Displaying similar documents to “The Euclidean plane kinematics”

Two-parametric motions in E 3

Adolf Karger (1987)

Aplikace matematiky

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The paper deals with the local differential geometry of two-parametric motions in the Euclidean space. The first part of the paper contains contemporary formulation of classical results in this area together with the connection to the elliptical differential geometry. The remaining part contains applications. Necessary and sufficient conditions for splitting of a two-parametric motion into a product of two one-parametric motions, characterization of motions with constant invariants and...

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...