| Title:
|
On some cohomological properties of the Lie algebra of Euclidean motions (English) |
| Author:
|
Bakšová, Marta |
| Author:
|
Dekrét, Anton |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
337-348 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Lie group |
| Keyword:
|
Lie algebra |
| Keyword:
|
dual space |
| Keyword:
|
twist |
| Keyword:
|
wrench |
| Keyword:
|
cohomology |
| MSC:
|
22E60 |
| MSC:
|
22E70 |
| MSC:
|
70B15 |
| idZBL:
|
Zbl 1212.70005 |
| idMR:
|
MR2597229 |
| DOI:
|
10.21136/MB.2009.140665 |
| . |
| Date available:
|
2010-07-20T18:07:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140665 |
| . |
| Reference:
|
[1] Bakša, J.: Three-parametric robot manipulators with parallel rotational axes.Appl. Math., Praha 52 (2007), 303-319. Zbl 1164.53310, MR 2324729, 10.1007/s10492-007-0016-3 |
| Reference:
|
[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. Zbl 1076.70002, MR 2088029 |
| Reference:
|
[3] Dekrét, A., Bakša, J.: Applications of line objects in robotics.Acta Univ. M. Belii, Ser. Mat. 9 (2001), 29-42. Zbl 1046.70004, MR 1935681 |
| Reference:
|
[4] Fecko, M.: Differential Geometry and Lie Groups for Physicists.Cambridge University Press (2006). Zbl 1121.53001, MR 2260667 |
| Reference:
|
[5] Hao, K.: Dual number method, rank of a screw system and generation of Lie subalgebras.Mech. Mach. Theory 33 (1998), 1063-1084. MR 1653349, 10.1016/S0094-114X(97)00121-3 |
| Reference:
|
[6] Karger, A.: Robot-manipulators as submanifolds.Math. Pannonica 4 (1993), 235-247. Zbl 0793.53011, MR 1258929 |
| Reference:
|
[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. Zbl 0699.53013, MR 1047292, 10.1007/BF00822203 |
| Reference:
|
[8] Lerbet, J.: Some explicit relations in kinematics of mechanisms.Mech. Res. Commun. 27 (2000), 621-630. Zbl 0987.70002, MR 1808551, 10.1016/S0093-6413(00)00138-5 |
| Reference:
|
[9] Selig, J.: Geometrical Methods in Robotics.Springer, New York (1996). Zbl 0861.93001, MR 1411680 |
| . |
