caa a22 4500 46793942X CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7621-4 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7621-4 Noakes Lyle School of Mathematics and Statistics, The University of Western Australia, WA 6009, Nedlands, Perth, Australia aut Duality and Riemannian cubics [Elektronische Daten] [Lyle Noakes] Riemannian cubics are curves used for interpolation in Riemannian manifolds. Applications in trajectory planning for rigid bodiy motion emphasise the group SO(3) of rotations of Euclidean 3-space. It is known that a Riemannian cubic in a Lie group G with bi-invariant Riemannian metric defines a Lie quadratic V in the Lie algebra, and satisfies a linking equation. Results of the present paper include explicit solutions of the linking equation by quadrature in terms of the Lie quadratic, when G is SO(3) or SO(1,2). In some cases we are able to give examples where the Lie quadratic is also given in closed form. A basic tool for constructing solutions is a new duality theorem. Duality is also used to study asymptotics of differential equations of the form $\dot{x}(t)=(\beta_{0}+t\beta_{1})x(t)$ , where β0,β1 are skew-symmetric 3×3 matrices, and x :ℝ→ SO(3). This is done by showing that the dual of β0+tβ1 is a null Lie quadratic. Then results on asymptotics of x follow from known properties of null Lie quadratics. Springer, 2006 ? nationallicence Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 195-209 1019-7168 25:1-3<195 2006 25 10444 https://doi.org/10.1007/s10444-004-7621-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7621-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Noakes Lyle School of Mathematics and Statistics, The University of Western Australia, WA 6009, Nedlands, Perth, Australia aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 195-209 1019-7168 25:1-3<195 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer