Classical dynamics: a contemporary approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Edition: | Repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 670 S. graph. Darst. |
| ISBN: | 0521631769 0521636361 |
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| 100 | 1 | |a José, Jorge Valenzuela |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Classical dynamics |b a contemporary approach |c Josege V. José and Eugene J. Saletan |
| 250 | |a Repr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2002 | |
| 300 | |a XXV, 670 S. |b graph. Darst. | ||
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| _version_ | 1804135231299518464 |
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| adam_text | CONTENTS
List of Worked Examples page
Preface
Two Paths Through the Book
1
1.1
1.1.1
1.1.2
1.2
1.2.1
1.2.2
Principle
Principle
Discussion
1.2.3
Introduction
Force is a Vector
1.3
1.3.1
1.3.2
1.3.3
In Three Dimensions
Application to One-Dimensional Motion
1.4
1.4.1
Center of Mass
Momentum
Variable Mass
1.4.2
1.4.3
CONTENTS
VIM
1.5
1.5.1
The Cosine Potential
The Kepler Problem
1.5.2
1.5.3
Principle
Equivalence Principle
Rotating Frames
Problems
LAGRANGIAN FORMULATION OF MECHANICS
2.1
2.1.1
Constraint Equations
Constraints and Work
2.1.2
2.1.3
The Finite Line
The Circle
The Plane
The Two-Sphere S2
The Double Pendulum
Discussion
2.2
2.2.1
2.2.2
Equivalent Lagrangians
Coordinate Independence
Hessian Condition
2.2.3
2.2.4
The Lagrangian
A Time-Dependent Coordinate Transformation
2.3
2.3.1
Statement of the Problem; Reduced Mass
Reduction to Two Freedoms
The Equivalent One-Dimensional Problem
2.3.2
2.3.3
2.4
CONTENTS
їх
2.4.1 Dynamics
92
Velocities Do Not Lie in Q
92
Tangent Spaces and the Tangent Bundle
93
Lagrange s Equations and Trajectories on TQ
95
2.4.2
97
Differential Manifolds
97
Tangent Spaces and Tangent Bundles
100
Application to Lagrange s Equations
102
Problems
103
TOPICS IN LAGRANGIAN DYNAMICS
108
3.1
108
3.1.1
108
The Action
108
Hamilton s Principle
110
Discussion
112
3.1.2
114
3.2
118
3.2.1
118
Invariant Submanifolds and Conservation of
Momentum
118
Transformations, Passive and Active
119
Three Examples
123
3.2.2
124
Point Transformations
124
The Theorem
125
3.3
128
3.3.1
129
Rewriting the EL Equations
129
The Dissipative and Rayleigh Functions
129
3.3.2
131
3.3.3
134
3.4
134
3.4.1
134
Vector Fields
134
One-Forms
135
The Lie Derivative
136
3.4.2
138
3.4.3
139
One-Parameter Groups
139
The Theorem
140
Problems
143
CONTENTS
4
4.1
4.1.1
General Considerations
The Rutherford Cross Section
4.1.2
General Treatment
Example: Coulomb Scattering
4.1.3
Dimension
Two Disks
Three Disks, Cantor Sets
Fractal Dimension and Lyapunov Exponent
Some Further Results
4.1.4
Dipole 170
The
The Equatorial Limit
The General Case
4.2
4.2.1
Linearization
Normal Modes
4.2.2
Frequencies
The Invariant Torus T
The
4.2.3
General Solution
The Finite Chain
4.2.4
Forced Undamped Oscillator
Forced Damped Oscillator
Problems
5
5.1
5.1.1
From the Lagrangian to the Hamiltonian 202
A Brief Review of Special Relativity
The Relativistic Kepler Problem
5.1.2
CONTENTS xi
5.1.3
Brackets
The
Variational Derivation of Hamilton s Equations
Poisson
Poisson
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
Reduction on T*Q by Constants of the Motion
Definition of Canonical Transformations
Changes Induced by Canonical Transformations
Two Examples
5.3.2
5.3.3
Transformations
Generating Functions
The Generating Functions Gives the New
Hamiltonian
Generating Functions of Type
5.3.4
Transformations
Infinitesimal Generators of One-Parameter Groups;
Hamiltonian Flows
The Hamiltonian Noether Theorem
Flows and
5.4
5.4.1
Volume
Integration on T*Q; The Liouville Theorem
Poincaré
Density of States
5.4.2
The Theorem
Reduction
Problems
Canonicity Implies
CONTENTS
TOPICS IN HAMILTONIAN
6.1 The Hamilton-Jacobi
6.1.1 The Hamilton-Jacobi
Derivation 285
Properties of
Relation
6.1.2 Separation
The Method of Separation
Example: Charged Particle in a Magnetic Field
6.1.3
6.1.4
Method
6.2
6.2.1
Invariant Tori
The
The Canonical Transformation to AA Variables
Example: A Particle on a Vertical Cylinder
6.2.2
Complete Integrability
The Tori
The Ja
Example: the Neumann Problem
6.2.3
Rational and Irrational Winding Lines
Fourier Series
6.3
6.3.1
Perturbation Theory
6.3.2
Perturbation via Canonical Transformations
Averaging
Canonical Perturbation Theory in One Freedom
Canonical Perturbation Theory in Many Freedoms
The Lie Transformation Method
Example: The Quartic Oscillator
6.4
6.4.1
Oscillator with Time-Dependent Frequency
The Theorem
Remarks on
6.4.2
CONTENTS xiii
6.4.3
6.4.4
Field
The Action Integral
Three Magnetic Adiabatic Invariants
Problems
7
7.1
7.1.1
7.1.2
Damped Driven Quartic Oscillator; Harmonic
Analysis
Undamped Driven Quartic Oscillator
7.1.3
7.2
7.2.1
Definitions
The
Linearization
7.2.2
The
Linearization of Discrete Maps
Example: The Linearized
7.3
7.3.1
The Floquet Operator R
Standard Basis
Eigenvalues of R and Stability
Dependence on
7.3.2
The
Stability of the Pendulum
The Inverted Pendulum
Damping
7.4
7.4.1
Definition
Fixed Points
Period Doubling
Universality
Further Remarks
xiv
7.4.2
The Damped Driven Pendulum
The Standard Sine Circle Map
Rotation Number and the Devil s Staircase
Fixed Points of the Circle Map
7.5
Theorem
7.5.1
The Dynamical System
The Standard Map
Poincaré Map
7.5.2
7.5.3
Poincaré-Birkhoff
The Twist Map
Numbers and Properties of the Fixed Points
The Homoclinic Tangle
The Transition to Chaos
7.5.4
Background
Two Conditions: Hessian and Diophantine
The Theorem
A Brief Description of the Proof of
Problems
Number Theory
The Unit Interval
A Diophantine Condition
The Circle and the Plane
KAM
8
8.1
8.1.1
Definition
The Angular Velocity Vector
8.1.2
Kinetic Energy
Angular Momentum
8.1.3
Space and Body Systems
Dynamical Equations
Example: The Gyrocompass
CONTENTS
Motion
Fixed Points and Stability
The Poinsot Construction
8.2
8.2.1
Inertial, Space, and Body Systems
The Dimension of QR
The Structure of QR
8.2.2
Kinetic Energy
The Constraints
8.2.3
Derivation
The Angular Velocity Matrix
8.2.4
8.2.5
Antisymmetric Matrix-Vector Correspondence
The Torque
The Angular Velocity Pseudovector and
Kinematics
Transformations of Velocities
Hamilton s Canonical Equations
8.2.6
8.3
8.3.1
Definition
R in Terms of the Euler Angles
Angular Velocities
Discussion
8.3.2
8.3.3
The Lagrangian and Hamiltonian
The Motion of the Top
Nutation and Precession
Quadratic Potential; the Neumann Problem
8.4
8.4.1 2x2
Rotations
3-Vectors
Rotations
8.4.2
Definitions
CONTENTS
Finding Ru
Axis and Angle in terms of the CK Parameters
8.4.3
Problems
CONTINUUM DYNAMICS
9.1
Dynamics
9.1.1
The Sine-Gordon Equation
The Wave and Klein-Gordon Equations
9.1.2
Introduction
Variational Derivation of the EL Equations
The Functional Derivative
Discussion
9.1.3
Some Special Relativity
Electromagnetic Fields
The Lagrangian and the EL Equations
9.2
9.2.1
The Theorem
Conserved Currents
Energy and Momentum in the Field
Example: The Electromagnetic
Energy-Momentum Tensor
9.2.2
Lorentz Transformations
Lorentz Invariant
Free Klein-Gordon Fields
Complex K-G Field and Interaction with the
Maxwell Field
Discussion of the Coupled Field Equations
9.2.3
Spinor Fields
A Spinor Field Equation
9.3
9.3.1
Definitions
The Canonical Equations
Poisson
CONTENTS xvii
9.3.2 Expansion in
Orthonormal
Particle-like Equations
Example: Klein-Gordon
9.4
9.4.1
Soliton Solutions
Properties of sG
Multiple-Soliton Solutions
Generating Soliton Solutions
Nonsoliton Solutions
Josephson Junctions
9.4.2
The Lagrangian and the EL Equation
Kinks
9.5
9.5.1
Substantial Derivative and Mass Conservation
Euler s Equation
Viscosity and Incompressibility
The Navier-Stokes Equations
Turbulence
9.5.2
The Equation
Asymptotic Solution
9.5.3
Equations for the Waves
Linear Gravity Waves
Nonlinear Shallow Water Waves: the KdV Equation
Single KdV
Multiple KdV
9.6
9.6.1
From Particles to Fields
Dynamical Variables and Equations of Motion
9.6.2
The Gradient
The Symplectic Form
The Condition for Canonicity
Poisson
9.6.3
KdV as a Hamiltonian Field
xviii CONTENTS
Constants
Generating the Constants of the Motion
More on Constants of the Motion
9.6.4
Two-Component Field Variables
sG as a Hamiltonian Field
Problems
EPILOGUE
APPENDIX: VECTOR SPACES
General Vector Spaces
Linear Operators
Inverses and Eigenvalues
Inner Products and Hermitian Operators
BIBLIOGRAPHY
INDEX
|
| adam_txt |
CONTENTS
List of Worked Examples page
Preface
Two Paths Through the Book
1
1.1
1.1.1
1.1.2
1.2
1.2.1
1.2.2
Principle
Principle
Discussion
1.2.3
Introduction
Force is a Vector
1.3
1.3.1
1.3.2
1.3.3
In Three Dimensions
Application to One-Dimensional Motion
1.4
1.4.1
Center of Mass
Momentum
Variable Mass
1.4.2
1.4.3
CONTENTS
VIM
1.5
1.5.1
The Cosine Potential
The Kepler Problem
1.5.2
1.5.3
Principle
Equivalence Principle
Rotating Frames
Problems
LAGRANGIAN FORMULATION OF MECHANICS
2.1
2.1.1
Constraint Equations
Constraints and Work
2.1.2
2.1.3
The Finite Line
The Circle
The Plane
The Two-Sphere S2
The Double Pendulum
Discussion
2.2
2.2.1
2.2.2
Equivalent Lagrangians
Coordinate Independence
Hessian Condition
2.2.3
2.2.4
The Lagrangian
A Time-Dependent Coordinate Transformation
2.3
2.3.1
Statement of the Problem; Reduced Mass
Reduction to Two Freedoms
The Equivalent One-Dimensional Problem
2.3.2
2.3.3
2.4
CONTENTS
їх
2.4.1 Dynamics
92
Velocities Do Not Lie in Q
92
Tangent Spaces and the Tangent Bundle
93
Lagrange's Equations and Trajectories on TQ
95
2.4.2
97
Differential Manifolds
97
Tangent Spaces and Tangent Bundles
100
Application to Lagrange's Equations
102
Problems
103
TOPICS IN LAGRANGIAN DYNAMICS
108
3.1
108
3.1.1
108
The Action
108
Hamilton's Principle
110
Discussion
112
3.1.2
114
3.2
118
3.2.1
118
Invariant Submanifolds and Conservation of
Momentum
118
Transformations, Passive and Active
119
Three Examples
123
3.2.2
124
Point Transformations
124
The Theorem
125
3.3
128
3.3.1
129
Rewriting the EL Equations
129
The Dissipative and Rayleigh Functions
129
3.3.2
131
3.3.3
134
3.4
134
3.4.1
134
Vector Fields
134
One-Forms
135
The Lie Derivative
136
3.4.2
138
3.4.3
139
One-Parameter Groups
139
The Theorem
140
Problems
143
CONTENTS
4
4.1
4.1.1
General Considerations
The Rutherford Cross Section
4.1.2
General Treatment
Example: Coulomb Scattering
4.1.3
Dimension
Two Disks
Three Disks, Cantor Sets
Fractal Dimension and Lyapunov Exponent
Some Further Results
4.1.4
Dipole 170
The
The Equatorial Limit
The General Case
4.2
4.2.1
Linearization
Normal Modes
4.2.2
Frequencies
The Invariant Torus T
The
4.2.3
General Solution
The Finite Chain
4.2.4
Forced Undamped Oscillator
Forced Damped Oscillator
Problems
5
5.1
5.1.1
From the Lagrangian to the Hamiltonian 202
A Brief Review of Special Relativity
The Relativistic Kepler Problem
5.1.2
CONTENTS xi
5.1.3
Brackets
The
Variational Derivation of Hamilton's Equations
Poisson
Poisson
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
Reduction on T*Q by Constants of the Motion
Definition of Canonical Transformations
Changes Induced by Canonical Transformations
Two Examples
5.3.2
5.3.3
Transformations
Generating Functions
The Generating Functions Gives the New
Hamiltonian
Generating Functions of Type
5.3.4
Transformations
Infinitesimal Generators of One-Parameter Groups;
Hamiltonian Flows
The Hamiltonian Noether Theorem
Flows and
5.4
5.4.1
Volume
Integration on T*Q; The Liouville Theorem
Poincaré
Density of States
5.4.2
The Theorem
Reduction
Problems
Canonicity Implies
CONTENTS
TOPICS IN HAMILTONIAN
6.1 The Hamilton-Jacobi
6.1.1 The Hamilton-Jacobi
Derivation 285
Properties of
Relation
6.1.2 Separation
The Method of Separation
Example: Charged Particle in a Magnetic Field
6.1.3
6.1.4
Method
6.2
6.2.1
Invariant Tori
The
The Canonical Transformation to AA Variables
Example: A Particle on a Vertical Cylinder
6.2.2
Complete Integrability
The Tori
The Ja
Example: the Neumann Problem
6.2.3
Rational and Irrational Winding Lines
Fourier Series
6.3
6.3.1
Perturbation Theory
6.3.2
Perturbation via Canonical Transformations
Averaging
Canonical Perturbation Theory in One Freedom
Canonical Perturbation Theory in Many Freedoms
The Lie Transformation Method
Example: The Quartic Oscillator
6.4
6.4.1
Oscillator with Time-Dependent Frequency
The Theorem
Remarks on
6.4.2
CONTENTS xiii
6.4.3
6.4.4
Field
The Action Integral
Three Magnetic Adiabatic Invariants
Problems
7
7.1
7.1.1
7.1.2
Damped Driven Quartic Oscillator; Harmonic
Analysis
Undamped Driven Quartic Oscillator
7.1.3
7.2
7.2.1
Definitions
The
Linearization
7.2.2
The
Linearization of Discrete Maps
Example: The Linearized
7.3
7.3.1
The Floquet Operator R
Standard Basis
Eigenvalues of R and Stability
Dependence on
7.3.2
The
Stability of the Pendulum
The Inverted Pendulum
Damping
7.4
7.4.1
Definition
Fixed Points
Period Doubling
Universality
Further Remarks
xiv
7.4.2
The Damped Driven Pendulum
The Standard Sine Circle Map
Rotation Number and the Devil's Staircase
Fixed Points of the Circle Map
7.5
Theorem
7.5.1
The Dynamical System
The Standard Map
Poincaré Map
7.5.2
7.5.3
Poincaré-Birkhoff
The Twist Map
Numbers and Properties of the Fixed Points
The Homoclinic Tangle
The Transition to Chaos
7.5.4
Background
Two Conditions: Hessian and Diophantine
The Theorem
A Brief Description of the Proof of
Problems
Number Theory
The Unit Interval
A Diophantine Condition
The Circle and the Plane
KAM
8
8.1
8.1.1
Definition
The Angular Velocity Vector
8.1.2
Kinetic Energy
Angular Momentum
8.1.3
Space and Body Systems
Dynamical Equations
Example: The Gyrocompass
CONTENTS
Motion
Fixed Points and Stability
The Poinsot Construction
8.2
8.2.1
Inertial, Space, and Body Systems
The Dimension of QR
The Structure of QR
8.2.2
Kinetic Energy
The Constraints
8.2.3
Derivation
The Angular Velocity Matrix
8.2.4
8.2.5
Antisymmetric Matrix-Vector Correspondence
The Torque
The Angular Velocity Pseudovector and
Kinematics
Transformations of Velocities
Hamilton's Canonical Equations
8.2.6
8.3
8.3.1
Definition
R in Terms of the Euler Angles
Angular Velocities
Discussion
8.3.2
8.3.3
The Lagrangian and Hamiltonian
The Motion of the Top
Nutation and Precession
Quadratic Potential; the Neumann Problem
8.4
8.4.1 2x2
Rotations
3-Vectors
Rotations
8.4.2
Definitions
CONTENTS
Finding Ru
Axis and Angle in terms of the CK Parameters
8.4.3
Problems
CONTINUUM DYNAMICS
9.1
Dynamics
9.1.1
The Sine-Gordon Equation
The Wave and Klein-Gordon Equations
9.1.2
Introduction
Variational Derivation of the EL Equations
The Functional Derivative
Discussion
9.1.3
Some Special Relativity
Electromagnetic Fields
The Lagrangian and the EL Equations
9.2
9.2.1
The Theorem
Conserved Currents
Energy and Momentum in the Field
Example: The Electromagnetic
Energy-Momentum Tensor
9.2.2
Lorentz Transformations
Lorentz Invariant
Free Klein-Gordon Fields
Complex K-G Field and Interaction with the
Maxwell Field
Discussion of the Coupled Field Equations
9.2.3
Spinor Fields
A Spinor Field Equation
9.3
9.3.1
Definitions
The Canonical Equations
Poisson
CONTENTS xvii
9.3.2 Expansion in
Orthonormal
Particle-like Equations
Example: Klein-Gordon
9.4
9.4.1
Soliton Solutions
Properties of sG
Multiple-Soliton Solutions
Generating Soliton Solutions
Nonsoliton Solutions
Josephson Junctions
9.4.2
The Lagrangian and the EL Equation
Kinks
9.5
9.5.1
Substantial Derivative and Mass Conservation
Euler's Equation
Viscosity and Incompressibility
The Navier-Stokes Equations
Turbulence
9.5.2
The Equation
Asymptotic Solution
9.5.3
Equations for the Waves
Linear Gravity Waves
Nonlinear Shallow Water Waves: the KdV Equation
Single KdV
Multiple KdV
9.6
9.6.1
From Particles to Fields
Dynamical Variables and Equations of Motion
9.6.2
The Gradient
The Symplectic Form
The Condition for Canonicity
Poisson
9.6.3
KdV as a Hamiltonian Field
xviii CONTENTS
Constants
Generating the Constants of the Motion
More on Constants of the Motion
9.6.4
Two-Component Field Variables
sG as a Hamiltonian Field
Problems
EPILOGUE
APPENDIX: VECTOR SPACES
General Vector Spaces
Linear Operators
Inverses and Eigenvalues
Inner Products and Hermitian Operators
BIBLIOGRAPHY
INDEX |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | José, Jorge Valenzuela Saletan, Eugene J. |
| author_facet | José, Jorge Valenzuela Saletan, Eugene J. |
| author_role | aut aut |
| author_sort | José, Jorge Valenzuela |
| author_variant | j v j jv jvj e j s ej ejs |
| building | Verbundindex |
| bvnumber | BV021500440 |
| classification_rvk | UF 1950 UG 1000 |
| ctrlnum | (OCoLC)175058903 (DE-599)BVBBV021500440 |
| dewey-full | 531.1101515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.1101515 |
| dewey-search | 531.1101515 |
| dewey-sort | 3531.1101515 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | Repr. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV021500440 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:15:19Z |
| indexdate | 2024-07-09T20:37:13Z |
| institution | BVB |
| isbn | 0521631769 0521636361 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014717168 |
| oclc_num | 175058903 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| physical | XXV, 670 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | José, Jorge Valenzuela Verfasser aut Classical dynamics a contemporary approach Josege V. José and Eugene J. Saletan Repr. Cambridge [u.a.] Cambridge Univ. Press 2002 XXV, 670 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamik (DE-588)4013384-9 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf 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 Dynamik (DE-588)4013384-9 s Theoretische Mechanik (DE-588)4185100-6 s 2\p DE-604 Saletan, Eugene J. Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014717168&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | José, Jorge Valenzuela Saletan, Eugene J. Classical dynamics a contemporary approach Dynamik (DE-588)4013384-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4013384-9 (DE-588)4185100-6 (DE-588)4038168-7 (DE-588)4123623-3 |
| title | Classical dynamics a contemporary approach |
| title_auth | Classical dynamics a contemporary approach |
| title_exact_search | Classical dynamics a contemporary approach |
| title_exact_search_txtP | Classical dynamics a contemporary approach |
| title_full | Classical dynamics a contemporary approach Josege V. José and Eugene J. Saletan |
| title_fullStr | Classical dynamics a contemporary approach Josege V. José and Eugene J. Saletan |
| title_full_unstemmed | Classical dynamics a contemporary approach Josege V. José and Eugene J. Saletan |
| title_short | Classical dynamics |
| title_sort | classical dynamics a contemporary approach |
| title_sub | a contemporary approach |
| topic | Dynamik (DE-588)4013384-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Dynamik Theoretische Mechanik Mechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014717168&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT josejorgevalenzuela classicaldynamicsacontemporaryapproach AT saletaneugenej classicaldynamicsacontemporaryapproach |