Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 355, Issue 1732, 1997, Pages 2151-2174

  Champneys, A R ^a   Van Der Heijden, G H M ^b   Thompson, J M T ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142583750     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0115     Document Type: Article

References (14)

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2. Antman, S. & Jordan, K. 1974 Qualitative aspects of the spatial deformation of non-linearly elastic rods. Proc. R. Soc. Edinb. A 73, 85-105.
3. Champneys, A. R. & Spence, A. 1993 Hunting for homoclinic orbits in reversible systems: a shooting technique. Adv. Comp. Math. 1, 81-108.
4. Champneys, A. R. & Thompson, J. M. T. 1996 A multiplicity of localized buckling modes for twisted rod equations. Proc. R. Soc. Lond. A 452, 2467-2491.
5. Doedel, E., Keller, H. & Kernévez, J. 1991 Numerical analysis and control of bifurcation problems. I. Bifurcation in finite dimensions. Int. J. Bifurcation and Chaos 1, 493-520, 745-772.
6. Iooss, G. & Pérouème, M. 1993 Perturbed homoclinic solutions in reversible 1:1 resonance vector fields. J. Differ. Equat. 102, 62-88.
7. Kirchhoff, G. 1859 Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. für Mathematik (Crelle) 56, 285-313.
8. Love, A. E. H. 1927 A treatise on the mathematical theory of elasticity, IVth edn. Cambridge University Press.
9. Mielke, A. & Holmes, P. 1988 Spatially complex equilibria of buckled rods. Arch. Ration. Mech. Analysis 101, 319-348.
10. Thompson, J. M. T. & Champneys, A. R. 1996 From the helix to localized writhing in the torsional post buckling of elastic rods. Proc. R. Soc. Lond. A 452, 117-138.
11. Timoshenko, S. P. & Gere, J. M. 1961 Theory of elastic stability. New York: McGraw-Hill.
12. Van der Heijden, G. & Thompson, J. M. T. 1997 Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods. Physica D (In the press.)
13. Van der Heijden, G., Champneys, A. R. & Thompson, J. M. T. 1997 Load-deflection characteristics of localised torsional buckling modes in rods with non-circular cross-section. SIAM J. Appl. Math. (In the press.)
14. Van der Meer, J. C. 1985 The Hamiltonian Hopf bifurcation (Lecture Notes in Mathematics 1160). Berlin: Springer.