J. F. Marko and S. Neukirch, Competition between curls and plectonemes near the buckling transition of stretched supercoiled DNA, Phys. Rev. E, vol.85, issue.1, p.11908, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00667567

T. Mcmillen and P. Holmes, An elastic rod model for anguilliform swimming, J. Math. Biol, vol.53, issue.5, pp.843-886, 2006.

F. Corso, D. Misseroni, N. Pugno, A. Movchan, N. Movchan et al., Serpentine locomotion through elastic energy release, J. R. Soc. Interface, vol.14, issue.130, p.20170055, 2017.

V. G. Goss and R. Chaouki, Loading paths for an elastic rod in contact with a flat inclined surface, Int. J. Solids Struct, vol.88, pp.250-274, 2016.

L. N. Claverie, Y. Boubenec, G. Debrégeas, A. M. Prevost, and E. Wandersman, Whisker contact detection of rodents based on slow and fast mechanical inputs, Front. Behav. Neurosci, vol.10
URL : https://hal.archives-ouvertes.fr/hal-01464292

L. B. Kratchman, T. L. Bruns, J. J. Abbott, and R. J. Webster, Guiding elastic rods with a robot-manipulated magnet for medical applications, IEEE T. Robot, vol.33, issue.1, pp.227-233, 2017.

J. Fang and J. Chen, Deformation and vibration of a spatial elastica with fixed end slopes, Int. J. Solids Struct, vol.50, issue.5, pp.824-831, 2013.

S. Goyal, N. C. Perkins, and C. L. Lee, Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables, J. Comput. Phys, vol.209, issue.1, pp.371-389, 2005.

C. Pakleza and J. A. Cognet, Biopolymer Chain Elasticity: a novel concept and a least deformation energy principle predicts backbone 260 and overall folding of DNA TTT hairpins in agreement with NMR distances, Nucleic Acids Res, vol.31, issue.3, pp.1075-1085, 2003.

G. P. Santini, C. Pakleza, and J. A. Cognet, DNA tri-and tetra-loops and RNA tetra-loops hairpins fold as elastic biopolymer chains in agreement with PDB coordinates, Nucleic Acids Res, vol.31, issue.3, pp.1086-1096, 2003.

G. P. Santini, J. A. Cognet, D. Xu, K. K. Singarapu, C. Hervé et al., Nucleic acid folding determined by mesoscale modeling 265 and NMR spectroscopy: solution structure of d(GC GAAA GC), J. Phys. Chem. B, vol.113, issue.19, pp.6881-6893, 2009.

M. Baouendi, J. A. Cognet, C. S. Ferreira, S. Missailidis, J. Coutant et al., Hervé du Penhoat, Solution structure of a truncated anti-MUC1 DNA aptamer determined by mesoscale modeling and NMR, FEBS J, vol.279, issue.3, pp.479-490, 2012.

S. S. Antman, Nonlinear Problems of Elasticity, Applied Mathematical Sciences, 2005.

H. Tsuru, Equilibrium shapes and vibrations of thin elastic rod, J. Phys. Soc. Jpn, vol.56, issue.7, pp.2309-2324, 1987.

Y. Shi and J. E. Hearst, The Kirchhoff elastic rod, the nonlinear Schrödinger equation, and DNA supercoiling, J. Chem. Phys, vol.101, issue.6, pp.5186-5200, 1994.

I. Tobias, B. D. Coleman, and W. K. Olson, The dependence of DNA tertiary structure on end conditions: theory and implications for 275 topological transitions, J. Chem. Phys, vol.101, issue.12, pp.10990-10996, 1994.

J. Langer and D. A. Singer, Lagrangian aspects of the Kirchhoff elastic rod, SIAM Rev, vol.38, issue.4, pp.605-618, 1996.
DOI : 10.1137/s0036144593253290

D. J. Dichmann, Y. Li, and J. H. Maddocks, Hamiltonian formulations and symmetries in rod mechanics, Mathematical approaches to biomolecular structure and dynamics, pp.71-113, 1996.
DOI : 10.1007/978-1-4612-4066-2_6

M. Nizette and A. Goriely, Towards a classification of Euler-Kirchhoff filaments, J. Math. Phys, vol.40, issue.6, pp.2830-2866, 1999.
DOI : 10.1063/1.532731
URL : http://www.math.arizona.edu/~goriely/papers/JMP_kirck.pdf

J. H. Maddocks, R. S. Manning, R. C. Paffenroth, K. A. Rogers, and J. A. Warner, Interactive computation, parameter continuation, and visualization, Int. J. Bifurcat. Chaos, vol.7, issue.08, pp.1699-1715, 1997.
DOI : 10.1142/s0218127497001333

A. Balaeff, L. Mahadevan, and K. Schulten, Elastic rod model of a DNA loop in the Lac operon, Phys. Rev. Lett, vol.83, pp.4900-4903, 1999.

B. D. Coleman and D. Swigon, Theory of supercoiled elastic rings with self-contact and its application to DNA plasmids, J. Elasticity, vol.60, issue.3, pp.173-221, 2000.
DOI : 10.1103/physreve.61.759

G. H. Van-der-heijden, S. Neukirch, V. G. Goss, and J. Thompson, Instability and self-contact phenomena in the writhing of clamped rods, vol.45, pp.161-196, 2003.

M. E. Henderson and S. Neukirch, Classification of the spatial equilibria of the clamped elastica: numerical continuation of the solution set, Int. J. Bifurcat. Chaos, vol.14, issue.04, pp.1223-1239, 2004.

M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, and E. Grinspun, Discrete elastic rods, ACM T. Graphics, vol.27, p.63, 2008.
DOI : 10.1145/1508044.1508058

A. Lazarus, J. Miller, and P. Reis, Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method, p.295
URL : https://hal.archives-ouvertes.fr/hal-01447361

, J. Mech. Phys. Solids, vol.61, issue.8, pp.1712-1736, 2013.

R. S. Manning, A catalogue of stable equilibria of planar extensible or inextensible elastic rods for all possible Dirichlet boundary conditions, J. Elasticity, vol.115, issue.2, pp.105-130, 2014.

T. Bretl and Z. Mccarthy, Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations, Int. J. Robot Res, vol.33, issue.1, pp.48-68, 2014.

B. D. Coleman, I. Tobias, and D. Swigon, Theory of the influence of end conditions on self-contact in DNA loops, J. Chem. Phys, vol.103, issue.20, pp.9101-9109, 1995.

O. Ameline, S. Haliyo, X. Huang, and J. A. Cognet, Classifications of ideal 3D elastica shapes at equilibrium, J. Math. Phys, vol.58, issue.6, p.62902, 2017.

L. D. Landau, E. M. Lifshitz, A. M. Kosevich, and L. P. Pitaevski?, Theory of Elasticity, p.305

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, vol.12, 2002.

, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 2007.

C. Ridders, Accurate computation of F (x) and F (x)F (x), Adv. Eng. Softw, vol.4, issue.2, pp.75-76, 1982.

J. Bonnans, J. C. Gilbert, C. Lemaréchal, and C. A. Sagastizábal, Numerical optimization: theoretical and practical aspects, 2006.

Y. N. Dauphin, R. Pascanu, C. Gulcehre, K. Cho, S. Ganguli et al., Identifying and attacking the saddle point problem in high-dimensional non-convex optimization, Adv. Neur. In, pp.2933-2941, 2014.

R. Ge, F. Huang, C. Jin, and Y. Yuan, Escaping from saddle points-online stochastic gradient for tensor decomposition, pp.797-842, 2015.

M. A. Berger and C. Prior, The writhe of open and closed curves, J. Phys. A-Math. Gen, vol.39, issue.26, p.8321, 2006.

C. B. Prior and S. Neukirch, The extended polar writhe: a tool for open curves mechanics, J. Phys. A-Math. Gen, vol.49, issue.21, p.215201, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01228386