Essentials of Hamiltonian dynamics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 188 S. Ill., graph. Darst. |
| ISBN: | 9781107005204 1107005205 |
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MARC
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| 100 | 1 | |a Lowenstein, John H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Essentials of Hamiltonian dynamics |c John H. Lowenstein |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XIII, 188 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page
xi
Fundamentals of classical dynamics
1
1.1
Newtonian mechanics
1
1.2
Configuration space
2
1.2.1
Particle on a sphere
2
1.2.2
Planar double pendulum
2
1.2.3
Independence of constraints
4
1.2.4
Configuration space as a differential manifold
5
1.3
Lagrangian formulation of Newtonian mechanics
7
1.4
Hamiltonian formulation
8
1.4.1
Introduction of the Hamiltonian
8
1.4.2
Phase space
10
1.5
Examples
11
1.5.1
Harmonic oscillator
11
1.5.2
Simple pendulum
11
1.5.3
Exact solution of the pendulum equations
14
1.5.4
A bead on a rotating circle
15
1.5.5
Spherical pendulum
18
1.5.6
Rigid body with one point fixed
21
Exercises
26
The Hamiltonian formalism
29
2.1
The
Poisson
bracket
29
2.2
Canonical transformations
30
2.3
Simple examples
32
2.4
Canonical
invariance
of
Lagrange
brackets
32
2.5
Generating functions for canonical transformations
34
2.6
Canonical
invariance
of phase-space volume
38
vu
viii Contents
2.7
Covariance
of Hamilton s equations with explicit time
dependence
39
2.8
Continuous one-parameter groups of canonical transformations
40
2.9
The Hamiltonian formulation of electrodynamics
42
2.10
Normal modes for linear oscillators
44
Exercises
54
3
Integrable
systems
56
3.1
The Liouville-Arnol d theorem
56
3.2
Fast track for separable systems
57
3.3
System with one degree of freedom
60
3.4
The Kepler problem in spherical polar coordinates
61
3.5
Proof of the Liouville-Arnol d theorem
64
3.6
Planar free-particle examples
69
3.6.1
A two-dimensional free particle, model
1 70
3.6.2
A two-dimensional free particle, model
2 71
3.6.3
Circular stadium billiard
73
3.7
Spherical pendulum
78
3.8
The three-particle
Toda
model
85
Exercises
91
4
Canonical perturbation theory
97
4.1
General approach
97
4.2
Simple pendulum revisited
98
4.3
Two harmonic oscillators with quartic coupling
102
4.4
Gyrating charge in an electrostatic wave
104
4.5
Birkhoff-Gustavson perturbation theory
109
4.6
A formal second integral for the
Hénon-Heiles
model
110
4.7
Integrability analysis of
Hénon-Heiles-like
systems
112
Exercises
115
5
Order and chaos in Hamiltonian systems
121
5.1
Nonlinear stability
122
5.2
The
KAM
theorem
122
5.3
Nonlinear stability of the
Lagrange
points
127
5.4
Kicked oscillators
129
5.5
Lyapunov exponents
136
5.6
Web-map Lyapunov exponents
138
5.7
A model of a chaotically rotating moon
139
Exercises
142
6
The swing-spring
148
6.1
Two-dimensional motion
149
Contents ix
6.2
Integrable
approximations
for small
oscillations
152
6.3
Three commuting integrals
154
6.4
Dynamics on the level sets
156
6.5
Constraints among the integrals
158
6.6
Flow coordinates and the period lattice
165
6.7
Monodromy
168
6.8
Periodic shift of the swing plane
172
6.9
The swing-spring in molecular modeling
176
Exercises
177
Appendix
Mathematica®
samples
178
A.
1
Numerical integration of equations of motion
178
A.2 Hyperion movie
179
A.3 Simple pendulum perturbation theory
181
A.4 Birkhoff-Gustavson perturbation theory
181
References
184
Index
186
|
| any_adam_object | 1 |
| author | Lowenstein, John H. |
| author_facet | Lowenstein, John H. |
| author_role | aut |
| author_sort | Lowenstein, John H. |
| author_variant | j h l jh jhl |
| building | Verbundindex |
| bvnumber | BV039680406 |
| classification_rvk | UF 1950 |
| ctrlnum | (OCoLC)754168378 (DE-599)BVBBV039680406 |
| dewey-full | 531.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.11 |
| dewey-search | 531.11 |
| dewey-sort | 3531.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039680406 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:08:50Z |
| institution | BVB |
| isbn | 9781107005204 1107005205 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024529420 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-20 |
| physical | XIII, 188 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Lowenstein, John H. Verfasser aut Essentials of Hamiltonian dynamics John H. Lowenstein 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 XIII, 188 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hamiltonian systems Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Hamilton-Formalismus (DE-588)4376155-0 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lowenstein, John H. Essentials of Hamiltonian dynamics Hamiltonian systems Hamilton-Formalismus (DE-588)4376155-0 gnd |
| subject_GND | (DE-588)4376155-0 |
| title | Essentials of Hamiltonian dynamics |
| title_auth | Essentials of Hamiltonian dynamics |
| title_exact_search | Essentials of Hamiltonian dynamics |
| title_full | Essentials of Hamiltonian dynamics John H. Lowenstein |
| title_fullStr | Essentials of Hamiltonian dynamics John H. Lowenstein |
| title_full_unstemmed | Essentials of Hamiltonian dynamics John H. Lowenstein |
| title_short | Essentials of Hamiltonian dynamics |
| title_sort | essentials of hamiltonian dynamics |
| topic | Hamiltonian systems Hamilton-Formalismus (DE-588)4376155-0 gnd |
| topic_facet | Hamiltonian systems Hamilton-Formalismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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