Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Lie group; Lie algebra; dual space; twist; wrench; cohomology
Lie group; Lie algebra; dual space; twist; wrench; cohomology
Summary:
The external derivative $d$ on differential manifolds inspires graded operators on complexes of spaces $\Lambda ^rg^\ast $, $\Lambda ^rg^\ast \otimes g$, $\Lambda ^rg^\ast \otimes g^\ast $ stated by $g^\ast $ dual to a Lie algebra $g$. Cohomological properties of these operators are studied in the case of the Lie algebra $g=se( 3 )$ of the Lie group of Euclidean motions.
References:
[1] Bakša, J.: Three-parametric robot manipulators with parallel rotational axes. Appl. Math., Praha 52 (2007), 303-319. DOI 10.1007/s10492-007-0016-3 | MR 2324729 | Zbl 1164.53310
[2] Chevallier, D. P.: On the foundations of ordinary and generalized rigid body dynamics and the principle of objectivity. Arch. Mech. 56 (2004), 313-353. MR 2088029 | Zbl 1076.70002
[3] Dekrét, A., Bakša, J.: Applications of line objects in robotics. Acta Univ. M. Belii, Ser. Mat. 9 (2001), 29-42. MR 1935681 | Zbl 1046.70004
[4] Fecko, M.: Differential Geometry and Lie Groups for Physicists. Cambridge University Press (2006). MR 2260667 | Zbl 1121.53001
[5] Hao, K.: Dual number method, rank of a screw system and generation of Lie subalgebras. Mech. Mach. Theory 33 (1998), 1063-1084. DOI 10.1016/S0094-114X(97)00121-3 | MR 1653349
[6] Karger, A.: Robot-manipulators as submanifolds. Math. Pannonica 4 (1993), 235-247. MR 1258929 | Zbl 0793.53011
[7] Karger, A.: Classification of three-parametric spatial motions with a transitive group of automorphisms and three-parametric robot manipulators. Acta Appl. Math. 18 (1990), 1-16. DOI 10.1007/BF00822203 | MR 1047292 | Zbl 0699.53013
[8] Lerbet, J.: Some explicit relations in kinematics of mechanisms. Mech. Res. Commun. 27 (2000), 621-630. DOI 10.1016/S0093-6413(00)00138-5 | MR 1808551 | Zbl 0987.70002
[9] Selig, J.: Geometrical Methods in Robotics. Springer, New York (1996). MR 1411680 | Zbl 0861.93001
Search
Partner of
