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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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at*C0?4h$PMo0经典力学和天体力学中的数学论题第2版(英文版)水利图书 ?xX r-FB

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作  者: V.I.Arnold ,V.V.Kozlov,A.I.Neishtadt 著水利图书Dk5aU;AF'r

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出 版 社: 世界图书出版公司

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fr-H'w] ~ M)QT0出版时间: 2000-6-1水利图书YM }Nb%iEo7j

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字  数:

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版  次: 2水利图书"Vr!d7f{C/}4p

]r O8XkxHX0页  数: 291

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fG]5u(m G&Pe0印刷时间: 2000-6-1水利图书!sb:qb/y

{ ZW8oxM9]0开  本:水利图书Dj xQo3wJS$M

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印  次:

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6W@*L6f$Io,h0I S B N : 9787506247092

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包  装: 平装水利图书A)IEO ^5X"z

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所属分类: 图书 >> 自然科学 >> 力学

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fS[/~/XH,U(`lYe0内容简介水利图书4Y"l'j ](x![8kt

1T%Y4q+P ]~\s0This 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.水利图书OC6jRP_

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目录水利图书H*? fa i J8A?

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Chapter 1. Basic Principles of Classical Mechanics水利图书6@(h4A)m} xb

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 1. Newtonian Mechanics

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tg[eku K2D0  1.1. Space. Time, Motion水利图书 q~e}5n

6n#^KSSRo0  1.2. The Newton-Laplace Principle of Determinacy

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OE7d3R$K:~ Z"GMN8Yo]0  1.3. The Principle of Relativity水利图书 ~:|g?&YV'm u

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  1.4. Basic Dynamical Quantities. Conservation Laws水利图书"Y4RA7vJ&]

;Xb6`'y%r@/R{ j0 2. Lagrangian Mechanics

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[*f;gH$C zovh#b0  2.1. Preliminary Remarks

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  2.2. Variations and Extremals

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  2.3. Lagrange''s Equations水利图书 b[^/HP&C

p-kZ%o4mM!k0  2.4. Poincare''s Equations水利图书Z.d9@/A}

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  2.5. Constrained Motion水利图书&[/}I%G }#G2@n

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 3. Hamiltonian Mechanics

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;oQ,wB"O v0  3.1. Symplectic Structures and Hamilton''s Equations

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qr,`V*o0  3.2. Generating Functions

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GF"Q9J${4a{dmW)@)z0  3.3. Symplectic Structure of the Cotangent Bundle水利图书.g5N1a/As yp#LP3`]

7? f2M*Eh7T l!Z|0  3.4. The Problem of n Point Vortices

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  3.5. The Action Functional in Phase Space

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Yb;r~'k1m }#z ~a0  3.6. Integral Invariants水利图书X^ cG U*nq h A~T

z%aQVC4{L i'EZ0  3.7. Applications to the Dynamics of Ideal Fluids

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@3@4z)YW0  3.8. Principle of Stationary Isoenergetic Action

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3]_${7v3P_(}RX&pEq0 4. Vakonomic Mechanics

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  4.1. Lagrange''s Problem

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Dp&`hJku$E9K0Ba0  4.2. Vakonomic Mechanics

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m;I3H;JreC:V `r0Chapter 2. The n-Body Problem水利图书v8P4A uJ+xc7Fn7JS^(Q

L*I+I|$vZV \0Chapter 3. Symmetry Groups and Reduction Lowering the Order

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Chapter 4. Integrable Systems and Integration Methods水利图书Ep'mdE0i

+cv-^k:`n i6I)ep0Chapter 5. Perturbation Theory for Integrable Systems水利图书q+wM&p"[L-Te+|

g7~ZuPHL0Chapter 6. Nonintegrable Systems水利图书@$[H5| _x

{fR"VFj/BH,WI F"b0Chapter 7. Theory of Small Oscillations

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'WJ T0Msh&De]0Comments on the Bibliography

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Recommended Reading

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Bibliography

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