| Title:
|
Two-parametric motions in $E_3$ (English) |
| Author:
|
Karger, Adolf |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1987 |
| Pages:
|
96-119 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the local differential geometry of two-parametric motions in the Euclidean space. The first part of the paper contains contemporary formulation of classical results in this area together with the connection to the elliptical differential geometry. The remaining part contains applications. Necessary and sufficient conditions for splitting of a two-parametric motion into a product of two one-parametric motions, characterization of motions with constant invariants and some others. The case of rolling of two isometric surfaces is treated in detail. (English) |
| Keyword:
|
kinematics |
| Keyword:
|
two-parametric motions |
| Keyword:
|
rolling of two isometric surfaces |
| Keyword:
|
differential geometry |
| Keyword:
|
Lie groups and Lie algebras |
| MSC:
|
53A17 |
| idZBL:
|
Zbl 0621.53010 |
| idMR:
|
MR0885757 |
| DOI:
|
10.21136/AM.1987.104240 |
| . |
| Date available:
|
2008-05-20T18:31:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104240 |
| . |
| Reference:
|
[1] W. Blaschke: Nicht-Euklidische Geometrie und Mechanik.Hamb. Math. Einzelschriften 34. Heft, (1942). Zbl 0027.13304, MR 0009861 |
| Reference:
|
[2] O. Bottema: Instantaneous kinematics for spatial two-parameter motion.Proceedings of Koninkl. Nedérl. Akad. van Wettenschappen - Amsterdam, Series B, 74, No. 1, (1971). Zbl 0208.24302, MR 0281104 |
| Reference:
|
[3] O. Kowalski: The invariant classification of 3-dim. linear subspaces of infinitesimal isometrics of $E_3$.Comm. Math. Univ. Car. 8 (1967), No. 4, 635-649. MR 0228629 |
| Reference:
|
[4] O. Kowalski: Orbits of transformation groups on certain Grasmann manifiolds.Czech. Math. Journ. 18 (93) (1968), 144-177 and 240-273. MR 0231939 |
| Reference:
|
[5] H. R. Müller: Sphärische Kinematik.Berlin 1962. MR 0145715 |
| Reference:
|
[6] A. Schoenflies M. Grübler: Kinematik.Encyklopädie der Mathematischen Wissenschaften, Band 4 (I), Heft 2, 3, Leipzig 1902. |
| . |
