| Title:
|
Double points on characteristics (English) |
| Title:
|
Doppelpunkte auf Charakteristiken (German) |
| Author:
|
Röschel, Otto |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
5 |
| Year:
|
1995 |
| Pages:
|
381-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Double Points on Characteristics. A fixed surface $\Phi $ of a moving space $\Sigma $ will envelope a surface of the fixed space $\Sigma ^{\prime }$, if we move $\Sigma $ with respect to $\Sigma ^{\prime }$. In the general case at each moment of the one-parameter motion there exists a curve $c$ on $\Phi $, along which the position of $\Phi $ and the enveloped surface are in contact. In the paper we study the interesting special case, where $c$ has some double point $P\in \Phi $. This depends on relations between differential geometric properties in the neighbourhood of $P$ of the moved surface and the instantaneous motion of the one-parameter motion. These properties are characterized in this paper. Then some further kinematic results for the characterized motions are shown. (English) |
| Keyword:
|
kinematics |
| Keyword:
|
characteristics |
| Keyword:
|
enveloped surfaces |
| MSC:
|
53A17 |
| idZBL:
|
Zbl 0842.53008 |
| idMR:
|
MR1342367 |
| DOI:
|
10.21136/AM.1995.134301 |
| . |
| Date available:
|
2009-09-22T17:49:01Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134301 |
| . |
| Reference:
|
[1] O. Bottema, B. Roth: Theoretical Kinematics.North-Holland, Amsterdam, 1979. MR 0533960 |
| Reference:
|
[2] H. Brauner: Lehrbuch der Konstruktiven Geometrie.Springer, Wien-New York, 1986. Zbl 0581.51018, MR 0833284 |
| Reference:
|
[3] K.H. Hunt: Screw Systems in Spatial Kinematics.MMERS3, Dept. of Mech. Eng., Monash University, 1970. |
| Reference:
|
[4] A. Karger, J. Novák: Space Kinematics and Lie Groups.Gordon and Breach, New York, 1985. MR 0801394 |
| Reference:
|
[5] E. Kruppa: Analytische und konstruktive Differentialgeometrie.Springer, Wien, 1957. Zbl 0077.15401, MR 0086326 |
| Reference:
|
[6] O. Röschel: Drehflächen zweiter Ordnung durch einen Kegelschnitt.Studia Sci. Math. Hung. 29 (1994), 379–386. MR 1304891 |
| Reference:
|
[7] O. Röschel: Eine interessante Famile von Drehquadriken.Grazer Math. Ber. 313 (1991), 45–56. MR 1143619 |
| . |
