Kinematic geometry of regular motions in homogeneous space

Adolf Karger

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Kinematic geometry in $n$ -dimensional Euclidean and spherical space

Adolf Karger (1972)

Czechoslovak Mathematical Journal

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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...

3D-Darboux motions in 4-dimensional Euclidean space.

Karger, Adolf (1995)

Mathematica Pannonica

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The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

A. Hulanicki (1976)

Studia Mathematica

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3-parametric robot manipulator with intersecting axes

Jerzy Gądek (1995)

Applications of Mathematics

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A $p$ -parametric robot manipulator is a mapping $g$ of $ℝ^{p}$ into the homogeneous space $P = (C_{6} \times C_{6}) / Diag (C_{6} \times C_{6})$ represented by the formula $g (u_{1}, u_{2}, \dots, u_{p}) = exp (u_{1} X^{1}) \cdot \dots \cdot exp (u_{p} X^{p})$ , where $C_{6}$ is the Lie group of all congruences of $E_{3}$ and $X^{1}, X^{2}, \dots, X^{p}$ are fixed vectors from the Lie algebra of $C_{6}$ . In this paper the $3$ -parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University...

Displaying similar documents to “Kinematic geometry of regular motions in homogeneous space”

Kinematic geometry in n -dimensional Euclidean and spherical space

Two-parametric motions in E 3

3D-Darboux motions in 4-dimensional Euclidean space.

The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

3-parametric robot manipulator with intersecting axes

Kinematic geometry in $n$ -dimensional Euclidean and spherical space

Two-parametric motions in $E_{3}$