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MISKOLC MATHEMATICAL NOTES, vol.20, no.2, pp.1273-1283, 2019 (SCI-Expanded)
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 parallel to V(t) parallel to = constant when G Lie group is SO(3).