Alternative View of Inextensible Flows of Curves and Ruled Surfaces via Alternative Frame

Ana Savić, Kemal Eren, Soley Ersoy () and Vladimir Baltić
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Ana Savić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Kemal Eren: Sakarya University Technology Developing Zones Manager Company, 54050 Sakarya, Turkey
Soley Ersoy: Department of Mathematics, Faculty of Sciences, Sakarya University, 54050 Sakarya, Turkey
Vladimir Baltić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia

Mathematics, 2024, vol. 12, issue 13, 1-16

Abstract: In this paper, we present the evolutions of ruled surfaces generated by the principal normal, the principal normal’s derivative, and the Darboux vector fields along a space curve that are the elements of an alternative frame. The comprehension of an object’s rotational behavior is crucial knowledge relevant to various realms, and this can be accomplished by analyzing the Darboux vector along the path of a point on the object as it moves through space. In that regard, examining the evolutions of the ruled surfaces based on the changes in their directrices, including the Darboux vector in the alternative frame along a space curve, is significant. As the first step of this study, we express the evolution of the alternative frame elements of a space curve. Subsequently, the conditions for the ruled surfaces generated by them to be minimal, developable, and inextensible are investigated. These findings can allow some physical phenomena to be well understood through surface evolutions satisfying these conditions. In the final step, we provide graphical representations of some examples of inextensible ruled surfaces and curve evolutions.

Keywords: ruled surface; alternative frame; evolution of curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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