Vol.3, No 11, 2001 pp.135-148
UDC 514.772.35
CHANGE OF
GEOMETRIC MAGNITUDES
UNDER INFINITESIMAL
BENDING
Ljubica S. Velimirović
Faculty of Science, Department of Mathematics, University of Niš
Ćirila i Metodija 2, 18000 Niš, Yugoslavia
E-mail: vljubica@archimed.filfak.ni.ac.yu
Abstract. In this paper variations
of some geometric magnitudes under infinitesimal bending are studied. Infinitesimal
bending of a curve is considered and infinitesimal bending field is determined.
Specially, the infinitesimal bending field that plane curve includes in
a family of plane curves is given. It is also proved that the area of the
region in the plane bounded by a closed curve is stationary under the infinitesimal
bending of a curve remaining plane. The variation of the volume bounded
by rotational surface, under infinitesimal bending of the meridian, remaining
closed plane curve, is given.
Key words: Infinitesimal
bending, curve, infinitesimal bending of meridian, variation, area, volume.
PROMENA GEOMETRIJSKIH
VELIČINA
PRI BESKONAČNO
MALOM SAVIJANJU
U ovom radu se razmatraju varijacije nekih geometrijskih veličina pri beskonačno
malom savijanju. Beskonačno malo savijanje krive se razmatra i odredjuje
se polje beskonačno malog savijanja. Specijalno, dato je polje savijanja
koje ravnu krivu uključuje u familiju ravnih krivih. Dokazuje se da je
površina oblasti u ravni ograničena zatvorenom krivom stacionarna pri beskonačno
malom savijanju krive koja ostaje u ravni. Odredjena je varijacija zapremine
ograničena rotacionom površi, pri beskonačno malom savijanju meridijana,
koja ostaje u ravni.
