- 1. Review of fundamentals
- 1.1. Kinematics : basic notions
- 1.2. Dynamics : Newton's laws
- 1.3. Conservation laws
- 1.4. Potential energy and equilibrium
- 1.5. OK, we've got it--can we go home now?
- 1.6. Problems

- 2. Lagrangian analytical mechanics
- 2.1. Lagrange equations
- 2.2. Three simple examples
- 2.3. Hamiltonian function and energy
- 2.4. Other conservation laws
- 2.5. Problems

- 3. A few simple problems
- 3.1. One-dimensional and 1D-reducible systems
- 3.2. Equilibrium and stability
- 3.3. Hamiltonian 1D systems
- 3.4. Planetary problems
- 3.5. Elastic scattering
- 3.6. Problems

- 4. Rigid-body motion
- 4.1. Translation and rotation
- 4.2. Inertia tensor
- 4.3. Fixed-axis rotation
- 4.4. Free rotation
- 4.5. Torque-induced precession
- 4.6. Non-inertial reference frames
- 4.7. Problems

- 5. Oscillations
- 5.1. Free and forced oscillations
- 5.2. Weakly nonlinear oscillations
- 5.3. Reduced equations
- 5.4. Self-oscillations and phase-locking
- 5.5. Parametric excitation
- 5.6. Fixed-point classification
- 5.7. Numerical approaches
- 5.8. Higher harmonic and subharmonic oscillations
- 5.9. Problems

- 6. From oscillations to waves
- 6.1. Two coupled oscillators
- 6.2. N coupled oscillators
- 6.3. 1D waves
- 6.4. Acoustic waves
- 6.5. Standing waves
- 6.6. Wave decay and attenuation
- 6.7. Nonlinear and parametric effects
- 6.8. Problems

- 7. Deformations and elasticity
- 7.1. Strain
- 7.2. Stress
- 7.3. Hooke's law
- 7.4. Equilibrium
- 7.5. Rod bending
- 7.6. Rod torsion
- 7.7. 3D acoustic waves
- 7.8. Elastic waves in restricted geometries
- 7.9. Problems

- 8. Fluid mechanics
- 8.1. Hydrostatics
- 8.2. Surface tension effects
- 8.3. Kinematics
- 8.4. Dynamics : ideal fluids
- 8.5. Dynamics : viscous fluids
- 8.6. Turbulence
- 8.7. Problems

- 9. Deterministic chaos
- 9.1. Chaos in maps
- 9.2. Chaos in dynamic systems
- 9.3. Chaos in Hamiltonian systems
- 9.4. Chaos and turbulence
- 9.5. Problems

- 10. A bit more of analytical mechanics
- 10.1. Hamilton equations
- 10.2. Adiabatic invariance
- 10.3. The Hamilton principle
- 10.4. The Hamilton-Jacobi equation
- 10.5. Problems

- Appendices. A. Selected mathematical formulas
- B. Selected physical constants.

Essential Advanced Physics' is a series comprising four parts: 'Classical Mechanics', 'Classical Electrodynamics', 'Quantum Mechanics' and 'Statistical Mechanics'. Each part consists of two volumes, Lecture Notes and Problems with Solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, 'Classical Mechanics: Lecture Notes', is intended to be the basis for a one-semester graduate-level course on classical mechanics and dynamics, including the mechanics of continua, in particular deformations, elasticity, waves, and fluid dynamics.