On the integral invariants of a closed ruled surface

1990 ◽  
Vol 39 (1-2) ◽  
pp. 80-91 ◽  
Author(s):  
Osman G�rsoy
Keyword(s):  
Ruled Surface ◽  
Integral Invariants

scholarly journals On the Integral Invariants of a Time-Like Ruled Surface

2001 ◽  
Vol 6 (2) ◽  
pp. 137-145 ◽  
Author(s):  
Emin Özyılmaz ◽  
Yusuf Yaylı
Keyword(s):  
Ruled Surface ◽  
Integral Invariants

On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings

2015 ◽  
Vol 08 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Mehmet Önder ◽  
H. Hüseyin Uğurlu
Keyword(s):  
Ruled Surface ◽  
Ruled Surfaces ◽  
Lorentzian Space ◽  
Integral Invariants ◽  
Timelike Ruled Surface ◽  
Spherical Images

In this paper, we give the characterizations for Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space [Formula: see text]. We obtain the relations between terms of their integral invariants and also we give new characterization for the Mannheim offsets of developable timelike ruled surface. Moreover, we find relations between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.

scholarly journals A new approach to design the ruled surface

2019 ◽  
Vol 16 (06) ◽  
pp. 1950093
Author(s):  
Ferhat Taş ◽  
Kazım İlarslan
Keyword(s):  
Unit Sphere ◽  
Ruled Surface ◽  
Geometric Design ◽  
Control Points ◽  
Computer Aided Geometric Design ◽  
New Approach ◽  
Transference Principle ◽  
Integral Invariants ◽  
Computer Aided ◽  
Novel Method

This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples and the motion interpolation was shown as an embodiment of this method.

scholarly journals The dual spatial quaternionic expression of ruled surfaces

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 403-411
Author(s):  
Abdussamet Caliskan ◽  
Süleyman Şenyurt
Keyword(s):  
Unit Sphere ◽  
Dual Space ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Integral Invariants ◽  
Dual Expression

In this paper, the ruled surface which corresponds to a curve on dual unit sphere is rederived with the help of dual spatial quaternions. We extend the term of dual expression of ruled surface using dual spatial quaternionic method. The correspondences in dual space of closed ruled surfaces are quaternionically expressed. As a consequence, the integral invariants of these surfaces and the relationships between these invariants are shown

scholarly journals The quaternionic expression of ruled surfaces

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5753-5766 ◽  
Author(s):  
Süleyman Şenyurt ◽  
Abdussamet Çalışkan
Keyword(s):  
Ruled Surface ◽  
Distribution Parameter ◽  
Ruled Surfaces ◽  
Integral Invariants

In this paper, firstly, the ruled surface is expressed as a spatial quaternionic. Also, the spatial quaternionic definitions of the Striction curve, the distribution parameter, angle of pitch and the pitch are given. Finally, integral invariants of the closed spatial quaternionic ruled surfaces drawn by the motion of the Frenet vectors {t,n1,n2} belonging to the spatial quaternionic curve ? are calculated.

Integral invariants in chemical kinetics

1991 ◽  
Vol 44 (2) ◽  
pp. 409-414
Author(s):  
L. Ropolyi ◽  
P. Réti
Keyword(s):  
Chemical Kinetics ◽  
Integral Invariants
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