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http://dx.doi.org/10.5831/HMJ.2019.41.2.369

HYPERELASTIC LIE QUADRATICS  

Ozkan Tukel, Gozde (Isparta University of Applied Sciences)
Turhan, Tunahan (Isparta University of Applied Sciences)
Yucesan, Ahmet (Suleyman Demirel University)
Publication Information
Honam Mathematical Journal / v.41, no.2, 2019 , pp. 369-380 More about this Journal
Abstract
Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).
Keywords
Hyperelastic curve; Hyperelastic Lie quadratic; Lie group;
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