Conservation laws in the dynamics of rods
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OpenAlex topics: Elasticity and Material Modeling · Computational Fluid Dynamics and Aerodynamics · Nonlinear Waves and Solitons
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References (13)
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2. S. S. Antman, Nonlinear Problems of Elasticity, forthcoming, Springer Verlag, New York
3. T. B. Benjamin, Impulse, flow force and variational principles. IMA J. Applied Math. 32 (1984) 3?68.10.1093/imamat/32.1-3.3 ↗
4. R. E. Caflisch and J. H. Maddocks, Nonlinear dynamical theory of the elastica. Proc. Roy. Soc. Edinburgh 99A (1984) 1?23.10.1017/S0308210500025920 ↗
5. B. D. Coleman and E. H. Dill, Flexure waves in elastic rods. J. Acoust. Soc. Am. 91 (1992) 2663?2673.10.1121/1.402974 ↗
6. B. D. Coleman, E. H. Dill, M. Lembo, Z. Lu and I. Tobias, On the dynamics of rods in the theory of Kirchhoff and Clebsch. Arch. Rational Mech. Anal. 121 (1993) 339?359.10.1007/BF00375625 ↗
7. B. D. Coleman, Z. Lu and I. Tobias, Traveling waves in elastic rods, forthcoming.
8. D. J. Dichmann, J. H. Maddocks and R. L. Pego, Hamiltonian dynamics of an elastica and the stability of solitary waves. Arch. Rational Mech. Anal. (to appear).10.1007/BF02198477 ↗
9. R. S. Falk and J.-M. Xu, Convergence of a second-order scheme for the nonlinear dynamical equations of elastic rods. SIAM J. Numerical Analysis, (to appear).10.1137/0732055 ↗
10. T. J. Healey, Stability of shape-independent axial motions of strings, forthcoming.
11. P. J. Olver, Applications of Lie Groups to Differential Equations. Springer Verlag, New York (1986).10.1007/978-1-4684-0274-2 ↗
12. J. C. Simo, J. E. Marsden and P. K. Krishnaprasad, The Hamiltonian structure of nonlinear elasticity: the material and convective representations of solids, rods, and plates. Arch. Rational Mech. Anal. 104 (1988) 125?183.10.1007/BF00251673 ↗
13. J.-M. Xu, An analysis of the dynamical equations of elastic rods and their numerical approximation, Doctoral Dissertation, Rutgers University (1992).