Towards a classification of Euler-Kirchhoff filaments
نویسندگان
چکیده
Euler-Kirchhoff filaments are solutions of the static Kirchhoff equations for elastic rods with circular cross-sections. These equations are known to be formally equivalent to the Euler equations for spinning tops. This equivalence is used to provide a classification of the different shapes a filament can assume. Explicit formulas for the different possible configurations and specific results for interesting particular cases are given. In particular, conditions for which the filament has points of self-intersection, self-tangency, vanishing curvature or when it is closed or localized in space are provided. The average properties of generic filaments are also studied. They are shown to be equivalent to helical filaments on long length scales.
منابع مشابه
Resonant helical deformations in nonhomogeneous Kirchhoff filaments
We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young’s modulus. This type of variation may occur in long tandemly repeated sequences of DNA. We analyse the effects of the Young’s modulus frequence and amplitude of oscillation in the stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. O...
متن کاملVariational principles for spin systems and the Kirchhoff rod
We obtain the affine Euler-Poincaré equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff’s rod, where they provide a unified geometric interpretation.
متن کاملSpontaneous curvature-induced dynamical instability of Kirchhoff filaments: Application to DNA kink deformations
The Kirchhoff elastic theory of thin filaments with spontaneous curvature is employed in the understanding of the onset of the kink transitions observed in short DNA rings. Dynamical analysis shows that when its actual curvature is less than some threshold value determined by the spontaneous curvature, a circular DNA will begin to buckle to other shapes. The observable and the dominant deformat...
متن کاملComputing the additive degree-Kirchhoff index with the Laplacian matrix
For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.
متن کاملOn nonlocal elliptic system of $p$-Kirchhoff-type in $mathbb{R}^N$
Using Nehari manifold methods and Mountain pass theorem, the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.
متن کامل