Mechanics: From Theory to Computation : Essays in Honor of Juan-Carlos Simo

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. Dynamical Problems for Geometrically Exact Theories of Nonlinearly Viscoelastic Rods, S.S Antman The Limits of Hamiltonian Structures in Three-Dimensional Elasticity, Shells and Rods, Z. Ge, H.P. Kruse and J.E. Marsden The Membrane Shell Model in Nonlinear Elasticity: A Variational Asymptotic Derivation, H. Le Dret and A. Raoult Gravity Waves on the Surface of the Sphere, R. de la Llave and P. Panayotaros A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations, P. Betsch and E. Stein Multilayer Beams: A Geometrically Exact Formulation, L. Vu-Quoc, H. Deng, and I.K. Ebcioglu An Impetus-Striction Simulation of the Dynamics of an Elastica, D.J. Dichmann and J.H. Maddocks A Symplectic Integrator for Riemannian Manifolds, B. Leimkuhler and G.W. Patrick Time Integration and Discrete Hamiltonian Systems, O. Gonzalez Obstruction Results in Quantization Theory, M.J. Gotay, H.B. Grundling, and G.M. Tuynman Problems and Progress in Microswimming, J. Koiller, K. Ehlers, and R. Montgomery Symmetry Methods in Collisionless Many-Body Problems, I. Stewart Mathematical Analysis of Sideband Instabilities with Application to Rayleigh-Benard Convection, A. Mielke KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems Constrained Euler Buckling Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations Stacked Lagrange Tops On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges. Front Matter....Pages i-x Dynamical Problems for Geometrically Exact Theories of Nonlinearly Viscoelastic Rods....Pages 1-18 The Limits of Hamiltonian Structures in Three-Dimensional Elasticity, Shells, and Rods....Pages 19-57 The Membrane Shell Model in Nonlinear Elasticity: A Variational Asymptotic Derivation....Pages 59-84 Gravity Waves on the Surface of the Sphere....Pages 85-105 A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations....Pages 107-137 Multilayer Beams: A Geometrically Exact Formulation....Pages 139-170 Obstructions to Quantization....Pages 171-216 An Impetus-Striction Simulation of the Dynamics of an Elastica....Pages 217-238 A Symplectic Integrator for Riemannian Manifolds....Pages 239-256 Time Integration and Discrete Hamiltonian Systems....Pages 257-275 Problems and Progress in Microswimming....Pages 277-311 Symmetry Methods in Collisionless Many-Body Problems....Pages 313-333 Mathematical Analysis of Sideband Instabilities with Application to Rayleigh-Bénard Convection....Pages 335-377 KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems....Pages 379-411 Constrained Euler Buckling....Pages 413-446 Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations....Pages 447-474 Stacked Lagrange Tops....Pages 475-514 On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges....Pages 515-532