Publications:

• G.H.M. van der Heijden, Bifurcation and chaos in drillstring dynamics, Chaos, Solitons & Fractals 3, 219-247 (1993). [Full paper] [Abstract]
• G.H.M. van der Heijden, Resonant responses and chaos in nonlinear drillstring dynamics, in Proc. of the Seventh European Conference on Mathematics in Industry, 2-6 March 1993, Montecatini Terme, Italy, A. Fasano, M. Primicerio (eds) (Teubner, Stuttgart, 1994), pp. 347-354 (download preprint, 861 K).
• G.H.M. van der Heijden, Mode-locking in nonlinear rotordynamics, J. Nonlinear Sci. 5, 257-283 (1995). [Full paper] [Abstract]
• G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, Homoclinic bifurcation and localised torsional buckling of elastic rods, in Proc. of the IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems, 21-26 April 1996, Eindhoven, The Netherlands, D.H. van Campen (ed.), Solid Mechanics and its Applications, Vol. 52 (Kluwer, Dordrecht, 1997), pp. 143-150. [Volume]
• A.R. Champneys, G.H.M. van der Heijden, J.M.T. Thompson, Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature, Phil. Trans. R. Soc. Lond. A 355, 2151-2174 (1997). [Full paper] [Abstract]
• G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, The spatial complexity of localised buckling in rods with non-circular cross-section, SIAM J. Appl. Math. 59, 198-221 (1999). [Full paper] [Abstract]
• G.H.M. van der Heijden, J.M.T. Thompson, Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods, Physica D 112, 201-224 (1998). [Full paper] [Abstract]
• J.M.T. Thompson, G.H.M. van der Heijden, Homoclinic orbits, spatial chaos and localized buckling, in Proc. of the IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics, 27 July - 1 August 1997, Cornell University, Ithaca, New York, USA, F.C. Moon (ed.), Solid Mechanics and its Applications, Vol. 63 (Kluwer, Dordrecht, 1999), pp. 127-138. [Volume]
• J.M.T. Thompson, G.H.M. van der Heijden, A.R. Champneys, Twisting, writhing and buckling of pipelines, Proceedings of the 21st annual Offshore Pipeline Technology Conference (OPT '98), 23-24 February 1998, The Holmenkollen Park Hotel Rica, Oslo, Norway (IBC UK Conferences, London, 1998).
• G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, Spatially complex localisation in twisted elastic rods constrained to lie in the plane, J. Mech. Phys. Solids 47, 59-79 (1999).
[Full paper] [Abstract]
• G.H.M. van der Heijden, J.M.T. Thompson, Helical and localised buckling in twisted rods: a unified analysis of the symmetric case, Nonlinear Dynamics 21, 71-99 (2000). [Full paper] [Abstract]
• G.H.M. van der Heijden, Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: the zipper, Dynamics and Stability of Systems (now Dynamical Systems) 15, 159-183 (2000) [Full paper] (download preprint, 1137 K). [Abstract]
• D.M. Stump, G.H.M. van der Heijden, Matched asymptotic expansions for bent and twisted rods: applications for cable and pipeline laying, J. Eng. Math. 38, 13-31 (2000). [Full paper] [Abstract]
• D.M. Stump, A.R. Champneys, G.H.M. van der Heijden, The torsional buckling and writhing of a simply supported rod hanging under gravity, Int. J. Solids and Struct. 38, 795-813 (2001). [Full paper] [Abstract]
• G.H.M. van der Heijden, The static deformation of a twisted elastic rod constrained to lie on a cylinder, Proc. R. Soc. Lond. A 457, 695-715 (2001). [Full paper] [Abstract]
• D.M. Stump, G.H.M. van der Heijden, Birdcaging and the collapse of rods and cables in fixed-grip compression, Int. J. Solids Struct. 38, 4265-4278 (2001). [Full paper] [Abstract]
• S. Neukirch, J.M.T. Thompson, G.H.M. van der Heijden, Filaments enroulés en paires torsadées: application aux plasmides d'A.D.N., in Compte-rendus de la 4ème Rencontre du Non Linéaire, 15-16 March 2001, Institut Henri Poincaré, Paris, Y. Pomeau, R. Ribotta (eds) (Non Linéaire Publications, Orsay, 2001), pp. 189-194 (download PDF file, 341 K).
• G.H.M. van der Heijden, J.M.T. Thompson, The chaotic instability of a slowly spinning asymmetric top, Mathematical and Computer Modelling 36, 359-369 (2002) (download preprint, 954 K). [Full paper] [Abstract]
• G.H.M. van der Heijden, A.R. Champneys, J.M.T. Thompson, Spatially complex localisation in twisted elastic rods constrained to a cylinder, Int. J. Solids Struct. 39, 1863-1883 (2002). [Full paper] [Abstract]
• J.M.T. Thompson, G.H.M. van der Heijden, S. Neukirch, Supercoiling of DNA plasmids: mechanics of the generalized ply, Proc. R. Soc. Lond. A 458, 959-985 (2002). [Full paper] [Abstract]
• S. Neukirch, G.H.M. van der Heijden, J.M.T. Thompson, Writhing instabilities of twisted rods: from infinite to finite length, J. Mech. Phys. Solids 50, 1175-1191 (2002). [Full paper] [Abstract]
• S. Neukirch, G.H.M. van der Heijden, La triple hélice: vers une mécanique du collagène, in Compte-rendus de la 5ème Rencontre du Non Linéaire, 14-15 March 2002, Institut Henri Poincaré, Paris, Y. Pomeau, R. Ribotta (eds) (Non Linéaire Publications, Orsay, 2002), pp. 183-188 (download PDF file, 746 K).
• S. Neukirch, G.H.M. van der Heijden, Geometry and mechanics of uniform n-plies: from engineering ropes to biological filaments, Journal of Elasticity 69, 41-72 (2002) (download preprint, 1737 K). [Full paper] [Abstract]
• G.H.M. van der Heijden, W.B. Fraser, Helical collapse of a whirling elastic rod forced to lie on a cylinder, ASME J. Appl. Mech. 70, 771-774 (2003) [Full paper] (download PDF file of expanded preprint, 620 K). [Abstract]
• G.H.M. van der Heijden, J.M.T. Thompson, S. Neukirch, A variational approach to loaded ply structures, Journal of Vibration and Control 9, 175-185 (2003) (download preprint, 1024 K). [Full paper] [Abstract]
• G.H.M. van der Heijden, S. Neukirch, V.G.A. Goss, J.M.T. Thompson, Instability and self-contact phenomena in the writhing of clamped rods, Int. J. Mech. Sciences 45, 161-196 (2003) (download preprint, 1838 K). [Full paper] [Abstract]
• G.H.M. van der Heijden, A robust variational formulation for a rod subject to inequality constraints: a simple model for a drill string, in Complementarity, Duality and Symmetry in Nonlinear Mechanics: Proceedings of the IUTAM Symposium, D.Y. Gao (ed.), Advances in Mechanics and Mathematics, Vol. 6 (Kluwer, Dordrecht, 2004), pp. 313-325. [Volume]
• G.H.M. van der Heijden, J.M.T. Thompson, Patterns of bifurcation suppressing escape at internal resonance, in Proc. of the IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, 8-13 June 2003, Rome, Italy, G. Rega, F. Vestroni (eds), Solid Mechanics and its Applications, Vol. 122 (Springer, Dordrecht, 2005), pp. 69-78. [Full paper]
• V.G.A. Goss, G.H.M. van der Heijden, J.M.T. Thompson, S. Neukirch, Experiments on snap buckling, hysteresis and loop formation in twisted rods, Experimental Mechanics 45, 101-111 (2005) (download preprint, 1740 K). [Full paper] [Abstract]
• G.H.M. van der Heijden, J. Valverde, Instability of a whirling conducting rod in the presence of a magnetic field, in Proc. of the 5th EUROMECH Nonlinear Dynamics Conference (ENOC 2005), 7-12 August 2005, Eindhoven, The Netherlands, D.H. van Campen, M.D. Lazurko, W.P.J.M. van den Oever (eds), pp. 2624-2633, ISBN 90-386-2667-3 (2005) (download PDF file, 440 K). [Abstract]
• J. Valverde, G.H.M. van der Heijden, Instability of a whirling conducting rod in the presence of a magnetic field. Application to the problem of space tethers, in Proc. of the ASME International Design Engineering Technical Conferences & Computers and Information In Engineering Conference (IDETC/CIE 2005), 24-28 September 2005, Long Beach CA, USA, DETC2005-84845, ISBN 0-7918-3766-1 (2005).
• G.H.M. van der Heijden, A two-strand ply hanging under its own weight, Nonlinear Dynamics 43, 197-208 (2006). [Full paper] [Abstract]
• C.D. Tran, D.G. Phillips, G.H.M. van der Heijden, Issues in processing unstable twisted fibre assemblies, in Proc. of the 4th Industrial Simulation Conference (ISC2006), 5-7 June 2006, University of Palermo, Italy, A. Genco, A. Gentile, S. Sorce (eds) (Eurosis-ETI, Ghent, 2006), pp. 325-329.
• G.H.M. van der Heijden, Localisation, looping and pop-out in rod-like structures, in Proc. Symposium on Mechanics of Slender Structures, 28-29 September 2006, Division of Engineering, School of Applied Sciences, University of Northampton, UK, S. Kaczmarczyk (ed.) (in collaboration with the Stress and Vibration Group of the Institute of Physics) (2006) (download PDF file, 656 K).
• G.H.M. van der Heijden, M.A. Peletier, R. Planqué, Self-contact for rods on cylinders, Arch. Rat. Mech. Anal. 182, 471-511 (2006). [Full paper] [arXiv.org preprint] [Abstract]
• G.H.M. van der Heijden, M.A. Peletier, R. Planqué, On end rotation for open rods undergoing large deformations, Quarterly of Applied Mathematics 65, 385-402 (2007). [Full paper] (an earlier version of this paper exists as an arXiv.org preprint) [Abstract]
• Laurent Bozec, Gert van der Heijden, Michael Horton, Collagen fibrils: nanoscale ropes, Biophysical Journal 92, 70-75 (2007). [Full paper] [Abstract]
• C.D. Tran, D.G. Phillips, G.H.M. van der Heijden, Modelling of self-contact pressures in multi-ply yarns, in Proc. of the Fiber Society 2007 Spring Conference `Advanced polymer fiber materials science and its applications in novel engineered products', 23-25 May 2007, Clemson University, SC, USA, M. Ellison (ed.) (School of Materials Science and Engineering, Clemson University & The Fiber Society 2007).
• G.H.M. van der Heijden, J. Valverde, Buckling conducting wires and instabilities of electrodynamic space tethers, in Proc. 5th International Conference on Nonlinear Mechanics (ICNM-V), 11-14 June 2007, Shanghai, China, Chien Wei-zang (editor-in-chief), Dai Shi-qiang, Zhou Zhe-wei, Cheng Chang-jun (associate editors) (Shanghai University Press, Shanghai, 2007), pp. 679-685, ISBN 978-7-81118-164-7.
• Qiguo Sun, Gert van der Heijden, A model for a 3D spinning rigid electrodynamic tether, in Proc. 5th International Conference on Nonlinear Mechanics (ICNM-V), 11-14 June 2007, Shanghai, China, Chien Wei-zang (editor-in-chief), Dai Shi-qiang, Zhou Zhe-wei, Cheng Chang-jun (associate editors) (Shanghai University Press, Shanghai, 2007), pp. 672-678, ISBN 978-7-81118-164-7.
• G.H.M. van der Heijden, W.B. Fraser, Bifurcation and stability of a whirling transported thread, in Proc. of EUROMECH Colloquium 483, Geometrically Non-linear Vibrations of Structures, 9-11 July 2007, Porto, Portugal, P. Ribeiro, M. Amabili (eds) (DEMEGI - FEUP, University of Porto, Portugal, 2007), pp. 221-224, ISBN 978-989-95208-2-0 (download PDF file, 174 K).
• E.L. Starostin, G.H.M. van der Heijden, The shape of a Möbius strip, Nature Materials 6, 563-567 (2007). [Full paper] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, The equilibrium shape of an elastic developable Möbius strip, Proc. Appl. Math. Mech. (PAMM) 7, 2020115-2020116 (2007) (Proceedings of the 6th International Congress on Industrial and Applied Mathematics, 16-20 July 2007, Zürich, Switzerland) [Full paper] (download PDF file, 728 K).
• D. Sinden, G.H.M. van der Heijden, Integrability of a conducting elastic rod in a magnetic field, Journal of Physics A: Mathematical and Theoretical 41, 045207 (2008). [Full paper] [arXiv.org preprint] [Abstract]
• G.H.M. van der Heijden, Magnetically-induced buckling of conducting wires and instabilities of electrodynamic space tethers, in Proc. Symposium on Mechanics of Slender Structures (MoSS 2008), 23-25 July 2008, University of Maryland Baltimore County, USA, W. Zhu (ed.) (2008).
• W.B. Fraser, G.H.M. van der Heijden, On the theory of localised snarling instabilities in false-twist yarn processes, Journal of Engineering Mathematics 61, 81-95 (2008). [Full paper] [Abstract]
• C.D. Tran, G.H.M. van der Heijden, D.G. Phillips, Application of topological conservation to model key features of zero-torque multi-ply yarns, The Journal of the Textile Institute 99, 325-337 (2008). [Full paper] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Tension-induced multistability in inextensible helical ribbons, Physical Review Letters 101, 084301 (2008). [Full paper] [arXiv.org preprint] [Abstract]
• P. Ribeiro, G.H.M. van der Heijden, Elasto-plastic and geometrically nonlinear vibrations of beams by the p-version finite element method, Journal of Sound and Vibration 325, 321-337 (2009). [Full paper] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Cascade unlooping of a low-pitch helical spring under tension, Journal of the Mechanics and Physics of Solids 57, 959-969 (2009). [Full paper] [arXiv.org preprint] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Force and moment balance equations for geometric variational problems on curves, Physical Review E 79, 066602 (2009). [Full paper] [arXiv.org preprint] [Abstract]
• D. Sinden, G.H.M. van der Heijden, Spatial chaos of an extensible conducting rod in a uniform magnetic field, Journal of Physics A: Mathematical and Theoretical 42, 375207 (2009). [Full paper] [arXiv.org preprint] [Abstract]
• A.P. Korte, G.H.M. van der Heijden, Curvature-induced electron localization in developable Möbius-like nanostructures, J. Phys.: Condens. Matter 21, 495301 (2009). [Full paper] (an earlier version of this paper exists as an arXiv.org preprint) [Abstract]
• D.G. Phillips, C.-D. Tran, W.B. Fraser, G.H.M. van der Heijden, Torsional properties of staple fibre plied yarns, The Journal of the Textile Institute 101, 595-612 (2010). [Full paper] [Abstract]
• J. Valverde, G.H.M. van der Heijden, Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers, Journal of Nonlinear Science 20, 309-339 (2010). [Full paper] [arXiv.org preprint] [Abstract]
• A.P. Korte, G.H.M. van der Heijden, A new triangular buckling pattern of twisted inextensible sheets, in Advances and Trends in Structural Engineering, Mechanics and Computation: Proceedings of the Fourth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2010), 6-8 September 2010, Cape Town, South Africa, A. Zingoni (ed.) (CRC Press/Balkema, Leiden, The Netherlands, 2010), pp. 545-548, ISBN 978-0-415-58472-2. [Volume]
[Abstract]
• A.P. Korte, E.L. Starostin, G.H.M. van der Heijden, Triangular buckling patterns of twisted inextensible strips, Proceedings of the Royal Society A 467, 285-303 (2011). [Full paper] [arXiv.org preprint] [Abstract]
• D. Sinden, G.H.M. van der Heijden, Localisation of a twisted conducting rod in a uniform magnetic field: the Hamiltonian-Hopf-Hopf bifurcation, submitted to Physica D. [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, An elastic two-strand ply theory, in Proc. of the 7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome, Italy, D. Bernardini, G. Rega, F. Romeo (eds) (Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 2011), 2 pages, ISBN 978-88-906234-2-4. [Full paper] [Abstract]
• G.H.M. van der Heijden, D. Sinden, Localisation of a twisted conducting rod in a uniform magnetic field: the Hamiltonian-Hopf-Hopf bifurcation, in Proc. of the 7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome, Italy, D. Bernardini, G. Rega, F. Romeo (eds) (Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 2011), 2 pages, ISBN 978-88-906234-2-4. [Full paper] [Abstract]
• D. Sinden, G.H.M. van der Heijden, The buckling of magneto-strictive Cosserat rods, in Proc. of the 7th European Nonlinear Dynamics Conference (ENOC 2011), 24-29 July 2011, Rome, Italy, D. Bernardini, G. Rega, F. Romeo (eds) (Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 2011), 2 pages, ISBN 978-88-906234-2-4. [Full paper] [Abstract]
• G.H.M. van der Heijden, K. Yagasaki, Nonintegrability of an extensible conducting rod in a uniform magnetic field, Journal of Physics A: Mathematical and Theoretical 44, 495101 (2011). [Full paper] [arXiv.org preprint] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Comment on "Statistical mechanics of developable ribbons", Physical Review Letters 107, 239801 (2011). [Full comment] [arXiv.org preprint]
• J. Valverde, G.H.M. van der Heijden, Helical buckling of a whirling conducting rod in a uniform magnetic field, International Journal of Non-Linear Mechanics 47, 38-53 (2012). [Full paper] [arXiv.org preprint] [Abstract]
• J.M.T. Thompson, M. Silveira, G.H.M. van der Heijden, M. Wiercigroch, Helical post-buckling of a rod in a cylinder: with applications to drill-strings, Proceedings of the Royal Society A 468, 1591-1614 (2012). [Full paper] [Video supplement] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Equilibria of elastic knots, in Book of Abstracts of the 8th European Solid Mechanics Conference (ESMC 2012), 9-13 July 2012, Graz, Austria, G.A. Holzapfel, R.W. Ogden (eds) (European Mechanics Society, 2012), 2 pages, ISBN 978-3-85125-223-1.
• J.M.T. Thompson, G.H.M. van der Heijden, A graphical criterion for the instability of elastic equilibria under multiple loads: with applications to drill-strings, International Journal of Mechanical Sciences 68, 160-170 (2013).
[Full paper] [Abstract]
• G.H.M. van der Heijden, K. Yagasaki, Horseshoes for the nearly symmetric heavy top, Z. Angew. Math. Phys. (ZAMP), [out online.] [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Theory of equilibria of elastic 2-braids with interstrand interaction, submitted. [Abstract]
• E.L. Starostin, G.H.M. van der Heijden, Tightening elastic torus knots (n, 2), submitted. [Abstract]

Special issues:

Modern Trends in Theoretical and Applied Mechanics: A Special Issue in Honour of Michael Thompson, G.H.M. van der Heijden (ed.), Nonlinear Dynamics 43(1-2), January 2006. [Full issue]

Non-linear Mechanics and Dynamics of Macromolecules, H. Dankowicz, G.H.M. van der Heijden & N. Perkins (eds), International Journal of Non-Linear Mechanics 43(10), December 2008. [Full issue]

Encyclopedia contributions:

Book reviews:

I.I. Blekhman, Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications (transl. M. Perelman) (World Scientific, Singapore, 2000), in Dynamical Systems Magazine, April 2004 (PDF file).

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