an:06262430
Zbl 1283.49061
Osipov, Yu. S.; Zelikin, M. I.
Higher-order elastics and elastic hulls
EN
Russ. J. Math. Phys. 19, No. 2, 234-243 (2012).
00303067
2012
j
49Q20
integral minimization; quadratic forms; multidimensional curves; curvature; torsion
Summary: By higher-order elastics we mean solutions of the problem to minimize integrals of quadratic forms of curvatures of multidimensional curves. Differential equations of second-order elastics (minimizing a quadratic form of the curvature and torsion of the curve) are obtained. Surfaces minimizing integrals of the squared Gaussian curvature are found.