Geodesic
Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 19-31
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We study an isomorphism between the group of rigid body displacements and the group of dual quaternions modulo the dual number multiplicative group from the viewpoint of differential geometry in a projective space over the dual numbers. Some seemingly weird phenomena in this space have lucid kinematic interpretations. An example is the existence of non-straight curves with a continuum of osculating tangents which correspond to motions in a cylinder group with osculating vertical Darboux motions. We also suggest geometrically meaningful ways to select osculating conics of a curve in this projective space and illustrate their corresponding motions. Furthermore, we investigate factorizability of these special motions and use the obtained results for the construction of overconstrained linkages.
Classification : 16S36, 53A20, 70B10
Mots-clés : Rational motion, motion polynomial, factorization, vertical Darboux motion, helical motion, osculating line, osculating conic, null cone motion, linkage 
@article{JGG_2021_25_1_JGG_2021_25_1_a1,
     author = {J. Siegele and M. Pfurner and H.-P. Schr\~A{\textparagraph}cker},
     title = {Space {Kinematics} and {Projective} {Differential} {Geometry} {Over} the {Ring} of {Dual} {Numbers}},
     journal = {Journal for geometry and graphics},
     pages = {19--31},
     year = {2021},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a1/}
}
TY  - JOUR
AU  - J. Siegele
AU  - M. Pfurner
AU  - H.-P. Schröcker
TI  - Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
JO  - Journal for geometry and graphics
PY  - 2021
SP  - 19
EP  - 31
VL  - 25
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a1/
ID  - JGG_2021_25_1_JGG_2021_25_1_a1
ER  - 
%0 Journal Article
%A J. Siegele
%A M. Pfurner
%A H.-P. Schröcker
%T Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers
%J Journal for geometry and graphics
%D 2021
%P 19-31
%V 25
%N 1
%U http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a1/
%F JGG_2021_25_1_JGG_2021_25_1_a1
J. Siegele; M. Pfurner; H.-P. Schröcker. Space Kinematics and Projective Differential Geometry Over the Ring of Dual Numbers. Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 19-31. http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a1/