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

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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\"ocker },
     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/}
}
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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/