Ebook: Elasticity and geometry: from hair curls to the non-linear response of shells

In the last 20 years, researchers in the field of celestial mechanics have achieved spectacular results in their effort to understand the structure and evolution of our solar system. Modern Celestial Mechanics uses a solid theoretical basis to describe recent results on solar system dynamics, and it emphasizes the dynamics of planets and of small bodies. To grasp celestial mechanics, one must comprehend the fundamental concepts of Hamiltonian systems theory, so this volume begins with an explanation of those concepts. Celestial mechanics itself is then considered, including the secular motion of planets and small bodies and mean motion resonances. Graduate students and researchers of astronomy and astrophysics will find Modern Celestial Mechanics an essential addition to their bookshelves We experience elasticity everywhere in daily life: in the straightening or curling of hairs, the irreversible deformations of car bodies after a crash, or the bouncing of elastic balls in table tennis or football. The theory of elasticity is essential to the recent developments of applied and fundamental science, such as the bio-mechanics of DNA filaments and other macro-molecules, and the animation of virtual characters in computer graphics and materials science. In this book, the emphasis is on the elasticity of thin bodies (plates, shells, rods) in connection with geometry. It covers such topics as the mechanics of hairs (curled and straight), the buckling instabilities of stressed plates, including folds and conical points appearing at larger stresses, the geometric rigidity of elastic shells, and the delamination of thin compressed films. It applies general methods of classical analysis, including advanced non-linear aspects (bifurcation theory, boundary layer analysis), to derive detailed, fully explicit solutions to specific problems. These theoretical concepts are discussed in connection with experiments. The book is self-contained. Mathematical prerequisites are vector analysis and differential equations. The book can serve as a concrete introduction to non-linear methods in analysis. --Book Jacket.  Read more... 1. Introduction ; 2. Three-dimensional elasticity ; I: RODS ; 3. Equations for elastic rods ; 4. Mechanics of the human hair ; 5. Rippled leaves, uncoiled springs ; II: PLATES ; 6. The equations for elastic plates ; 7. End effects in plate buckling ; 8. Finite amplitude buckling of a strip ; 9. Crumpled paper ; 10. Fractal buckling near edges ; III: SHELLS ; 11. Geometric rigidity of surfaces ; 12. Shells of revolution ; 13. The elastic torus ; 14. Spherical shell pushed by a wall ; Appendix A: Calculus of variations: a worked example ; Appendix B: Boundary and interior layers ; Appendix C: The geometry of helices ; Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity