Double points on characteristics
Applications of Mathematics (1995)
- Volume: 40, Issue: 5, page 381-390
- ISSN: 0862-7940
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topRöschel, Otto. "Double points on characteristics." Applications of Mathematics 40.5 (1995): 381-390. <http://eudml.org/doc/32926>.
@article{Röschel1995,
abstract = {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.},
author = {Röschel, Otto},
journal = {Applications of Mathematics},
keywords = {kinematics; characteristics; enveloped surfaces; kinematics; characteristics; enveloping surfaces},
language = {eng},
number = {5},
pages = {381-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Double points on characteristics},
url = {http://eudml.org/doc/32926},
volume = {40},
year = {1995},
}
TY - JOUR
AU - Röschel, Otto
TI - Double points on characteristics
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 5
SP - 381
EP - 390
AB - 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.
LA - eng
KW - kinematics; characteristics; enveloped surfaces; kinematics; characteristics; enveloping surfaces
UR - http://eudml.org/doc/32926
ER -
References
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- Analytische und konstruktive Differentialgeometrie, Springer, Wien, 1957. (1957) Zbl0077.15401MR0086326
- Drehflächen zweiter Ordnung durch einen Kegelschnitt, Studia Sci. Math. Hung. 29 (1994), 379–386. (1994) MR1304891
- Eine interessante Famile von Drehquadriken, Grazer Math. Ber. 313 (1991), 45–56. (1991) MR1143619
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