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Stabilization via symmetry switching in hybrid dynamical systems
A rigorous derivation of hemitropy in nonlinearly elastic rods
1. | Department of Mathematics and Department of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY, United States |
References:
[1] |
S. S. Antman, "Problems of Nonlinear Elasticity," Springer-Verlag, New York, 2cnd edition, 2005. |
[2] |
J. M. Ball, Remarques sur l'existence et la régularité des solutions d'elatostatique non linéar, Recent Contributions to Nonlinear Partial Differential Equations, eds., H Berestycki & H. Brezis, Pitman, London, (1981), 50-62. |
[3] |
A. Braides, "Gamma Convergence for Beginners,'' Oxford University Press, Oxford, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[4] |
D. Cioranescu and P. Donato, "An Introduction to Homogenization,'' Oxford University Press, Oxford, 2002. |
[5] |
B. Dacorogna, "Direct Methods in the Calculus of Variations,'' Springer-Verlag, New York, 1989. |
[6] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillation, Dynamical Systems, and Bifurcations of Vector Fields,'' Springer-Verlag, New York, 1983. |
[7] |
T. J. Healey, Material symmetry and chirality in nonlinearly elastic rods, Math. Mech. Solids, 7 (2002), 405-420. |
[8] |
T. J. Healey and P. Mehta, Straightforward computation of spatial equilibria of geometrically exact Cosserat rods, Int. J. Bifur.Chaos, 15 (2005), 949-965.
doi: 10.1142/S0218127405012387. |
[9] |
J. Jost and X. Li-Jost, "Calculus of Variations,'' Cambridge University Press, Cambridge, 2008. |
[10] |
S. Kerhbaum and J. H. Maddocks, Effective properties of elastic rods with high intrinsic twist, in M. Deville and R. Owens, editors, "Proceedings of the 16th IMACS World Congress 2000,'' pp. 1-8, 2000. |
[11] | |
[12] |
R. T. Rockafellar, "Convex Analysis,'' Princeton University Press, Princeton, N.J., 1970. |
show all references
References:
[1] |
S. S. Antman, "Problems of Nonlinear Elasticity," Springer-Verlag, New York, 2cnd edition, 2005. |
[2] |
J. M. Ball, Remarques sur l'existence et la régularité des solutions d'elatostatique non linéar, Recent Contributions to Nonlinear Partial Differential Equations, eds., H Berestycki & H. Brezis, Pitman, London, (1981), 50-62. |
[3] |
A. Braides, "Gamma Convergence for Beginners,'' Oxford University Press, Oxford, 2002.
doi: 10.1093/acprof:oso/9780198507840.001.0001. |
[4] |
D. Cioranescu and P. Donato, "An Introduction to Homogenization,'' Oxford University Press, Oxford, 2002. |
[5] |
B. Dacorogna, "Direct Methods in the Calculus of Variations,'' Springer-Verlag, New York, 1989. |
[6] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillation, Dynamical Systems, and Bifurcations of Vector Fields,'' Springer-Verlag, New York, 1983. |
[7] |
T. J. Healey, Material symmetry and chirality in nonlinearly elastic rods, Math. Mech. Solids, 7 (2002), 405-420. |
[8] |
T. J. Healey and P. Mehta, Straightforward computation of spatial equilibria of geometrically exact Cosserat rods, Int. J. Bifur.Chaos, 15 (2005), 949-965.
doi: 10.1142/S0218127405012387. |
[9] |
J. Jost and X. Li-Jost, "Calculus of Variations,'' Cambridge University Press, Cambridge, 2008. |
[10] |
S. Kerhbaum and J. H. Maddocks, Effective properties of elastic rods with high intrinsic twist, in M. Deville and R. Owens, editors, "Proceedings of the 16th IMACS World Congress 2000,'' pp. 1-8, 2000. |
[11] | |
[12] |
R. T. Rockafellar, "Convex Analysis,'' Princeton University Press, Princeton, N.J., 1970. |
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