Essential Advanced Physics: Lecture notes in Classical Mechanics

Essential Advanced Physics: Lecture notes in Classical Mechanics

by Konstantin K. Likharev

Hardcover(Volume 1)

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Product Details

ISBN-13: 9780750313995
Publisher: Iop Publishing Ltd
Publication date: 03/09/2018
Edition description: Volume 1
Pages: 344
Product dimensions: 7.42(w) x 10.58(h) x 0.94(d)

Table of Contents

Preface to the EAP Series viii

Preface to Classical Mechanics: Lecture Notes xi

Acknowledgments xiii

Notation xiv

1 Review of fundamentals 1-1

1.1 Kinematics: basic notions 1-1

1.2 Dynamics: Newton's laws 1-3

1.3 Conservation laws 1-6

1.4 Potential energy and equilibrium 1-10

1.5 OK, we've got it-can we go home now? 1-12

1.6 Problems 1-13

References 1-16

2 Lagrangian analytical mechanics 2-1

2.1 Lagrange equations 2-1

2.2 Three simple examples 2-6

2.3 Hamiltonian function and energy 2-8

2.4 Other conservation laws 2-11

2.5 Problems 2-12

References 2-16

3 A few simple problems 3-1

3.1 One-dimensional and ID-reducible systems 3-1

3.2 Equilibrium and stability 3-2

3.3 Hamiltonian ID systems 3-6

3.4 Planetary problems 3-8

3.5 Elastic scattering 3-17

3.6 Problems 3-20

4 Rigid-body motion 4-1

4.1 Translation and rotation 4-1

4.2 Inertia tensor 4-4

4.3 Fixed-axis rotation 4-9

4.4 Free rotation 4-14

4.5 Torque-induced precession 4-19

4.6 Non-inertial reference frames 4-24

4.7 Problems 4-31

References 4-37

5 Oscillations 5-1

5.1 Free and forced oscillations 5-1

5.2 Weakly nonlinear oscillations 5-10

5.3 Reduced equations 5-14

5.4 Self-oscillations and phase-locking 5-17

5.5 Parametric excitation 5-20

5.6 Fixed-point classification 5-25

5.7 Numerical approaches 5-29

5.8 Higher harmonic and subharmonic oscillations 5-32

5.9 Problems 5-37

References 5-39

6 From oscillations to waves 6-1

6.1 Two coupled oscillators 6-1

6.2 N coupled oscillators 6-5

6.3 1D waves 6-7

6.4 Acoustic waves 6-13

6.5 Standing waves 6-18

6.6 Wave decay and attenuation 6-23

6.7 Nonlinear and parametric effects 6-26

6.8 Problems 6-29

References 6-33

7 Deformations and elasticity 7-1

7.1 Strain 7-1

7.2 Stress 7-5

7.3 Hooke's law 7-9

7.4 Equilibrium 7-15

7.5 Rod bending 7-18

7.6 Rod torsion 7-23

7.7 3D acoustic waves 7-28

7.8 Elastic waves in restricted geometries 7-35

7.9 Problems 7-40

References 7-43

8 Fluid mechanics 8-1

8.1 Hydrostatics 8-1

8.2 Surface tension effects 8-5

8.3 Kinematics 8-8

8.4 Dynamics: ideal fluids 8-10

8.5 Dynamics: viscous fluids 8-17

8.6 Turbulence 8-24

8.7 Problems 8-28

References 8-31

9 Deterministic chaos 9-1

9.1 Chaos in maps 9-1

9.2 Chaos in dynamic systems 9-5

9.3 Chaos in Hamiltonian systems 9-10

9.4 Chaos and turbulence 9-14

9.5 Problems 9-15

References 9-15

10 A bit more of analytical mechanics 10-1

10.1 Hamilton equations 10-1

10.2 Adiabatic invariance 10-6

10.3 The Hamilton principle 10-10

10.4 The Hamilton-Jacobi equation 10-14

10.5 Problems 10-17

References 10-19

Appendices

A Selected mathematical formulas A-1

B Selected physical constants B-1

Bibliography 13-1

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