Nonlinear mechanics: a supplement to Theoretical mechanics of particles and continua
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publ.
2006
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis Klappentext |
| Physical Description: | VI, 154 S. graph. Darst. |
| ISBN: | 9780486450315 0486450317 |
Staff View
MARC
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| 245 | 1 | 0 | |a Nonlinear mechanics |b a supplement to Theoretical mechanics of particles and continua |c Alexander L. Fetter ; John Dirk Walecka |
| 264 | 1 | |a Mineola, NY |b Dover Publ. |c 2006 | |
| 300 | |a VI, 154 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Continuum mechanics | |
| 650 | 4 | |a Field theory (Physics) | |
| 700 | 1 | |a Walecka, John Dirk |d 1932- |e Verfasser |0 (DE-588)132844788 |4 aut | |
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Record in the Search Index
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| adam_text | CONTENTS
PART I: INTRODUCTION
1
1.
Motivation
2
PART II: NONLINEAR CONTINUOUS SYSTEMS
9
2.
Linearized stability analysis
10
Rayleigh-Taylor instability
10
Kelvin-Helmholtz instability
15
3.
Rayleigh-Bénard
problem: basic formulation
18
Boussinesq approximation and thermal expansion
20
Linearized perturbation equations
23
Boundary conditions
24
4.
Rayleigh-Bénard
problem: linearized theory of convective instability
26
Proof that solutions are not oscillatory
26
Vorticity and the eigenvalue equation
29
Free-free boundary conditions: exact solution
32
Rigid-rigid boundary conditions: sketch of exact solution
35
5.
Rayleigh-Bénard
problem: expansion in Fourier modes
37
6. Lorenz
equations: direct derivation for simple physical configuration
45
PART III: DISCRETE DYNAMICAL SYSTEMS
51
7.
Example of a nonlinear oscillator
52
Duffing oscillator: general form
52
Duffing oscillator: perturbed simple harmonic oscillator
54
8.
Phase-space dynamics and fixed points
58
Action-angle variables
61
Simple harmonic oscillator
64
Pendulum
66
Linearized stability analysis
74
9. Lorenz
model
77
Stationary solutions and fixed points
78
Linearized stability analysis
79
Periodic oscillatory solutions
82
Chaotic solutions
84
Two theorems on phase-space convergence of solutions
85
10.
Model finite-difference equation: logistic map
87
Logistic map
88
Power spectrum
89
Numerical analysis
90
Some analytic results
93
11.
Liouville s theorem revisited
97
12.
Action-angle variables revisited
101
Separable, periodic hamiltonian systems
101
Phase plots and motion on tori
106
13.
Perturbation of periodic hamiltonian systems 111
Hamilton-Jacobi theory revisited 111
Direct perturbation analysis of the anharmonic oscillator
115
Model one-body problem with time-periodic perturbation
117
Resonant disruption of phase space
120
Overlap of disrupted regions
125
14.
Coupled separable periodic hamiltonian systems
125
Two weakly coupled degrees of freedom
126
Resonant disruption of phase space
129
The
Kolmogorov-Arnold-Moser (KAM)
theorem
134
PART IV: PROBLEMS
136
15.
Problems
137
REFERENCES
147
INDEX
150
vi
NONLINEAR
MECHANICS
A Supplement to Theoretical Mechanics
of Particles and
Continua
Alexander
L
Fetter and John Dirk
Wałecka
In their prior Dover book, Theoretical Mechanics of Particles
and
Continua,
Alexander L. Fetter and John Dirk
Wałecka
provided a lucid and self-contained account of classical
mechanics, together with appropriate mathematical methods.
This supplement
—
an update of that volume
—
offers a bridge
to contemporary mechanics.
The original book s focus on continuum mechanics
—
with
chapters on sound waves in fluids, surface waves on fluids,
heat conduction, and viscous fluids
—
forms the basis for this
supplement s discussion of nonlinear continuous systems.Topics
include linearized stability analysis; a detailed examination of
the
Rayleigh-Bénard
problem, from its formulation to issues
of linearized theory of convective instability and expansion in
Fourier modes; and the direct derivation of
Lorenz
equations
for simple physical configuration.The first half of the original
text deals with particle mechanics, and this supplement returns
to the study of systems with a finite number of degrees of
freedom. A concluding section presents a series of problems
that reinforce the supplement s teachings.
Dover
(2006)
original publication. References. Index. 160pp.
6%
x
9/4.
Paperbound.
See every Dover book in print at
www.doverpublications.com
$12.95
USA
$19.50
CANADA
С^вОАвб ЧбОЗТЭ1
|
| any_adam_object | 1 |
| author | Fetter, Alexander L. 1937- Walecka, John Dirk 1932- |
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| dewey-ones | 531 - Classical mechanics |
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| dewey-tens | 530 - Physics |
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| id | DE-604.BV036621053 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:22Z |
| institution | BVB |
| isbn | 9780486450315 0486450317 |
| language | English |
| lccn | 2006040221 |
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| spelling | Fetter, Alexander L. 1937- Verfasser (DE-588)13284477X aut Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua Alexander L. Fetter ; John Dirk Walecka Mineola, NY Dover Publ. 2006 VI, 154 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Continuum mechanics Field theory (Physics) Walecka, John Dirk 1932- Verfasser (DE-588)132844788 aut http://www.loc.gov/catdir/enhancements/fy0629/2006040221-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020541083&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020541083&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Fetter, Alexander L. 1937- Walecka, John Dirk 1932- Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua Continuum mechanics Field theory (Physics) |
| title | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua |
| title_auth | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua |
| title_exact_search | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua |
| title_full | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua Alexander L. Fetter ; John Dirk Walecka |
| title_fullStr | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua Alexander L. Fetter ; John Dirk Walecka |
| title_full_unstemmed | Nonlinear mechanics a supplement to Theoretical mechanics of particles and continua Alexander L. Fetter ; John Dirk Walecka |
| title_short | Nonlinear mechanics |
| title_sort | nonlinear mechanics a supplement to theoretical mechanics of particles and continua |
| title_sub | a supplement to Theoretical mechanics of particles and continua |
| topic | Continuum mechanics Field theory (Physics) |
| topic_facet | Continuum mechanics Field theory (Physics) |
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