Displaying similar documents to “Affine Darboux motions”

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...

Similarity motions in E 3 with plane trajectories

Adolf Karger (1981)

Aplikace matematiky

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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).