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Introduction to mechanics and symmetry

- J. Marsden, T. Ratiu
- Mathematics
- 1994

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

- J. Marsden, Matthew West
- Mathematics
- Acta Numerica
- 1 May 2001

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 of… Expand

Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

- S. Shadden, F. Lekien, J. Marsden
- Mathematics
- 15 December 2005

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 as… Expand

Mathematical foundations of elasticity

- J. Marsden, T. Hughes, D. Carlson
- Mathematics
- 1 November 1982

[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

- R. Abraham, J. Marsden, T. Ratiu, C. DeWitt-Morette
- Physics
- 1983

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 of… Expand

Groups of diffeomorphisms and the motion of an incompressible fluid

- D. Ebin, J. Marsden
- Mathematics
- 1 July 1970

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 classical… Expand

Reduction of symplectic manifolds with symmetry

- J. Marsden, A. Weinstein
- Mathematics
- 1 February 1974

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 result… Expand

The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories

- Darryl D. Holm, J. Marsden, T. Ratiu
- Mathematics, Physics
- 13 January 1998

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–Poincare… Expand

Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems

- J. Marsden, T. Ratiu
- Computer Science
- 1999

TLDR

Discrete exterior calculus

- Mathieu Desbrun, Anil N. Hirani, M. Leok, J. Marsden
- Mathematics
- 18 August 2005

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 complex… Expand

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