an:02074205
Zbl 1046.70004
Dekr??t, Anton; Bak??a, J??n
Applications of line objects in robotics
EN
Acta Univ. M. Belii, Ser. Math. 9, 29-42 (2001).
00079423
2001
j
70B15 70G65 22E70
Lie algebra; Lie group; Euclidean motions; Klein form
Summary: The Lie algebra of Lie group of Euclidean motions in \(E_3\) is represented as the vector space \(A_6\) of couples of vectors in \(E_3\). We describe all subalgebras and all 3-dimensional subspaces of \(A_6\) which are orthogonal to themselves according to the Klein form, and give their kinematic interpretations. Vector fields in \(E_3\) determined by elements of \(A_6\) and their kinematic and dynamic interpretations are investigated.