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Introduction to mechanics and symmetry
Note: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27
Discrete mechanics and variational integrators
This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment ofExpand
Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
This paper develops the theory and computation of Lagrangian Coherent Structures (LCS), which are defined as ridges of Finite-Time Lyapunov Exponent (FTLE) fields. These ridges can be seen asExpand
Mathematical foundations of elasticity
[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians,Expand
Manifolds, Tensor Analysis, and Applications
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge ofExpand
Groups of diffeomorphisms and the motion of an incompressible fluid
In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and with the use of this structure to obtain sharp existence and uniqueness theorems for the classicalExpand
Reduction of symplectic manifolds with symmetry
We give a unified framework for the construction of symplectic manifolds from systems with symmetries. Several physical and mathematical examples are given; for instance, we obtain Kostant’s resultExpand
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
We study Euler–Poincare systems (i.e., the Lagrangian analogue of Lie–Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–PoincareExpand
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. Expand
Discrete exterior calculus
This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complexExpand