Rațiu, Tudor S.
Overview
Works:  54 works in 307 publications in 4 languages and 5,401 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Collector, Thesis advisor, Contributor 
Classifications:  QA805, 531 
Publication Timeline
.
Most widely held works by
Tudor S Rațiu
Manifolds, tensor analysis, and applications by
Ralph Abraham(
Book
)
39 editions published between 1983 and 2009 in 3 languages and held by 940 WorldCat member libraries worldwide
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 manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus
39 editions published between 1983 and 2009 in 3 languages and held by 940 WorldCat member libraries worldwide
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 manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus
Introduction to mechanics and symmetry : a basic exposition of classical mechanical systems by
Jerrold E Marsden(
Book
)
46 editions published between 1994 and 2011 in English and German and held by 779 WorldCat member libraries worldwide
"Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability, and bifurcation, and the study of specific rigid, fluid, plasma, and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and uptodate techniques, all of which make it accessible to a wide variety of readers, especially senior undergraduate and graduate students in mathematics, physics, and engineering."Jacket
46 editions published between 1994 and 2011 in English and German and held by 779 WorldCat member libraries worldwide
"Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability, and bifurcation, and the study of specific rigid, fluid, plasma, and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and uptodate techniques, all of which make it accessible to a wide variety of readers, especially senior undergraduate and graduate students in mathematics, physics, and engineering."Jacket
Turbulence Seminar, Berkeley 1976/77 by
P Bernard(
Book
)
28 editions published between 1977 and 2008 in 4 languages and held by 429 WorldCat member libraries worldwide
28 editions published between 1977 and 2008 in 4 languages and held by 429 WorldCat member libraries worldwide
Momentum maps and Hamiltonian reduction by
JuanPablo Ortega(
Book
)
11 editions published in 2004 in English and German and held by 263 WorldCat member libraries worldwide
"The focus of this work is a comprehensive and selfcontained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail." "This monograph is the first selfcontained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers."Jacket
11 editions published in 2004 in English and German and held by 263 WorldCat member libraries worldwide
"The focus of this work is a comprehensive and selfcontained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail." "This monograph is the first selfcontained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers."Jacket
The Geometry of Hamiltonian systems : proceedings of a workshop held June 516, 1989 by
Tudor S Rațiu(
Book
)
15 editions published in 1991 in English and German and held by 255 WorldCat member libraries worldwide
The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In cluded in the book is A.T. Fomenko's survey of the classification of integrable systems
15 editions published in 1991 in English and German and held by 255 WorldCat member libraries worldwide
The papers in this volume are an outgrowth of some of the lectures and informal discussions that took place during the workshop on the geometry of Hamiltonian systems, held at the MSRI in Berkeley in June of 1989. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, numerical simulations and dynamical systems in general. The articles are of differing lengths and scopes; some are research announcements while others are surveys of particularly active areas of interest where the results can only be found in scattered research articles and preprints. In cluded in the book is A.T. Fomenko's survey of the classification of integrable systems
Reduction, symmetry, and phases in mechanics by
Jerrold E Marsden(
Book
)
14 editions published in 1990 in English and held by 235 WorldCat member libraries worldwide
14 editions published in 1990 in English and held by 235 WorldCat member libraries worldwide
The breadth of symplectic and Poisson geometry : festschrift in honor of Alan Weinstein by
Jerrold E Marsden(
Book
)
19 editions published between 2005 and 2007 in English and held by 217 WorldCat member libraries worldwide
"Intended for graduate students and working mathematicians in symplectic and Poisson geometry as well as mechanics, this text is a distillation of prominent research and an indication of the future trends and directions in geometry, mechanics, and mathematical physics."Jacket
19 editions published between 2005 and 2007 in English and held by 217 WorldCat member libraries worldwide
"Intended for graduate students and working mathematicians in symplectic and Poisson geometry as well as mechanics, this text is a distillation of prominent research and an indication of the future trends and directions in geometry, mechanics, and mathematical physics."Jacket
Geometric mechanics and symmetry : the Peyresq lectures by
J Montaldi(
Book
)
11 editions published in 2005 in English and held by 216 WorldCat member libraries worldwide
These lectures are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They cover a range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symetric bifurcation theory
11 editions published in 2005 in English and held by 216 WorldCat member libraries worldwide
These lectures are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They cover a range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symetric bifurcation theory
Lagrangian reduction by stages by
Hernán Cendra(
Book
)
10 editions published in 2001 in English and held by 207 WorldCat member libraries worldwide
Introduction Preliminary constructions The LagrangePoincare equations Wong's equations and coordinate formulas The Lie algebra structure on sections of the reduced bundle Reduced tangent bundles Further examples The category $\mathfrak{LP}^*$ and Poisson geometry Bibliography
10 editions published in 2001 in English and held by 207 WorldCat member libraries worldwide
Introduction Preliminary constructions The LagrangePoincare equations Wong's equations and coordinate formulas The Lie algebra structure on sections of the reduced bundle Reduced tangent bundles Further examples The category $\mathfrak{LP}^*$ and Poisson geometry Bibliography
Hamiltonian structure and Lyapunov stability for ideal continuum dynamics by
Darryl D Holm(
Book
)
11 editions published in 1986 in English and held by 159 WorldCat member libraries worldwide
11 editions published in 1986 in English and held by 159 WorldCat member libraries worldwide
Northern California symplectic geometry seminar by Northern California Symplectic Geometry Seminar(
Book
)
3 editions published in 1999 in English and held by 151 WorldCat member libraries worldwide
This seminar was established to encourage ongoing interaction between geometers at Stanford University and the University of California (Berkeley, Davis, and Santa Cruz). Over the years, lectures presented have provided a panorama of developments in symplectic and contact geometry and topology, Poisson geometry, quantization theory, and applications. This volume includes papers by several of the distinguished seminar participants. The diversity of the topics from the seminar are reflected in the informative presentations. A wide range of topics are presented in the book, including symplectic t
3 editions published in 1999 in English and held by 151 WorldCat member libraries worldwide
This seminar was established to encourage ongoing interaction between geometers at Stanford University and the University of California (Berkeley, Davis, and Santa Cruz). Over the years, lectures presented have provided a panorama of developments in symplectic and contact geometry and topology, Poisson geometry, quantization theory, and applications. This volume includes papers by several of the distinguished seminar participants. The diversity of the topics from the seminar are reflected in the informative presentations. A wide range of topics are presented in the book, including symplectic t
Mechanics day by
Toronto) Mechanics Day (1992(
Book
)
6 editions published in 1996 in English and held by 105 WorldCat member libraries worldwide
This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial diffe
6 editions published in 1996 in English and held by 105 WorldCat member libraries worldwide
This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of "Foundations of Mechanics" by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial diffe
Foundations of mechanics; a mathematical exposition of classical mechanics by
Ralph Abraham(
Book
)
20 editions published between 1977 and 1998 in English and held by 65 WorldCat member libraries worldwide
Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. Zentralblatt für Mathematik For many years, this book has been viewed as a classic treatment of geometric mechanics. It is known for its broad exposition of the subject, with many features that cannot be found elsewhere. The book is recommended as a textbook and as a basic reference work for the foundations of differentiable and Hamiltonian dynamics
20 editions published between 1977 and 1998 in English and held by 65 WorldCat member libraries worldwide
Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. Zentralblatt für Mathematik For many years, this book has been viewed as a classic treatment of geometric mechanics. It is known for its broad exposition of the subject, with many features that cannot be found elsewhere. The book is recommended as a textbook and as a basic reference work for the foundations of differentiable and Hamiltonian dynamics
Lagrangian reduction by stages by
Hernán Cendra(
Book
)
2 editions published in 2001 in English and held by 25 WorldCat member libraries worldwide
2 editions published in 2001 in English and held by 25 WorldCat member libraries worldwide
Geometry, mechanics, and dynamics : the legacy of Jerry Marsden by
Dong Eui Chang(
Book
)
8 editions published in 2015 in English and held by 23 WorldCat member libraries worldwide
This book illustrates the broad range of Jerry Marsden's mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well
8 editions published in 2015 in English and held by 23 WorldCat member libraries worldwide
This book illustrates the broad range of Jerry Marsden's mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well
The Breadth of Symplectic and Poisson Geometry Festschrift in Honor of Alan Weinstein by
Jerrold E Marsden(
)
3 editions published between 2005 and 2007 in English and held by 9 WorldCat member libraries worldwide
3 editions published between 2005 and 2007 in English and held by 9 WorldCat member libraries worldwide
EulerPoisson equations on Lie algebras by
Tudor S Rațiu(
)
3 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 1980 in English and held by 8 WorldCat member libraries worldwide
Lectures on Poisson geometry : proceedings of the Summer School on Poisson Geometry, ICTP, Trieste, 2005 by Summer School on Poisson Geometry(
Book
)
8 editions published between 2010 and 2011 in English and held by 7 WorldCat member libraries worldwide
8 editions published between 2010 and 2011 in English and held by 7 WorldCat member libraries worldwide
Elemente de analizǎ locala by
M Craioveanu(
Book
)
3 editions published in 1976 in Romanian and held by 7 WorldCat member libraries worldwide
3 editions published in 1976 in Romanian and held by 7 WorldCat member libraries worldwide
Perspectives in fluid dynamics(
Book
)
1 edition published in 2008 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 6 WorldCat member libraries worldwide
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Related Identities
 Marsden, Jerrold E. Author Editor
 Abraham, Ralph Author
 Weinstein, Alan 1943 Honoree Dedicatee Editor
 Bernard, Peter 1950 Author Editor
 Holm, Darryl D. Author Editor
 Ortega, JuanPablo 1969 Author
 Montgomery, R. (Richard) 1956
 Cendra, Hernán 1943 Author
 Montaldi, J. (James) Author Editor
 Patrick, George W. (George William) 1958 Editor
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Associated Subjects
Calculus of tensors Celestial mechanics Cell aggregationMathematics Computer science Computer scienceMathematics Continuum mechanics Differentiable dynamical systems Differential equations Dynamics Ergodic theory Fluid dynamics Fluid mechanicsMathematics Geometric quantization Geometry Geometry, Differential Global analysis (Mathematics) Global differential geometry Hamiltonian systems Hilbert space Holonomy groups Lagrange equations Lie groups Lyapunov functions Lyapunov stability Manifolds (Mathematics) Mathematical optimization Mathematical physics Mathematics Mechanics Mechanics, Analytic Poisson manifolds Symmetry (Physics) Symmetry groups Symplectic geometry Symplectic groups Symplectic manifolds Topological dynamics Topological groups Turbulence Variational principles
Alternative Names
Ratiu, T.
Ratiu, T. 1950
Ratiu, T.S.
Ratiu, T. S. 1950
Ratiu, T.S. (Tudor S.)
Ratiu, T. (Tudor)
Ratiu, T. (Tudor), 1950
Ratiu, Tudor.
Ratiu Tudor 1950....
Ratiu, Tudor S.
Rațiu, Tudor S. 1950
Ratiu, Tudor Stefan.
Raţiu, Tudor Stefan 1950
Tudor Ratiu American mathematician
Tudor Ratiu Amerikaans wiskundige
Tudor Ratiu mathématicien américain
Tudor Ratiu rumänischUSamerikanischer Mathematiker
Тюдор Ратиу американский математик
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