Mathematical methods of classical mechanics
Author(s)
Bibliographic Information
Mathematical methods of classical mechanics
（Graduate texts in mathematics, 60）
Springer-Verlag, c1989
2nd ed., [1st corr. printing]
- : us
- : gw
- Other Title
-
Matematicheskie metody klassicheskoĭ mekhaniki
Related Bibliography 1 items
Available at / 62 libraries
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Science and Technology Library, Kyushu University
: usSER/GTM/60a023212002003464,
: gw026211996000968 -
The Institute for Solid State Physics Library. The University of Tokyo.図書室
: us423:M37210262189
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Note
Includes bibliographical references (p. 503-509) and index
Description and Table of Contents
- Volume
-
: us ISBN 9780387968902
Description
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Table of Contents
I Newtonian Mechanics.- 1 Experimental facts.- 2 Investigation of the equations of motion.- II Lagrangian Mechanics.- 3 Variational principles.- 4 Lagrangian mechanics on manifolds.- 5 Oscillations.- 6 Rigid bodies.- III Hamiltonian Mechanics.- 7 Differential forms.- 8 Symplectic manifolds.- 9 Canonical formalism.- 10 Introduction to perturbation theory.- Appendix 1 Riemannian curvature.- Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids.- Appendix 3 Symplectic structures on algebraic manifolds.- Appendix 4 Contact structures.- Appendix 5 Dynamical systems with symmetries.- Appendix 6 Normal forms of quadratic hamiltonians.- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories.- Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem.- Appendix 9 Poincare's geometric theorem, its generalizations and applications.- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters.- Appendix 11 Short wave asymptotics.- Appendix 12 Lagrangian singularities.- Appendix 13 The Korteweg-de Vries equation.- Appendix 14 Poisson structures.- Appendix 15 On elliptic coordinates.- Appendix 16 Singularities of ray systems.
- Volume
-
: gw ISBN 9783540968900
Description
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Table of Contents
- Part 1 Newtonian mechanics: experimental facts
- investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles
- Lagrangian mechanics on manifolds
- oscillations
- rigid bodies. Part 3 Hamiltonian mechanics: differential forms
- symplectic manifolds
- canonical formalism
- introduction to pertubation theory.
by "Nielsen BookData"
