A variational study on a natural Hamiltonian for curves

A variational study of finding critical points of the total squared torsion functional for curves in Euclidean3−spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves arecharacterized by two Euler−Lagrange equations in terms of curvature and torsion of a curve. To solve these balanceequations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved byquadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of thecritical curve and this curve is expressed by quadratures in a system of cylindrical coordinate. Finally, the problem isgeneralized to finding extremals of total squared torsion functional for nonnull curves in Minkowski 3−space.

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ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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