经典力学与天体力学中的数学问题

所属分类:力学  
出版时间:2009-1   出版时间:科学出版社   作者:阿诺德   页数:518  
Tag标签:数学,科学  

前言

要使我国的数学事业更好地发展起来,需要数学家淡泊名利并付出更艰苦地努力。另一方面,我们也要从客观上为数学家创造更有利的发展数学事业的外部环境,这主要是加强对数学事业的支持与投资力度,使数学家有较好的工作与生活条件,其中也包括改善与加强数学的出版工作。从出版方面来讲,除了较好较快地出版我们自己的成果外,引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说,施普林格(Springer)出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书,使我国广大数学家能以较低的价格购买,特别是在边远地区工作的数学家能普遍见到这些书,无疑是对推动我国数学的科研与教学十分有益的事。这次科学出版社购买了版权,一次影印了23本施普林格出版社出版的数学书,就是一件好事,也是值得继续做下去的事情。大体上分一下,这23本书中,包括基础数学书5本,应用数学书6本与计算数学书12本,其中有些书也具有交叉性质。这些书都是很新的,2000年以后出版的占绝大部分,共计16本,其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿,例如基础数学中的数论、代数与拓扑三本,都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点,基础数学类的书以“经典”为主,应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家,例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士,曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。

内容概要

This work describes the fundamental principles, problems, and methods of classical mechanics. The main attention is devoted to the mathematical side of the subject. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics. The book is significantly expanded compared to the previous edition. The authors have added two chapters on the variational principles and methods of classical mechanics as well as on tensor invariants of equations of dynamics. Moreover, various other sections have been revised, added or expanded. The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects.The book addresses all mathematicians, physicists and engineers.

作者简介

作者:(俄罗斯)阿诺德(Vladimir I.Arnold) 等

书籍目录

1
Basic
Principles
of
Classical
Mechanics
1.1
Newtonian
Mechanics
1.1.1
Space,
Time,
Motion
1.1.2
Newton-Laplace
Principle
of
Determinacy
1.1.3
Principle
of
Relativity
1.1.4
Principle
of
Relativity
and
Forces
of
Inertia
1.1.5
Basic
Dynamical
Quantities.
Conservation
Laws...
1.2
Lagrangian
Mechanics
1.2.1
Preliminary
Remarks
1.2.2
Variations
and
Extremals
1.2.3
Lagrange's
Equations
1.2.4
Poincare's
Equations
1.2.5
Motion
with
Constraints
1.3
Hamiltonian
Mechanics
1.3.1
Symplectic
Structures
and
Hamilton's
Equations
1.3.2
Generating
Functions
1.3.3
Symplectic
Structure
of
the
Cotangent
Bundle
1.3.4
The
Problem
of
n
Point
Vortices
1.3.5
Action
in
the
Phase
Space
1.3.6
Integral
Invariant
1.3.7
Applications
to
Dynamics
of
Ideal
Fluid
1.4
Vakonomic
Mechanics
1.4.1
Lagrange's
Problem
1.4.2
Vakonomic
Mechanics
1.4.3
Principle
of
Determinacy
1.4.4
Hamilton's
Equations
in
Redundant
Coordinates
1.5
Hamiltonian
Formalism
with
Constraints
1.5.1
Dirac's
Problem
1.5.2
Duality
'
1.6
Realization
of
Constraints
1.6.1
Various
Methods
of
Realization
of
Constraints
1.6.2
Holonomic
Constraints
1.6.3
Anisotropic
Friction
1.6.4
Adjoint
Masses
1.6.5
Adjoint
Masses
and
Anisotropic
Friction
1.6.6
Small
Masses2
The
n-Body
Problem
2.1
The
Two-Body
Problem
2.1.1
Orbits
2.1.2
Anomalies
2.1.3
Collisions
and
Regularization
2.1.4
Geometry
of
Kepler's
Problem
2.2
Collisions
and
Regularization
2.2.1
Necessary
Condition
for
Stability
2.2.2
Simultaneous
Collisions
2.2.3
Binary
Collisions
2.2.4
Singularities
of
Solutions
of
the
n-Body
Problem
2.3
Particular
Solutions
2.3.1
Central
Configurations
2.3.2
Homographic
Solutions
2.3.3
Effective
Potential
and
Relative
Equilibria
2.3.4
Periodic
Solutions
in
the
Case
of
Bodies
cf
Equal
Masses
2.4
Final
Motions
in
the
Three-Body
Problem
2.4.1
Classification
of
the
Final
Motions
According
to
Chazy.
2.4.2
Symmetry
of
the
Past
and
Future
2.5
Restricted
Three-Body
Problem
2.5.1
Equations
of
Motion.
The
Jacobi
Integral
2.5.2
Relative
Equilibria
and
Hill
Regions
2.5.3
Hill's
Problem
2.6
Ergodic
Theorems
of
Celestial
Mechanics
2.6.1
Stability
in
the
Sense
of
Poisson
2.6.2
Probability
of
Capture
2.7
Dynamics
in
Spaces
of
Constant
Curvature
2.7.1
Generalized
Bertrand
Problem
2.7.2
Kepler's
Laws
2.7.3
Celestial
Mechanics
in
Spaces
of
Constant
Curvature
2.7.4
Potential
Theory
in
Spaces
of
Constant
Curvature3
Symmetry
Groups
and
Order
Reduction.
3.1
Symmetries
and
Linear
Integrals
3.1.1
NSther's
Theorem
3.1.2
Symmetries
in
Non-Holonomic
Mechanics
3.1.3
Symmetries
in
Vakonomic
Mechanics
3.1.4
Symmetries
in
Hamiltonian
Mechanics
3.2
Reduction
of
Systems
with
Symmetries
……4
Variational
Principles
and
Methods5
Integrable
Systems
and
Integration
Methods6
Perturbation
Theory
for
Integrable
Systems7
Non-Integrable
Systems8
Theory
of
Small
Oscillations9
Tensor
Invariants
of
Equations
of
DynamicsRecommended
ReadingBibliographyIndex
of
NamesSubject
Index

章节摘录

插图:This
problem
has
many
common
features
with
the
classical
n-body
prob-lem
in
Euclidean
space.
However,
there
are
also
essential
differences.
First,the
two-body
problem
on
S3
proves
to
be
non-integrable:
there
are
not
suffi-ciently
many
first
integrals
for
its
solution
and
its
orbits
look
quite
complicated(see
[137]).
Here
the
main
difficulty
is
related
to
the
fact
that
the
Galileo-Newton
law
of
inertia
does
not
hold:
the
centre
of
mass
of
gravitating
pointsno
longer
moves
along
an
arc
of
a
great
circle.Furthermore,
as
in
the
classical
case,
binary
collisions
admit
regularization.However,
the
question
whether
the
generalized
Sundman
theorem
is
valid
forthe
three-body
problem
in
spaces
of
constant
curvature
remains
open.
Thisquestion
essentially
reduces
to
the
problem
of
elimination
of
triple
collisions.Recall
that
in
the
ordinary
three-body
problem
the
absence
of
simultaneouscollisions
is
guaranteed
by
a
non-zero
constant
value
of
the
angular
momentumof
the
system
of
n
points
with
respect
to
their
centre
of
mass
(Theorem
2.3).Of
interest
is
the
problem
of
finding
partial
solutions
for
n
gravitatingbodies
in
spaces
of
constant
curvature
(similar
to
the
classical
solutions
ofEuler
and
Lagrange).
Results
in
this
direction
can
be
found
in
the
book
[137].The
restricted
three-body
problem
was
studied
in
this
book:
relative
equilibriawere
found
and
the
Hill
regions
were
constructed.

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《经典力学与天体力学中的数学问题(第3版)》:国外数学名著系列

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用户评论 (总计22条)

 
 

  •     这个书与那个 经典力学的数学方法 是一脉相承呀
  •     杰作,虽然比较难,凝聚了深刻的数学思考,不适合抱着学习力学或数学的角度去看,而是抱着理解这个世界的角度去看有可能参透。
  •     但是拍案大叫看不懂!,最近迷漫画
  •     但大师的著作毋庸置疑,这本书内容非常丰富
  •     这套书就是好!虽然现在只有3岁,书有点贵
  •     冲击140以上的,帮助建立知识框架
  •     希望这本书能对我有大的帮助,锻炼思维吧
  •     包装还行,不像别人写书全是抄抄国外的
  •     就是本专业教材,真心挺好要好好分析总结
  •     做完后及格没问题,就比较喜欢在当当。这书的翻译的也挺不错的。
  •     不过内容分析有点少,适合孩子复习用
  •     她看不懂不喜欢看,孩子每晚睡前都看的书
  •     书本的质量比我在店里面买到的要好,看看总好
  •     具体内容需要时间看练习,幽默的语言方式使枯燥的数学知识有趣易懂!对孩子的思维锻炼很有帮助
  •     很好的代数几何书,内容还没看
  •     建议复习完一遍之后在做。。。,解析很详细的
  •     很好的一本辅助教材,很值得孩子去学习这些策略
  •     不过应该是一本不错的数学建模教材,买的书很实惠
  •     上课前可以作为备课参考!,但是貌似是考研必备啊
  •     书本有点折痕,很好很经典
  •     感觉李永乐老师线代教的很好,好好看看
  •     非常不错,孩子很有兴致做
 

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