Cushman, Richard H. 1942
Overview
Works:  19 works in 81 publications in 1 language and 2,106 library holdings 

Roles:  Author, Collector, Contributor, Editor 
Classifications:  QA805, 531.0151 
Publication Timeline
.
Most widely held works by
Richard H Cushman
Global aspects of classical integrable systems by
Richard H Cushman(
Book
)
25 editions published between 1997 and 2015 in English and held by 286 WorldCat member libraries worldwide
This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2dimensional harmonic oscillator, the geodesic flow on the 3sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis
25 editions published between 1997 and 2015 in English and held by 286 WorldCat member libraries worldwide
This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2dimensional harmonic oscillator, the geodesic flow on the 3sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis
Geometry of nonholonomically constrained systems by
Richard H Cushman(
Book
)
19 editions published between 2009 and 2010 in English and held by 122 WorldCat member libraries worldwide
"This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Caratheodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat." "The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trailblazers in their respective fields."Jacket
19 editions published between 2009 and 2010 in English and held by 122 WorldCat member libraries worldwide
"This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Caratheodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat." "The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trailblazers in their respective fields."Jacket
Foundations of mechanics; a mathematical exposition of classical mechanics by
Ralph Abraham(
Book
)
14 editions published between 1977 and 1994 in English and held by 57 WorldCat member libraries worldwide
14 editions published between 1977 and 1994 in English and held by 57 WorldCat member libraries worldwide
Nathan A. Cushman : a rugged individualist (18691952)(
Book
)
1 edition published in 1984 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 16 WorldCat member libraries worldwide
Proceedings of the Pacific Institute of Mathematical Sciences workshop on nonholonomic constraints in dynamics : August 2630,
1997 Calgary, Alberta, Canada by
Workshop on Nonholonomic Constraints in Dynamics(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Differential structure of orbit spaces by
Richard H Cushman(
Book
)
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
Lifted actions and the local geometry of orbit spaces by
Richard H Cushman(
Book
)
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
Nilpotent normal forms and representation theory of sl(2,R)+ by
Richard H Cushman(
Book
)
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
Versal normal form at Lagrange equilibrium L4 by
Richard H Cushman(
Book
)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
Richard Cushman on the occasion of his 65th birthday(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator by
Richard H Cushman(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Hyperbolic points of integrable areapreserving mappings of the 2disk by
Richard H Cushman(
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Classical integrable systems by
Richard H Cushman(
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Splitting algorithm for nilpotent normal forms by
Richard H Cushman(
Book
)
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
Geometry of Nonholonomically Constrained Systems (Advanced series in nonlinear dynamics ; v. 26) by
Jędrzej Śniatycki(
Book
)
1 edition published in 2010 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 2010 in Undetermined and held by 1 WorldCat member library worldwide
In honor of Henk Broer for his 60th birthday(
Book
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
Structure of dynamical systems : a symplectic view of physics by
J.M Souriau(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization. The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. The first tow chapters provide the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In Chapter 3 a coherent symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and nonrelativistic, with or without spin, with or without mass). In Chapter 4 statistical mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. Finally, in Chapter 5 the author presents his theory of geometric quantization. Highlights of this chapter are the derivations of various wave equations and the construction of the Fock space
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization. The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. The first tow chapters provide the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In Chapter 3 a coherent symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and nonrelativistic, with or without spin, with or without mass). In Chapter 4 statistical mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. Finally, in Chapter 5 the author presents his theory of geometric quantization. Highlights of this chapter are the derivations of various wave equations and the construction of the Fock space
Normal form and representation theory by
Richard H Cushman(
)
1 edition published in 1982 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Śniatycki, Jędrzej Author
 Duistermaat, J. J. (Johannes Jisse) 1942
 Bates, Larry M. (Larry Meredith) 1957
 Marsden, Jerrold E. (1942....).
 Ratiu, Tudor Stefan Collector Contributor
 Abraham, Ralph H. (1936....). Author
 Cushman, Nathan A.
 Cole, Franklin P.
 World Scientific (Firm)
 Sanders, J. A. (Jan A.)
Associated Subjects
Caratheodory measure Celestial mechanics Cell aggregationMathematics Differentiable dynamical systems Dynamics Geometry, Differential Hamiltonian systems Lagrangian points Manifolds (Mathematics) Mathematical physics Mathematics Mechanics Mechanics, Analytic Nonholonomic dynamical systems Physics Quantum theory Rigidity (Geometry) Statistical mechanics Symplectic manifolds Threebody problem Transformations (Mathematics) Vector fields
Alternative Names
Cushman, R. H.
Cushman, Richard
Cushman Richard 1942....
Cushman, Richard H.
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