Mechanics: From Theory to Computation

1. Front Matter

   Pages i-x

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2. Dynamical Problems for Geometrically Exact Theories of Nonlinearly Viscoelastic Rods

   • S. S. Antman

   Pages 1-18

3. The Limits of Hamiltonian Structures in Three-Dimensional Elasticity, Shells, and Rods

   • Z. Ge, H. P. Kruse, J. E. Marsden

   Pages 19-57

4. The Membrane Shell Model in Nonlinear Elasticity: A Variational Asymptotic Derivation

   • H. Le Dret, A. Raoult

   Pages 59-84

5. Gravity Waves on the Surface of the Sphere

   • R. de la Llave, P. Panayotaros

   Pages 85-105

6. A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations

   • P. Betsch, E. Stein

   Pages 107-137

7. Multilayer Beams: A Geometrically Exact Formulation

   • L. Vu-Quoc, H. Deng, I. K. Ebcioğlu

   Pages 139-170

8. Obstructions to Quantization

   • M. J. Gotay

   Pages 171-216

9. An Impetus-Striction Simulation of the Dynamics of an Elastica

   • D. J. Dichmann, J. H. Maddocks

   Pages 217-238

10. A Symplectic Integrator for Riemannian Manifolds

    • B. Leimkuhler, G. W. Patrick

    Pages 239-256

11. Time Integration and Discrete Hamiltonian Systems

    • O. Gonzalez

    Pages 257-275

12. Problems and Progress in Microswimming

    • J. Koiller, K. Ehlers, R. Montgomery

    Pages 277-311

13. Symmetry Methods in Collisionless Many-Body Problems

    • I. Stewart

    Pages 313-333

14. Mathematical Analysis of Sideband Instabilities with Application to Rayleigh-Bénard Convection

    • A. Mielke

    Pages 335-377

15. KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems

    • M. Rudnev, S. Wiggins

    Pages 379-411

16. Constrained Euler Buckling

    • G. Domokos, P. Holmes, B. Royce

    Pages 413-446

17. Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations

    • J. M. Ball

    Pages 447-474

18. Stacked Lagrange Tops

    • D. Lewis

    Pages 475-514

19. On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges

    • H.-P. Kruse, J. Scheurle

    Pages 515-532

Starting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me­ chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic­ ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me­ chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci­ plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community.

• Area
• Navier-Stokes equation
• Volume
• convection
• dynamics
• stability
• waves
• fluid- and aerodynamics

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