MMN-2900

Generalized elastica in SO(3)

Gözde Özkan Tükel; Tunahan Turhan; Ahmet Yücesan;

Abstract

In a Lie group $G$ equipped with bi-invariant Riemannian metric, we characterize the generalized elastica by an Euler-Lagrange equation in terms of the Lie reduction V of a curve gamma in G. We define a generalized elastic Lie quadratic in the Lie algebra of G. For a generalized elastic Lie quadratic, we construct the Lax equation that is crucial to the solution of a generalized elastica with regard to its generalized elastic Lie quadratic. Then we solve this equation for a null generalized elastic Lie quadratic with $\left\Vert \dot{V}%\right\Vert=$ constant when G Lie group is SO(3).


Vol. 20 (2019), No. 2, pp. 1273-1283
DOI: 10.18514/MMN.2019.2900


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