Second order infinitesimal bending of curves
Keyword(s):
We investigate a second order infinitesimal bending of curves in a three-dimensional Euclidean space in this paper. We give the necessary and sufficient conditions for the vector fields to be infinitesimal bending fields of the corresponding order, as well as explicit formulas which determine these fields. We examine the first and the second variation of some geometric magnitudes which describe a curve, specially a change of the curvature. Two illustrative examples (a circle and a helix) are studied not only analytically but also by drawing curves using computer program Mathematica.
2007 ◽
Vol 463
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pp. 1199-1210
2016 ◽
Vol 13
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pp. 1550132
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2019 ◽
Vol 28
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pp. 1950005
Keyword(s):
2021 ◽
Vol 62
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pp. 53-66
2017 ◽
Vol 4(62)
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pp. 9-16
2021 ◽
Vol 27
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pp. 15
1993 ◽
Vol 45
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pp. 183-192
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