Stability and bifurcation of rotating nonlinearly elastic loops
Author:
Timothy J. Healey
Journal:
Quart. Appl. Math. 48 (1990), 679-698
MSC:
Primary 73H10; Secondary 35B32, 35B35, 58F14, 73K12
DOI:
https://doi.org/10.1090/qam/1079913
MathSciNet review:
MR1079913
Full-text PDF Free Access
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Additional Information
T. J. Healey and J. Papadopoulos, Steady axial motions of strings, J. Appl. Mech. (1990), in press
E. J. Routh, stability of a Given State of Motion, Macmillan, London, 1877
- Darryl D. Holm, Jerrold E. Marsden, Tudor Ratiu, and Alan Weinstein, Nonlinear stability of fluid and plasma equilibria, Phys. Rep. 123 (1985), no. 1-2, 116. MR 794110, DOI https://doi.org/10.1016/0370-1573%2885%2990028-6
- J. Baillieul and M. Levi, Rotational elastic dynamics, Phys. D 27 (1987), no. 1-2, 43–62. MR 912850, DOI https://doi.org/10.1016/0167-2789%2887%2990004-2
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E. J. Routh, A Treatise on Analytical Statics, Vol. I, Cambridge University Press, Cambridge, 1891
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H. Lamb, Higher Mechanics, Cambridge University Press, London, 1920
H. Ziegler, Principles of Structural Stability, 2nd ed., Birkhauser Verlag, Basel, 1977
T. J. Healey and J. Papadopoulos, Steady axial motions of strings, J. Appl. Mech. (1990), in press
E. J. Routh, stability of a Given State of Motion, Macmillan, London, 1877
D. D. Holm, J. E. Marsden, T. Ratiu, and A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Physics Reports 123, 1–116 (1985)
J. Bailieul and M. Levi, Rotational elastic dynamics, Physica 27b, 43–62 (1987)
V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems III, Encyclopedia of Mathematical Sciences, Ed. V. I. Arnold, Springer-Verlag, New York, 1988
E. Zeidler, Nonlinear Functional Analysis, Vol. III: Variational Methods and Optimization, Springer-Verlag, New York, 1985
E. J. Routh, A Treatise on Analytical Statics, Vol. I, Cambridge University Press, Cambridge, 1891
A. Vanderbauwhede, Local Bifurcation and Symmetry, Pitman, Boston, 1982
M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. II, Springer Verlag, New York, 1988
H. Kilehöfer, Multiple eigenvalue bifurcation for Fredholm operators, J. Reine Angew. Math. 358, 104–124 (1985)
M. Golubitsky and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, Springer Verlag, New York, 1985
H. Lamb, Higher Mechanics, Cambridge University Press, London, 1920
H. Ziegler, Principles of Structural Stability, 2nd ed., Birkhauser Verlag, Basel, 1977
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Article copyright:
© Copyright 1990
American Mathematical Society
