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.
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.
@article{10_21136_AM_1995_134301,
author = {R\"oschel, Otto},
title = {Double points on characteristics},
journal = {Applications of Mathematics},
pages = {381--390},
year = {1995},
volume = {40},
number = {5},
doi = {10.21136/AM.1995.134301},
mrnumber = {1342367},
zbl = {0842.53008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134301/}
}
TY - JOUR
AU - Röschel, Otto
TI - Double points on characteristics
JO - Applications of Mathematics
PY - 1995
SP - 381
EP - 390
VL - 40
IS - 5
UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134301/
DO - 10.21136/AM.1995.134301
LA - en
ID - 10_21136_AM_1995_134301
ER -
%0 Journal Article
%A Röschel, Otto
%T Double points on characteristics
%J Applications of Mathematics
%D 1995
%P 381-390
%V 40
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134301/
%R 10.21136/AM.1995.134301
%G en
%F 10_21136_AM_1995_134301
