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Russ. J. Math. Phys., 2012, Volume 19, Issue 2, Pages 234–243 (Mi rjmph13)  

Higher-order elastics and elastic hulls

Yu. S. Osipova, M. I. Zelikinb

a Presidium of the Russian Academy of Sciences, Moscow, Russia
b Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00293-a
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work was financially supported by the Russian Foundation for Basic Research (grant no. 10-01-00293-a) and also by the Program of the Presidium of the Russian Academy of Sciences “Mathematical Theory of Control.”


DOI: https://doi.org/10.1134/S1061920812020094

Full text: https:/.../S1061920812020094

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