Timelike hyperelastic strips

Gözde Özkan Tükel; Tunahan Turhan; Gözde Özkan Tükel; Tunahan Turhan

doi:10.3934/math.2025557

AIMS Mathematics

2025, Volume 10, Issue 5: 12299-12311. doi: 10.3934/math.2025557

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Timelike hyperelastic strips

Gözde Özkan Tükel ^1,2,
Tunahan Turhan ^{3
,
,}

1.
Isparta University of Applied Sciences, Faculty of Technology, Department of Basic Sciences, Türkiye
2.
Süleyman Demirel University Graduate School Of Natural And Applied Sciences, Türkiye
3.
Süleyman Demirel University, Faculty of Education, Department of Division of Elementary Mathematics Education, Türkiye

Received: 18 March 2025 Revised: 18 April 2025 Accepted: 30 April 2025 Published: 27 May 2025
MSC : 53A04, 53A35, 53B30, 74B99

We explore certain extremals of the Sadowsky-type functional in Minkowski 3-space $ \mathbb{R}_{1}^{3} $. Focusing on timelike rectifying strips, we provide a detailed characterization of the hyperelastic configurations. Specifically, we introduce timelike hyperelastic strips as surfaces derived from the solution curves of the minimization of this variational problem. Our investigation extends to the timelike planar critical points of the modified Sadowsky-type functional, where we demonstrate that these correspond to timelike hyperelastic curves situated on a timelike plane. Our research on timelike hyperelastic strips not only uncovers the fundamental Euler-Lagrange equations governing these structures but also highlights the geometric conservation laws that dictate their behavior. By deriving conserved quantities specific to these strips, we formulate the first and second conservation laws. This allows us to present significant insights into how these strips behave under both translational and rotational symmetries. We anticipate that these findings will pave the way for future studies exploring novel types of hyperelastic surfaces and their broader applications in geometric and physical contexts, particularly in relation to de Sitter and pseudo-hyperbolic spaces.
- p-elastic strips,
- Sadowsky-type functional,
- timelike hyperelastic strips,
- variational calculus
Citation: Gözde Özkan Tükel, Tunahan Turhan. Timelike hyperelastic strips[J]. AIMS Mathematics, 2025, 10(5): 12299-12311. doi: 10.3934/math.2025557

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Abstract

We explore certain extremals of the Sadowsky-type functional in Minkowski 3-space $ \mathbb{R}_{1}^{3} $. Focusing on timelike rectifying strips, we provide a detailed characterization of the hyperelastic configurations. Specifically, we introduce timelike hyperelastic strips as surfaces derived from the solution curves of the minimization of this variational problem. Our investigation extends to the timelike planar critical points of the modified Sadowsky-type functional, where we demonstrate that these correspond to timelike hyperelastic curves situated on a timelike plane. Our research on timelike hyperelastic strips not only uncovers the fundamental Euler-Lagrange equations governing these structures but also highlights the geometric conservation laws that dictate their behavior. By deriving conserved quantities specific to these strips, we formulate the first and second conservation laws. This allows us to present significant insights into how these strips behave under both translational and rotational symmetries. We anticipate that these findings will pave the way for future studies exploring novel types of hyperelastic surfaces and their broader applications in geometric and physical contexts, particularly in relation to de Sitter and pseudo-hyperbolic spaces.

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