On the Torsional Energy of Deformed Curves and Knots
This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by v...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-09-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/10/661 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850205997318012928 |
|---|---|
| author | Svetozar R. Rančić Ljubica S. Velimirović Marija S. Najdanović |
| author_facet | Svetozar R. Rančić Ljubica S. Velimirović Marija S. Najdanović |
| author_sort | Svetozar R. Rančić |
| collection | DOAJ |
| description | This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool. |
| format | Article |
| id | doaj-art-ea177ea2e6924fc5af46effe52dc9bae |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-ea177ea2e6924fc5af46effe52dc9bae2025-08-20T02:10:57ZengMDPI AGAxioms2075-16802024-09-01131066110.3390/axioms13100661On the Torsional Energy of Deformed Curves and KnotsSvetozar R. Rančić0Ljubica S. Velimirović1Marija S. Najdanović2Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, SerbiaFaculty of Sciences and Mathematics, University of Niš, 18000 Niš, SerbiaFaculty of Sciences and Mathematics, University of Priština in Kosovska Mitrovica, 38220 Kosovska Mitrovica, SerbiaThis paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool.https://www.mdpi.com/2075-1680/13/10/661second-order infinitesimal bendingfirst variationsecond variationtorsional energycurveknot |
| spellingShingle | Svetozar R. Rančić Ljubica S. Velimirović Marija S. Najdanović On the Torsional Energy of Deformed Curves and Knots Axioms second-order infinitesimal bending first variation second variation torsional energy curve knot |
| title | On the Torsional Energy of Deformed Curves and Knots |
| title_full | On the Torsional Energy of Deformed Curves and Knots |
| title_fullStr | On the Torsional Energy of Deformed Curves and Knots |
| title_full_unstemmed | On the Torsional Energy of Deformed Curves and Knots |
| title_short | On the Torsional Energy of Deformed Curves and Knots |
| title_sort | on the torsional energy of deformed curves and knots |
| topic | second-order infinitesimal bending first variation second variation torsional energy curve knot |
| url | https://www.mdpi.com/2075-1680/13/10/661 |
| work_keys_str_mv | AT svetozarrrancic onthetorsionalenergyofdeformedcurvesandknots AT ljubicasvelimirovic onthetorsionalenergyofdeformedcurvesandknots AT marijasnajdanovic onthetorsionalenergyofdeformedcurvesandknots |