• Corpus ID: 119318734

Equivalent elastica knots

  title={Equivalent elastica knots},
  author={Alain J. Brizard and David Pfefferl'e},
  journal={arXiv: Mathematical Physics},
The problem of an elastica knot in three-dimensional space is solved explicitly by expressing the Frenet-Serret curvature and torsion of the knot in terms of the Weierstrass and Jacobi elliptic functions. This solution is obtained by variational methods and is derived by minimizing of the squared-curvature energy integral. In the present work, an equivalency is established between pairs of Jacobi elliptic solutions that are described by the same values for curvature and torsion functionals. 



Lectures on Elastic Curves and Rods

These five lectures constitute a tutorial on the Euler elastica and the Kirchhoff elastic rod. We consider the classical variational problem in Euclidean space and its generalization to Riemannian

Elliptic Functions and Applications

1 Theta Functions.- 2 Jacobi's Elliptic Functions.- 3 Elliptic Integrals.- 4 Geometrical Applications.- 5 Physical Applications.- 6 Weierstrass's Elliptic Function.- 7 Applications of the Weierstrass

Notes on the Weierstrass Elliptic Function

A consistent notation for the Weierstrass elliptic function $\wp(z;g_{2},g_{3})$, for $g_{2} > 0$ and arbitrary values of $g_{3}$ and $\Delta \equiv g_{2}^{3} - 27 g_{3}^{2}$, is introduced based on

Jacobian Elliptic Functions sn‚ cn‚ dn

Weierstrass elliptic and modular functions


  • 20, 1
  • 1984