euclidean space motions with the property that the trajectory of every point is an affine image of a given space curve. Such motions split into plane motions and translations and their trajectories are cylindrical curves. They are characterized as motions with the following property: Not all trajectories are plane curves and if any trajectory has a planar point, it lies in a plane. Motions with infinitely many straight trajectories form a special subclass of those...

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.