Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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HYPERELASTIC LIE QUADRATICS

  • Received : 2018.10.25
  • Accepted : 2019.05.05
  • Published : 2019.06.25
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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).

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References

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