Advanced mechanics: from Euler's determinism to Arnold's chaos
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2013
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 163 S. graph. Darst. |
| ISBN: | 9780199670857 9780199670864 0199670862 |
Internformat
MARC
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| 100 | 1 | |a Rajeev, Sarada G. |d 1959- |e Verfasser |0 (DE-588)1038558972 |4 aut | |
| 245 | 1 | 0 | |a Advanced mechanics |b from Euler's determinism to Arnold's chaos |c S. G. Rajeev |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2013 | |
| 300 | |a XIII, 163 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Continuum mechanics | |
| 650 | 0 | 7 | |a Mechanik |0 (DE-588)4038168-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1818239795834388480 |
|---|---|
| adam_text |
Contents
List of Figures
xv
1
The variational principle
1
1.1
Euler-Lagrange equations
3
1.2
The Variational principle of mechanics
4
1.3
Deduction from quantum mechanics*
5
2
Conservation laws
7
2.1
Generalized momenta
7
2.2
Conservation laws
7
2.3
Conservation of energy
8
2.4
Minimal surface of revolution
9
3
The simple pendulum
11
3.1
Algebraic formulation
12
3.2
Primer on Jacobi functions
13
3.3
Elliptic curves*
14
3.4
Imaginary time
15
3.5
The arithmetic-geometric mean*
16
3.6
Doubly periodic functions*
19
4
The Kepler problem
21
4.1
The orbit of a planet lies on a plane which contains the Sun
21
4.2
The line connecting the planet to the Sun sweeps equal areas
in equal times
21
4.3
Planets move along elliptical orbits with the Sun at a focus
22
4.4
The ratio of the cube of the semi-major axis to the square
of the period is the same for all planets
22
4.5
The shape of the orbit
23
5
The rigid body
27
5.1
The moment of inertia
27
5.2
Angular momentum
28
5.3
Euler
"s
equations
29
5.4
Jacobi
"s
solution
30
6
Geometric theory of ordinary differential equations
33
6.1
Phase space
33
6.2
Differential manifolds
34
6.3
Vector fields as derivations
36
6.4
Fixed points
38
xii Contents
7
Hamilton's principle
7.1
Generalized momenta
7.2
Poisson
brackets
7.3
The star product*
7.4
Canonical transformation
7.5
Infinitesimal canonical transformations
7.6
Symmetries and conservation laws
7.7
Generating function
43
43
45
46
47
48
51
52
8
Geodesies
55
8.1
The metric
55
8.2
The variational principle
56
8.3
The sphere
58
8.4
Hyperbolic space
60
8.5
Hamiltonian formulation of geodesies
61
8.6
Geodesic formulation of Newtonian mechanics*
62
8.7
Geodesies in general relativity*
63
9
Hamilton-Jacobi theory
69
9.1
Conjugate variables
69
9.2
The Hamilton-Jacobi equation
70
9.3
The
Euler
problem
71
9.4
The classical limit of the
Schrödinger
equation*
73
9.5
Hamilton-Jacobi equation in Riemannian manifolds*
74
9.6
Analog}- to optics*
75
10
Integrable
systems
77
10.1
The simple harmonic oscillator
78
10.2
The general one-dimensional system
79
10.3
Bohr-Sommerfeld quantization
80
10.4
The Kepler problem
81
10.5
The reiativistic Kepler problem*
83
10.6
Several degrees of freedom
83
10.7
The heavy top
84
11
The three body problem
87
11.1
Preliminaries
87
11.2
Scale
invariance
88
11.3
Jacobi co-ordinates
89
11.4
The
~¡
potential
92
11.5
Montgomery's pair of pants
93
12
The restricted three body problem
95
12.1
The motion of the primaries
95
12.2
The Lagrangian
95
12.3
A useful identity
97
12.4
Equilibrium points
97
12.5
Hilľs
regions
98
Contents xiii
12.6
The second derivative of the potential
98
12.7
Stability theory
100
13
Magnetic fields
103
13.1
The equations of motion
103
13.2
Hamiltonian formalism
103
13.3
Canonical momentum
105
13.4
The Lagrangian
105
13.5
The magnetic
monopole*
106
13.6
The Penning trap
108
14
Poisson
and symplectic manifolds
111
14.1
Poisson
brackets on the sphere
Ш
14.2
Equations of motion
112
14.3
Poisson
manifolds
113
14.4
Liouville's theorem
114
15
Discrete time
117
15.1
First order symplectic integrators
117
15.2
Second order symplectic integrator
119
15.3
Chaos with one degree of freedom
121
16
Dynamics in one real variable
125
16.1
Maps
125
16.2
Doubling modulo one
126
16.3
Stability of fixed points
128
16.4
Unimodal maps
130
16.5
Invariant measures
133
17
Dynamics on the complex plane
137
17.1
The Riemann sphere
137
17.2
Mobius transformations
138
17.3
Dynamics of a Mobius transformation
139
17.4
The map
z
н-
►
z2
141
17.5
Metric on the sphere
142
17.6
Metric spaces
143
17.7
Julia and Fatou sets
144
18 KAM
theory
149
18.1
Newton's iteration
149
18.2
Diagonalization of matrices
150
18.3
Normal form of circle maps
152
18.4
Diophantine approximation
155
18.5
Hamiltonian systems
156
Further reading
159
Index
161 |
| any_adam_object | 1 |
| author | Rajeev, Sarada G. 1959- |
| author_GND | (DE-588)1038558972 |
| author_facet | Rajeev, Sarada G. 1959- |
| author_role | aut |
| author_sort | Rajeev, Sarada G. 1959- |
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| building | Verbundindex |
| bvnumber | BV041198331 |
| classification_rvk | UB 2405 UF 1000 |
| ctrlnum | (OCoLC)856866324 (DE-599)BVBBV041198331 |
| discipline | Physik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV041198331 |
| illustrated | Illustrated |
| indexdate | 2024-12-12T13:03:14Z |
| institution | BVB |
| isbn | 9780199670857 9780199670864 0199670862 |
| language | English |
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| physical | XIII, 163 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Rajeev, Sarada G. 1959- Verfasser (DE-588)1038558972 aut Advanced mechanics from Euler's determinism to Arnold's chaos S. G. Rajeev 1. ed. Oxford Oxford Univ. Press 2013 XIII, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Continuum mechanics Mechanik (DE-588)4038168-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Mechanik (DE-588)4038168-7 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026173270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rajeev, Sarada G. 1959- Advanced mechanics from Euler's determinism to Arnold's chaos Continuum mechanics Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4123623-3 |
| title | Advanced mechanics from Euler's determinism to Arnold's chaos |
| title_auth | Advanced mechanics from Euler's determinism to Arnold's chaos |
| title_exact_search | Advanced mechanics from Euler's determinism to Arnold's chaos |
| title_full | Advanced mechanics from Euler's determinism to Arnold's chaos S. G. Rajeev |
| title_fullStr | Advanced mechanics from Euler's determinism to Arnold's chaos S. G. Rajeev |
| title_full_unstemmed | Advanced mechanics from Euler's determinism to Arnold's chaos S. G. Rajeev |
| title_short | Advanced mechanics |
| title_sort | advanced mechanics from euler s determinism to arnold s chaos |
| title_sub | from Euler's determinism to Arnold's chaos |
| topic | Continuum mechanics Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Continuum mechanics Mechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026173270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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