Classical Mechanics Course Notes (Marko Horbatsch)

Text: Jens M. Knudsen, Poul G. Hjorth: Elements of Newtonian Mechanics, 3rd edition, Springer-Verlag 2000

 

1                    Newtonian Mechanics in one dimension

1.1   Introduction           Free Fall           Definite Integration

1.2  Harmonic Oscillator            Total Energy     Visualize Motion

1.3  Damped Harmonic Motion             Weak and Strong Damping       Critical Damping           Energy in the Damped HO

1.4  Driven Harmonic Oscillator             Solution            Discussion

1.5  Chaos in the Duffing Oscillator        Poincare Section

1.6  Work and Energy in1D Motion

1.7  Example: Free Fall towards the Sun

1.8  Conservation of Linear Momentum

1.9  Gravitational and Inertial Mass

1.10          Galilei Transformation

 

 

1                    Mechanics in three dimensions

 

2.1 Charged Particle in a Magnetic Field           Solution

2.2 Earth’s Motion       Cross Product              Test1Problem1

2.3 Accelerated Reference Frames       Transformation             Transformation(…)       Transformation Results

2.4 Einstein’s Equivalence Principle

2.5 Centrifugal Force

2.6 Tidal Forces           Ocean Tides

2.7 Coriolis Force

2.8 Foucault Pendulum             Solution

 

 

2                    Advanced Concepts

 

3.1 Work and Energy

3.2 Conservative Force Fields  curl F = 0         Stokes’ Theorem

3.3 Gravitational Potential Energy Calculation    Solid Sphere                 Self-Energy of the Sun (Pr 8.9)

Summary: Problem-Solving: 6.1,8.2,8.3, 8.8

3.4 Centre-of-Mass Theorem

3.5 Angular Momentum            Kepler’s 2nd Law

3.6 Effective Potential in the Kepler Problem

3.7 Angular Momentum in a Many-Body System

3.8 Classical Spin of a Rigid Body

 

 

3                    Rotational Rigid-Body Motion

 

4.1 Rigid-body rotation basics  Rotational kinetic energy

4.2 Moments of inertia about different axes

4.3 Torsion pendulum and physical pendulum

4.4 Arbitrary rigid body in rotation around fixed axis

4.5 Calculation of moments of inertia

4.6 Equation of motion for rotation about fixed axis       Rotational energy consideration

4.7 Example: Atwood machine

4.8 Example: when L and w are not aligned

4.9 Example: precession in the gyroscope

4.10 The Inertia tensor

4.11 Euler’s equations  Derivation

4.12 Principal axes determination example         General case

Tumbling Textbook using Energy and Angular Momentum Conservation

4.13 Gyroscope           Simple cases

Nutation from Energy Considerations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Problem-Solving