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经典力学和天体力学中的数学论题第2版(英文版)

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h\[$@v(r5G0作  者: V.I.Arnold ,V.V.Kozlov,A.I.Neishtadt 著

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出 版 社: 世界图书出版公司

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出版时间: 2000-6-1水利图书E h ?O;Ll"F0{

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字  数:水利图书H)s9O+ZDk:Z:B*T

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版  次: 2水利图书{8k(B?8\y:?"w

GS^n({CU0页  数: 291

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L4FZD.wve&l`0印刷时间: 2000-6-1

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开  本:

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印  次:水利图书0k/E-f.xj"]O'|N

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纸  张: 胶版纸

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I S B N : 9787506247092

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包  装: 平装水利图书e+O;g:O_w4N:W

&d]{p'[ BSX0所属分类: 图书 >> 自然科学 >> 力学

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内容简介

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This work describes the fundamental principles, problems, and methods of classical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of classical mechanics, rather than its physical foundations or applications. This apparatus is basically contained in Chapters 1, 3, 4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. This work describes the fundamental principles, problems, and methods of classical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of classical mechanics, rather than its physical foundations or applications. This apparatus is basically contained in Chapters 1, 3, 4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics.

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Chapter 1. Basic Principles of Classical Mechanics水利图书ekY_$z H6_+dO$B

M{7C9t(tN0 1. Newtonian Mechanics

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/Y.d;^-Q,NU$L{Y!\&PL0  1.1. Space. Time, Motion

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nxVm)S SW.C0  1.2. The Newton-Laplace Principle of Determinacy水利图书4x9A1o7^+La7l _

8u,YCc~ P0  1.3. The Principle of Relativity

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)]9{-}| W hp hO0  1.4. Basic Dynamical Quantities. Conservation Laws

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@c_i!}7|$^)C0 2. Lagrangian Mechanics水利图书H1C6PQR

5v&g%G WAn,s(n}q0  2.1. Preliminary Remarks水利图书'KoO.x"I P$a-t

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  2.2. Variations and Extremals

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  2.3. Lagrange''s Equations

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  2.4. Poincare''s Equations水利图书bFmtut}

JR ~vFh0  2.5. Constrained Motion

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 3. Hamiltonian Mechanics水利图书 H`ue0c-f GWO

!ex.}&vx;b0  3.1. Symplectic Structures and Hamilton''s Equations

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  3.2. Generating Functions

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@G"\.J3A%vZ` as'n0  3.3. Symplectic Structure of the Cotangent Bundle

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  3.4. The Problem of n Point Vortices水利图书d3P*h|Rw8w

Qx9{$T6G.WA0  3.5. The Action Functional in Phase Space

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)p,gzl bo%~Pa$q0  3.6. Integral Invariants

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3o d9MQ&a K L0  3.7. Applications to the Dynamics of Ideal Fluids水利图书-O+C`X2vg

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  3.8. Principle of Stationary Isoenergetic Action

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 4. Vakonomic Mechanics

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  4.1. Lagrange''s Problem水利图书m2~E#Las+I KN e

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  4.2. Vakonomic Mechanics

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Chapter 2. The n-Body Problem水利图书 LqH U-REu

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Chapter 3. Symmetry Groups and Reduction Lowering the Order水利图书NRx6u K2s;u)GO

BUPG6[(t7{VC0Chapter 4. Integrable Systems and Integration Methods水利图书6vD/R'EVmc

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Chapter 5. Perturbation Theory for Integrable Systems水利图书p_2QPfo

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Chapter 6. Nonintegrable Systems

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x_HG1Ds0Chapter 7. Theory of Small Oscillations水利图书 e`U4Ol^7D g5VI S+W

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Comments on the Bibliography水利图书UV9FcSQ@

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Recommended Reading

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Bibliography

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Index

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