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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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\-J3S7h]-QA0P0g0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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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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J%GV/e Z3Pg0出版时间: 2000-6-1

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字  数:

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gx*ioF0版  次: 2

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ku'Ak1B'Rs9o0页  数: 291水利图书 R+j.`w i^ Z5y

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印刷时间: 2000-6-1水利图书/xGIH"lu9\

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开  本:

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纸  张: 胶版纸

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Z/oN7u*SX?J2~0I S B N : 9787506247092

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vbN1m0J^0包  装: 平装水利图书 f,P qb*[H P

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所属分类: 图书 >> 自然科学 >> 力学水利图书;{&i&s;Cy%hj e

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内容简介水利图书4cJ8f]#Vk$sK B

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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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目录

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h3D)K ~ i0Chapter 1. Basic Principles of Classical Mechanics

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 1. Newtonian Mechanics

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DwvV&c0  1.1. Space. Time, Motion水利图书9a/c#^:w5b

6zb ]+tYI1O+T0  1.2. The Newton-Laplace Principle of Determinacy

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5LU4Z3I.\R(R0  1.3. The Principle of Relativity水利图书x(sGg$|2N#{

|l+{,y:Y,_O0  1.4. Basic Dynamical Quantities. Conservation Laws水利图书I6u5i }!Hj0iY&\

Y$qd Kv!h nwmZ0 2. Lagrangian Mechanics

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-V%A8Yg;_1d+]n` ~0  2.1. Preliminary Remarks水利图书"eP+Fn?-{/c

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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

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i)B"QG'A%N-v0  2.5. Constrained Motion

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 3. Hamiltonian Mechanics

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:k#PL#i&it4l1D-V2T0  3.1. Symplectic Structures and Hamilton''s Equations水利图书KK~b$nuzI

H;Lj&I?d!l(i0  3.2. Generating Functions水利图书]Z4Y.w3MXg'K

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  3.3. Symplectic Structure of the Cotangent Bundle水利图书 ]M3j"cg-f

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  3.4. The Problem of n Point Vortices

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-Zc%\{yMz-h0  3.5. The Action Functional in Phase Space

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%gC,[Al0  3.6. Integral Invariants

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f4^E#b*_#]w*VM4r0  3.7. Applications to the Dynamics of Ideal Fluids水利图书-^8f0l#e$?U1W

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  3.8. Principle of Stationary Isoenergetic Action水利图书 v`a f V5sH0J#tT

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 4. Vakonomic Mechanics水利图书5h.xQHL8Z:r5YTe}

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  4.1. Lagrange''s Problem

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m)T^|q F u0  4.2. Vakonomic Mechanics水利图书K&k9t]%z!fJo

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3L s-Y\a7K0Chapter 2. The n-Body Problem水利图书+mN(L w/C`!F y WC"\

U2MFh+|0Chapter 3. Symmetry Groups and Reduction Lowering the Order

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$k,~6ajf5F0Chapter 4. Integrable Systems and Integration Methods水利图书2c6_6k"f.LN

5p*iKk,~&j0}0Chapter 5. Perturbation Theory for Integrable Systems

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Chapter 6. Nonintegrable Systems

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Chapter 7. Theory of Small Oscillations水利图书D)w3p` P)`

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Comments on the Bibliography水利图书p|ru B

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Recommended Reading水利图书^Z*i7oh{p!m;vW

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Bibliography

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Index

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