Mechanics: from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Dt. Ausg. u.d.T.: Scheck, Florian: Mechanik |
| Beschreibung: | XIV, 547 S. graph. Darst. |
| ISBN: | 3540219250 |
Internformat
MARC
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| 020 | |a 3540219250 |9 3-540-21925-0 | ||
| 035 | |a (OCoLC)634200614 | ||
| 035 | |a (DE-599)BVBBV019582679 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
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| 084 | |a PHY 200f |2 stub | ||
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| 100 | 1 | |a Scheck, Florian |d 1936-2024 |e Verfasser |0 (DE-588)121611493 |4 aut | |
| 245 | 1 | 0 | |a Mechanics |b from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions |c Florian Scheck |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XIV, 547 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Dt. Ausg. u.d.T.: Scheck, Florian: Mechanik | ||
| 650 | 0 | 7 | |a Mechanik |0 (DE-588)4038168-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Mechanik |0 (DE-588)4038168-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012919667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012919667 | ||
Datensatz im Suchindex
| _version_ | 1804132939780325376 |
|---|---|
| adam_text | Contents
1.
Elementary Newtonian Mechanics
............................. 1
1.1
Newton s Laws
(1687)
and Their Interpretation
................ ]
1.2
Uniform Rectilinear Motion and Inertia! Systems
............... 4
1.3
Inerţial
Frames in Relative Motion
........................... 6
1.4
Momentum and Force
...................................... 6
1.5
Typical Forces. A Remark About Units
....................... 8
1.6
Space, Time, and Forces
.................................... 10
1.7
The Two-Body System with Internal Forces
...................
Π
1.7.1
Center-of-Mass and Relative Motion
................... 11
1.7.2
Example: The Gravitational Force
Between Two Celestial Bodies (Kepler s Problem)
....... 13
1.7.3
Center-of-Mass and Relative Momentum
in the Two-Body System
............................. 19
1.8
Systems of Finitely Many Particles
........................... 20
1.9
The Principle of Center-of-Mass Motion
...................... 21
1.10
The Principle of Angular-Momentum Conservation
............. 21
1.11
The Principle of Energy Conservation
......................... 22
1.12
The Closed n-Particle System
................................ 23
1.13
Galilei Transformations
..................................... 24
1.14
Space and Time with Galilei
Invariance
....................... 27
1.15
Conservative Force Fields
................................... 29
1.16
One-Dimensional Motion of a Point Particle
................... 32
1.17
Examples of Motion in One Dimension
....................... 33
1.17.1
The Harmonic Oscillator
............................. 33
1.17.2
The Planar Mathematical Pendulum
.................... 35
1.18
Phase Space for the n-Particle System (in R3)
.................. 37
1.19
Existence and Uniqueness of the Solutions of
χ
=
F{x, t)
....... 38
1.20
Physical Consequences of the Existence and Uniqueness Theorem
39
1.21
Linear Systems
............................................ 41
1.21.1
Linear, Homogeneous Systems
........................ 41
1.21.2
Linear, Inhomogeneous Systems
....................... 42
1.22
Integrating One-Dimensional Equations of Motion
.............. 42
1.23
Example: The Planar Pendulum for Arbitrary Deviations
from the Vertical
........................................... 44
X
Contents
1.24
Example: The Two-Body System with a Central Force
.......... 47
1.25
Rotating Reference Systems: Coriolis and Centrifugal Forces
.... 54
1.26
Examples of Rotating Reference Systems
..................... 55
1.27
Scattering of Two Particles that Interact via a Central Force:
Kinematics
................................................ 63
1.28
Two-Particle Scattering with a Central Force: Dynamics
......... 67
1.29
Example: Coulomb Scattering of Two Particles
with Equal Mass and Charge
................................ 71
1.30
Mechanical Bodies of Finite Extension
........................ 75
1.31
Time Averages and the Virial Theorem
....................... 79
Appendix: Practical Examples
.................................... 81
2.
The Principles of Canonical Mechanics
........................ 87
2.1
Constraints and Generalized Coordinates
...................... 87
2.1.1
Definition of Constraints
............................. 87
2.1.2
Generalized Coordinates
.............................. 89
2.2
D Alembert s Principle
...................................... 89
2.2.1
Definition of Virtual Displacements
.................... 89
2.2.2
The Static Case
..................................... 90
2.2.3
The Dynamical Case
................................. 90
2.3
Lagrange s Equations
....................................... 92
2.4
Examples of the Use of Lagrange s Equations
.................. 93
2.5
A Digression on Variational Principles
........................ 95
2.6
Hamilton s Variational Principle
(1834)....................... 98
2.7
The Euler-Lagrange Equations
............................... 98
2.8
Further Examples of the Use of Lagrange s Equations
........... 99
2.9
A Remark About Nonuniqueness of the Lagrangian Function
___101
2.10
Gauge Transformations of the Lagrangian Function
.............102
2.11
Admissible Transformations of the Generalized Coordinates
.....103
2.12
The Hamiltonian Function and Its Relation
to the Lagrangian Function
L
................................104
2.13
The Legendre Transformation for the Case of One Variable
......105
2.14
The Legendre Transformation for the Case of Several Variables
.. 107
2.15
Canonical Systems
.........................................108
2.16
Examples of Canonical Systems
..............................109
2.17
The Variational Principle Applied to the Hamiltonian Function
...
Ill
2.18
Symmetries and Conservation Laws
..........................112
2.19
Noether s Theorem
.........................................113
2.20
The Generator for Infinitesimal Rotations About an Axis
........115
2.21
More About the Rotation Group
.............................117
2.22
Infinitesimal Rotations and Their Generators
...................119
2.23
Canonical Transformations
..................................121
2.24
Examples of Canonical Transformations
.......................125
2.25
The Structure of the Canonical Equations
.....................126
2.26
Example: Linear Autonomous Systems in One Dimension
.......127
Contents
XI
2.27
Canonical Transformations in Compact Notation
...............129
2.28
On the Symplectic Structure of Phase Space
...................131
2.29
Liouvilie s Theorem
........................................134
2.29.1
The Local Form
.....................................135
2.29.2
The Global Form
....................................136
2.30
Examples for the Use of Liouvilie s Theorem
..................137
2.31
Poisson
Brackets
...........................................140
2.32
Properties of
Poisson
Brackets
...............................143
2.33
Infinitesimal Canonical Transformations
.......................145
2.34
Integrals of the Motion
.....................................146
2.35
The Hamilton-Jacobi Differential Equation
....................149
2.36
Examples for the Use of the Hamilton-Jacobi Equation
.........150
2.37
The Hamilton-Jacobi Equation and
Integrable
Systems
..........154
2.37.1
Local Rectification of Hamiltonian Systems
.............154
2.37.2
Integrable
Systems
...................................158
2.37.3
Angle and Action Variables
...........................163
2.38
Perturbing Quasiperiodic Hamiltonian Systems
.................164
2.39
Autonomous,
Nondegenerate
Hamiltonian Systems
in the Neighborhood of
Integrable
Systems
....................
1
67
2.40
Examples. The Averaging Principle
...........................168
2.40.1
The Anharmonic Oscillator
...........................168
2.40.2
Averaging of Perturbations
............................170
2.41
Generalized Theorem of Noether
.............................172
Appendix: Practical Examples
....................................180
3.
The Mechanics of Rigid Bodies
............................... 185
3.1
Definition of Rigid Body
....................................185
3.2
Infinitesimal Displacement of a Rigid Body
...................187
3.3
Kinetic Energy and the Inertia Tensor
.........................189
3.4
Properties of the Inertia Tensor
..............................191
3.5
Steiner s Theorem
..........................................195
3.6
Examples of the Use of Steiner s Theorem
....................196
3.7
Angular Momentum of a Rigid Body
.........................201
3.8
Force-Free Motion of Rigid Bodies
...........................203
3.9
Another Parametrization of Rotations: The
Euler
Angles
........205
3.10
Definition of Euierian Angles
................................207
3.11
Equations of Motion of Rigid Bodies
.........................208
3.12
Euler s Equations of Motion
.................................211
3.13
Euler s Equations Applied to a Force-Free Top
.................214
3.14
The Motion of a Free Top and Geometric Constructions
.........218
3.15
The Rigid Body in the Framework of Canonical Mechanics
......221
3.16
Example: The Symmetric Children s Top
in a Gravitational Field
.....................................225
3.17
More About the Spinning Top
...............................227
3.18
Spherical Top with Friction: The
Tippe Top .................229
XII Contents
3.18.1
Conservation
Law and Energy Considerations
...........230
3.18.2
Equations of Motion and Solutions
with Constant Energy
................................232
Appendix: Practical Examples
....................................236
4.
Relativistic Mechanics
....................................... 239
4.1
Failures of Nonrelativistic Mechanics
.........................240
4.2
Constancy of the Speed of Light
.............................243
4.3
The
Lorentz
Transformations
................................244
4.4
Analysis of
Lorentz
and
Poincaré
Transformations
..............250
4.4.1
Rotations and Special
Lorentz
Tranformations
( Boosts )
..........................................252
4.4.2
Interpretation of Special
Lorentz
Transformations
........256
4.5
Decomposition of
Lorentz
Transformations
into Their Components
.....................................257
4.5.1
Proposition on Orthochronous,
Proper
Lorentz
Transformations
.......................257
4.5.2
Corollary of the Decomposition Theorem
and Some Consequences
..............................259
4.6
Addition of Relativistic Velocities
............................262
4.7
Galilean and Lorentzian Space-Time Manifolds
................264
4.8
Orbital Curves and Proper Time
.............................268
4.9
Relativistic Dynamics
.......................................270
4.9.1
Newton s Equation
...................................270
4.9.2
The Energy-Momentum Vector
........................272
4.9.3
The
Lorentz
Force
...................................275
4.10
Time Dilatation and Scale Contraction
........................277
4.11
More About the Motion of Free Particles
......................279
4.12
The
Conformai
Group
......................................282
5.
Geometric Aspects of Mechanics
.............................. 283
5.1
Manifolds of Generalized Coordinates
........................284
5.2
Differentiable Manifolds
....................................287
5.2.1
The Euclidean Space
W
.............................287
5.2.2
Smooth or Differentiable Manifolds
....................289
5.2.3
Examples of Smooth Manifolds
.......................291
5.3
Geometrical Objects on Manifolds
............................295
5.3.1
Functions and Curves on Manifolds
....................296
5.3.2
Tangent Vectors on a Smooth Manifold
.................298
5.3.3
The Tangent Bundle of a Manifold
.....................300
5.3.4
Vector Fields on Smooth Manifolds
....................301
5.3.5
Exterior Forms
......................................305
5.4
Calculus on Manifolds
......................................307
5.4.1
Differentiable Mappings of Manifolds
..................307
5.4.2
Integral Curves of Vector Fields
.......................309
Contenis
ХШ
5.4.3
Exterior
Product
of One-Forms
........................311
5.4.4
The Exterior Derivative
...............................313
5.4.5
Exterior Derivative and Vectors in R3
..................315
5.5
Hamilton-Jacobi and Lagrangian Mechanics
...................317
5.5.1
Coordinate Manifold Q, Velocity Space TQ,
and Phase Space T*Q
...............................317
5.5.2
The Canonical One-Form on Phase Space
...............321
5.5.3
The Canonical, Symplectic Two-Form on
M
............324
5.5.4
Symplectic Two-Form and Darboux s Theorem
..........326
5.5.5
The Canonical Equations
.............................329
5.5.6
The
Poisson
Bracket
.................................332
5.5.7
Time-Dependent Hamiltonian Systems
..................335
5.6
Lagrangian Mechanics and
Lagrange
Equations
................337
5.6.1
The Relation Between the Two Formulations
of Mechanics
.......................................337
5.6.2
The Lagrangian Two-Form
............................339
5.6.3
Energy Function on
Γ
Q
and Lagrangian Vector Field
___340
5.6.4
Vector Fields on Velocity Space
T Q
and
Lagrange
Equations
..............................342
5.6.5
The Legendre Transformation and the Correspondence
of Lagrangian and Hamiltonian Functions
...............344
5.7
Riemannian Manifolds in Mechanics
..........................347
5.7.1 Affine
Connection and Parallel Transport
...............348
5.7.2
Parallel Vector Fields and Geodesies
...................350
5.7.3
Geodesies as Solutions of Euler-Lagrange Equations
.....351
5.7.4
Example: Force-Free Asymmetric Top
..................352
6.
Stability and Chaos
......................................... 355
6.1
Qualitative Dynamics
.......................................355
6.2
Vector Fields as Dynamical Systems
..........................356
6.2.1
Some Definitions of Vector Fields
and Their Integral Curves
.............................358
6.2.2
Equilibrium Positions and Linearization
of Vector Fields
.....................................360
6.2.3
Stability of Equilibrium Positions
......................363
6.2.4
Critical Points of Hamiltonian Vector Fields
.............367
6.2.5
Stability and Instability of the Free Top
................369
6.3
Long-Term Behavior of Dynamical Flows and Dependence
on External Parameters
.....................................371
6.3.1
Flows in Phase Space
................................372
6.3.2
More General Criteria for Stability
.....................373
6.3.3
Attractors
...........................................376
6.3.4
The
Poincaré
Mapping
...............................380
6.3.5
Bifurcations of Flows at Critical Points
.................384
6.3.6
Bifurcations of Periodic Orbits
........................388
XIV Contents
6.4
Deterministic Chaos
........................................390
6.4.1
Iterative Mappings in One Dimension
..................390
6.4.2
Qualitative Definitions of Deterministic Chaos
...........392
6.4.3
An Example: The Logistic Equation
...................396
6.5
Quantitative Measures of Deterministic Chaos
.................401
6.5.1
Routes to Chaos
.....................................401
6.5.2
Liapunov Characteristic Exponents
.....................405
6.5.3
Strange Attractors
...................................407
6.6
Chaotic Motions in Celestial Mechanics
.......................409
6.6.1
Rotational Dynamics of Planetary Satellites
.............409
6.6.2
Orbital Dynamics of Asteroids with Chaotic Behavior
.... 415
7.
Continuous Systems
......................................... 419
7.1
Discrete and Continuous Systems
............................419
7.2
Transition to the Continuous System
..........................423
7.3
Hamilton s Variational Principle for Continuous Systems
........425
7.4
Canonically Conjugate Momentum and Hamiltonian Density
.....427
7.5
Example: The Pendulum Chain
..............................428
7.6
Comments and Outlook
.....................................432
Exercises
...................................................... 437
Chapter
1 :
Elementary Newtonian Mechanics
.......................437
Chapter
2:
The Principles of Canonical Mechanics
..................444
Chapter
3:
The Mechanics of Rigid Bodies
.........................452
Chapter
4:
Relativistic Mechanics
.................................455
Chapter
5:
Geometric Aspects of Mechanics
........................458
Chapter
6:
Stability and Chaos
...................................460
Solution of Exercises
............................................ 463
Chapter
1 :
Elementary Newtonian Mechanics
.......................463
Chapter
2:
The Principles of Canonical Mechanics
..................478
Chapter
3:
The Mechanics of Rigid Bodies
.........................497
Chapter
4:
Relativistic Mechanics
.................................505
Chapter
5:
Geometric Aspects of Mechanics
........................517
Chapter
6:
Stability and Chaos
...................................522
Author Index
................................................... 541
Subject Index
.................................................. 543
|
| any_adam_object | 1 |
| author | Scheck, Florian 1936-2024 |
| author_GND | (DE-588)121611493 |
| author_facet | Scheck, Florian 1936-2024 |
| author_role | aut |
| author_sort | Scheck, Florian 1936-2024 |
| author_variant | f s fs |
| building | Verbundindex |
| bvnumber | BV019582679 |
| classification_rvk | UF 1000 |
| classification_tum | PHY 200f MTA 001f |
| ctrlnum | (OCoLC)634200614 (DE-599)BVBBV019582679 |
| discipline | Physik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV019582679 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:48Z |
| institution | BVB |
| isbn | 3540219250 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012919667 |
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| physical | XIV, 547 S. graph. Darst. |
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| publisher | Springer |
| record_format | marc |
| spelling | Scheck, Florian 1936-2024 Verfasser (DE-588)121611493 aut Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions Florian Scheck 4. ed. Berlin [u.a.] Springer 2005 XIV, 547 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dt. Ausg. u.d.T.: Scheck, Florian: Mechanik Mechanik (DE-588)4038168-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mechanik (DE-588)4038168-7 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012919667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scheck, Florian 1936-2024 Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4123623-3 |
| title | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions |
| title_auth | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions |
| title_exact_search | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions |
| title_full | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions Florian Scheck |
| title_fullStr | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions Florian Scheck |
| title_full_unstemmed | Mechanics from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions Florian Scheck |
| title_short | Mechanics |
| title_sort | mechanics from newton s laws to deterministic chaos with 174 figures and 117 problems with complete solutions |
| title_sub | from Newton's laws to deterministic chaos ; with 174 figures and 117 problems with complete solutions |
| topic | Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012919667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scheckflorian mechanicsfromnewtonslawstodeterministicchaoswith174figuresand117problemswithcompletesolutions |