| Title:
|
Geometry of the rolling ellipsoid (English) |
| Author:
|
Krakowski, Krzysztof Andrzej |
| Author:
|
Silva Leite, Fátima |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
209-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two. (English) |
| Keyword:
|
ellipsoid |
| Keyword:
|
rolling maps |
| Keyword:
|
Gaussian curvature |
| Keyword:
|
geodesics |
| Keyword:
|
hypersurface |
| MSC:
|
35B06 |
| MSC:
|
53A05 |
| MSC:
|
53B21 |
| MSC:
|
58E10 |
| MSC:
|
70B10 |
| idZBL:
|
Zbl 1374.53033 |
| idMR:
|
MR3501158 |
| DOI:
|
10.14736/kyb-2016-2-0209 |
| . |
| Date available:
|
2016-07-17T12:01:19Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145771 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/146744 |
| . |
| Reference:
|
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