Introduction to Hamiltonian dynamical systems and the Nbody problem
 Responsibility
 Kenneth R. Meyer, Daniel C. Offin.
 Edition
 Third edition.
 Publication
 Cham, Switzerland : Springer International Publishing AG, [2017]
 Physical description
 xiii, 384 pages : illustrations (some color) ; 24 cm.
 Series
 Applied mathematical sciences (SpringerVerlag New York Inc.) ; v. 90.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA614.83 .M49 2017  Unknown 
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Description
Creators/Contributors
 Author/Creator
 Meyer, Kenneth R. (Kenneth Ray), 1937 author.
 Contributor
 Offin, Daniel C. (Daniel Clyde), 1953 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (373379 pages) and index.
 Contents

 Beginnings
 Hamiltonian equations
 The poisson bracket
 Harmonic oscillator
 Flows on a sphere
 Dense flow on the Torus
 Lemniscate functions
 Forced nonlinear oscillator
 Newtonian system
 Eulerlagrange equations
 Spherical Pendulum
 Problems
 Hamiltonian systems
 Linear equations
 Symplectic linear spaces
 Canonical forms
 Sp(2, R)
 Floquetlyapunov theory
 Symplectic transformations
 The variational equations
 Poisson brackets
 Symplectic scaling
 Equations near an equilibrium point
 Problems
 Celestial mechanics
 The Nbody problem
 The 2body problem
 The kepler problem
 Symmetries and integrals
 Symmetries
 The classical integrals
 Noether's theorem
 Reduction
 Foundations
 Equilibrium and central configurations
 Equilibrium solutions
 Central configurations
 Rotating coordinates
 Total collapse
 Problems
 The restricted problem
 Defining
 Discrete symmetry
 Equilibria of the restricted problem
 Hill's regions
 Spectrum at the equilibrium points
 Mass ratios
 Canonical forms for the matrix at ...
 Other restricted problems
 Hill's lunar equations
 Elliptic restricted problem
 Problems
 Topics in linear theory
 Parametric stability
 Logarithm of a symplectic matrix
 Functions of a matrix
 Logarithm of a matrix
 Symplectic logarithm
 Spectral decomposition
 Normal forms for hamiltonian matrices
 Zero eigenvalue
 Pure imaginary eigenvalues
 Topology of Sp(2n, R)
 Angle function
 Fundamental group
 Maslov index
 Problems
 Local geometric theory
 The dynamical system point of view
 Discrete dynamical systems
 Diffeomorphisms and symplectomorphisms
 The time ... map
 The period map
 Flow box theorems
 Periodic solutions and cross sections
 Equilibrium points
 Periodic solutions
 A simple example
 Systems with integrals
 The stable manifold theorem
 Problems
 Symplectic geometry
 Exterior algebra
 Linear symplectic form
 Tangent and cotangent spaces
 Vector fields and differential forms
 Poincař's lemma
 Changing variables
 Symplectic manifold
 Darboux's theorem
 Lie groups
 Group actions
 Moment maps and reduction
 Integrable systems
 Problems
 Special coordinates
 Differential forms and generating functions
 The symplectic form
 Generating functions
 Mathieu transformations
 Jacobi coordinates
 Actionangle variables
 d'alembert character
 General actionangle coordinates
 Lemniscate coordinates
 Polar coordinates
 Kepler's problem in polar coordinates
 The 3body problem in Jacobipolar coordinates
 Spherical coordinates
 Complex coordinates
 Levicivita regularization
 Delaunay and poincaré Elements
 Planar delaunay elements
 Planar poincaré elements
 Spatial delaunay elements
 Pulsating coordinates
 The elliptic restricted 3body problem
 Problems
 Poincaré's continuation method
 Continuation of solutions
 Lyapunov center theorem
 Lyapunov families at the euler and lagrange points
 Poincaré's orbits
 Hill's orbits
 Comets
 From the restricted to the full problem
 Some elliptic orbits
 Problems
 Normal forms
 Normal form theorems
 Normal form at an equilibrium point
 Normal form at a fixed point
 Forward transformations
 Nearidentity symplectic change of variables
 The forward algorithm
 The remainder function
 The lie transform perturbation algorithm
 Example : duffing's equation
 The general algorithm
 The general perturbation theorem
 Normal form at an equilibrium
 Normal form at ...
 Normal forms for periodic systems
 Problems
 Bifurcations of periodic orbits
 Bifurcations of periodic solutions
 Elementary fixed points
 Extremal fixed points
 Period doubling
 kBifurcation points
 Schmidt's bridges
 Bifurcations in the restricted problem
 Hamiltonianhopf bifurcation
 Problems
 Stability and KAM theory
 Lyapunov and chetaev's theorems
 Local geometry
 Moser's invariant curve theorem
 Morris' boundedness theorem
 Arnold's stability theorem
 Singular reduction
 2:1 resonance
 3:1 resonance
 1:1 resonance
 Stability of fixed points
 Applications to the restricted problem
 Invariant curves for small mass
 The stability of comet orbits
 Problems
 Variational techniques
 The Nbody and the kepler problem revisited
 Symmetry reduction for planar 3body problem
 Reduced lagrangian systems
 Discrete symmetry with equal masses
 The variational principle
 Isosceles 3body problem
 A variational problem for symmetric orbits
 Instability of the orbits and the maslov index
 Remarks
 References
 Index.
 Publisher's Summary
 ["This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view.This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition:\"The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The Nbody problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a wellorganized and accessible introduction to the subject ... . This is an attractive book ... .\" (William J. Satzer, The Mathematical Association of America, March, 2009) \"The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.\" (Marian Gidea, Mathematical Reviews, Issue 2010 d).", {"source"=>"(source: Nielsen Book Data)"}, "9783319536903", "20170807"]
Subjects
Bibliographic information
 Publication date
 2017
 Series
 Applied mathematical sciences, 00665452 ; volume 90
 ISBN
 9783319536903 (hd.bd.)
 9783319536910 (online)
 3319536907