This book is an excellent introduction to the world of classical physics for NON-PHYSICISTS. While some physicists will no doubt find it accessible, there is considerable reduction of physical concepts in order to get to the heart of the ideas underlying the formalism. Also, the material goes beyond what most physicists (non-theoreticians) will find practical.
He focuses largely on a geometric presentation, in the language of differential geometry, symplectic geometry, differential forms, Riemannian manifolds and includes a large amount of algebraic necessities. This is not a cookbook for learning how to solve classical mechanics, nor is it a math book per se, but it is a wonderful collection of introductions to a vast amount of useful mathematical formalism that permeates the physical literature. I would strongly recommend it to someone needing a thorough supplementary mechanics text, one that relies on very little physical insight and focuses on the geometric and algebraic structures underlying them.
The chapters are very well self-contained for the most part so you can skip to topics you find more appealing without feeling lost. Also, his presentation style is very clever, in case you're a fan of quick thinking and novel presentations (who isn't?).
The prerequisites are familiarity with somewhat advanced calculus and "mathematical maturity". Basic knowledge of group theory would also make it an easier read.

lgli/Springer.Mathematical.Methods.Of.Classical.Mechanics.(2Ed.1989).pdf

lgrsnf/Springer.Mathematical.Methods.Of.Classical.Mechanics.(2Ed.1989).pdf

zlib/Mathematics/Mathematical Physics/V. I. Arnold, A. Weinstein, K. Vogtmann/Mathematical Methods Of Classical Mechanics_542417.pdf

Matematicheskie metody klassicheskoĭ mekhaniki

V.I. Arnold; translated by K. Vogtmann and A. Weinstein

V. I. Arnold; Transl. by K. Vogtmann a. A. Weinstein

Vladimir I. Arnold; K. Vogtmann; A. Weinstein

Arnolʹd, V. I., V. I. Arnol'd

Vladimir Igorevich Arnolʹd

Арнольд, Владимир Игоревич

Springer Spektrum. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Copernicus

Telos

Graduate Texts in Mathematics, Volume 60, Second edition, Berlin, Germany, 1989

Graduate texts in mathematics ;, 60, 2nd ed., New York, New York State, 1997

Graduate texts in mathematics, 60, 2nd ed., 3rd corr. print, New York, ©1989

Springer Nature (Textbooks & Major Reference Works), New York, NY, 1989

United States, United States of America

2. ed., New York [etc.], Unknown, 1989

Germany, Germany

2nd, PS, 1989

2000

Springer -- 1

lg114217

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Translated from the Russian by K.Vogtmann & A.Weinstein.

Includes bibliographical references and index.
Translation of: Mathematicheskie metody klassicheskoĭ mekhaniki.

Includes bibliographical references and index.
"Corrected fourth printing"--T.p. verso.

Bookmarks: p1 (p1): Part I NEWTONIAN MECHANICS
p1-1 (p3): Chapter 1 Experimental facts
p1-1-1 (p3): 1. The principles of relativity and determinacy
p1-1-2 (p4): 2. The galilean group and Newton's equations
p1-1-3 (p11): 3. Examples of mechanical systems
p1-2 (p15): Chapter 2 Investigation of the equations of motion
p1-2-1 (p15): 4. Systems with one degree of freedom
p1-2-2 (p22): 5. Systems with two degrees of freedom
p1-2-3 (p28): 6. Conservative force fields
p1-2-4 (p30): 7. Angular momentum
p1-2-5 (p33): 8. Investigation of motion in a central field
p1-2-6 (p42): 9. The motion of a point in three-space
p1-2-7 (p44): 10. Motions of a system of n pomts
p1-2-8 (p50): 11. The method of similarity
p2 (p53): Part Ⅱ LAGRANGIAN MECHANICS
p2-1 (p55): Chapter 3 Variational principles
p2-1-1 (p55): 12. Calculus of variations
p2-1-2 (p59): 13. Lagrange's equations
p2-1-3 (p61): 14. Legendre transformations
p2-1-4 (p65): 15. Hamilton's equations
p2-1-5 (p68): 16. Liouville's theorem
p2-2 (p75): Chapter 4 Lagrangian mechanics on manifolds
p2-2-1 (p75): 17. Holonomic constraints
p2-2-2 (p77): 18. Differentiable manifolds
p2-2-3 (p83): 19. Lagrangian dynamical systems
p2-2-4 (p88): 20. E. Noether's theorem
p2-2-5 (p91): 21. D'Alembert's principle
p2-3 (p98): Chapter 5 Oscillations
p2-3-1 (p98): 22. Linearization
p2-3-2 (p103): 23. Small oscillations
p2-3-3 (p110): 24. Behavior of characteristic frequencies
p2-3-4 (p113): 25. Parametric resonance
p2-4 (p123): Chapter 6 Rigid Bodies
p2-4-1 (p123): 26. Motion in a moving coordinate system
p2-4-2 (p129): 27. Inertial forces and the Coriolis force
p2-4-3 (p133): 28. Rigid bodies
p2-4-4 (p142): 29. Euler's equations. Poinsot's description of the motion
p2-4-5 (p148): 30. Lagrange's top
p2-4-6 (p154): 31. Sleeping tops and fast tops
p3 (p161): Part Ⅲ HAMILTONIAN MECHANICS
p3-1 (p163): Chapter 7 Differential forms
p3-1-1 (p163): 32. Exterior forms
p3-1-2 (p170): 33. Exterior multiplication
p3-1-3 (p174): 34. Differential forms
p3-1-4 (p181): 35. Integration of differential forms
p3-1-5 (p188): 36. Exterior differentiation
p3-2 (p201): Chapter 8 Symplectic manifolds
p3-2-1 (p201): 37. Symplectic structures on manifolds
p3-2-2 (p204): 38. Hamiltonian phase flows and their integral invariants
p3-2-3 (p208): 39. The Lie algebra of vector fields
p3-2-4 (p214): 40. The Lie algebra of hamiltonian functions
p3-2-5 (p219): 41. Symplectic geometry
p3-2-6 (p225): 42. Parametric resonance in systems with many degrees of freedom
p3-2-7 (p229): 43. A symplectic atlas
p3-3 (p233): Chapter 9 Canonical formalism
p3-3-1 (p233): 44. The integral invariant of Poincare-Cartan
p3-3-2 (p240): 45. Applications of the integral invariant of Poincare-Cartan
p3-3-3 (p248): 46. Huygens' principle
p3-3-4 (p258): 47. The Hamilton-Jacobi method for integrating Hamilton's canonical equations
p3-3-5 (p266): 48. Generating functions
p3-4 (p271): Chapter 10 Introduction to perturbation theory
p3-4-1 (p271): 49. Integrable systems
p3-4-2 (p279): 50. Action-angle variables
p3-4-3 (p285): 51. Averaging
p3-4-4 (p291): 52. Averaging of perturbations
p4 (p301): Appendix 1 Riemannian curvature
p5 (p318): Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids
p6 (p343): Appendix 3 Symplectic structures on algebraic manifolds
p7 (p349): Appendix 4 Contact structures
p8 (p371): Appendix 5 Dynamical systems with symmetries
p9 (p381): Appendix 6 Normal forms of quadratic hamiltonians
p10 (p385): Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories
p11 (p399): Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem
p12 (p416): Appendix 9 Poincare's geometric theorem, its generalizations and applications
p13 (p425): Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters
p14 (p438): Appendix 11 Short wave asymptotics
p15 (p446): Appendix 12 Lagrangian singularities
p16 (p453): Appendix 13 The Korteweg-de Vries equation
p17 (p456): Appendix 14 Poisson structures
p18 (p469): Appendix 15 On elliptic coordinates
p19 (p480): Appendix 16 Singularities of ray systems
p20 (p503): Index

Библиогр.: с. 503-509
Указ.

РГБ

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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.
Erscheinungsdatum: 16.05.1989

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 approach, based on the theory of the geometry of manifolds, distinguishes itself 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

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.

V.i. Arnolʹd ; Translated By K. Vogtmann And A. Weinstein. Translation Of: Mathematicheskie Metody Klassicheskoĭ Mekhaniki. Includes Index. Bibliography: P.

2009-08-06