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                     Problem 1.6

1.2  Harmonic Oscillator           Total Energy    Visualize Motion          Problem 1.12

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

1.4  Driven Harmonic Oscillator           Solution             Discussion        Problem 15.4

1.5  Chaos in the Duffing Oscillator     Poincare Section           Maple-demo

1.6  Work and Energy in1D Motion                     Problem 2.4

1.7  Example: Free Fall towards the Sun          Problem 2.9

1.8  Conservation of Linear Momentum             Problem 2.17

1.9  Gravitational and Inertial Mass

1.10            Galilei Transformation              Problem 4.2

 

2          Mechanics in three dimensions

2.1 Charged Particle in a Magnetic Field        Solution

2.2 Earth’s Motion       Cross Product                Problem 5.1

2.3 Accelerated Reference Frames     Transformation              Transformation(…)      Transformation Results

2.4 Einstein’s Equivalence Principle                Problem 6.2

2.5 Centrifugal Force                 Problem 6.4

2.6 Tidal Forces           Ocean Tides

2.7 Coriolis Force        Problem 6.6                    Demo

2.8 Foucault Pendulum              Solution             Detail             Maple-demo

 

 

3          Advanced Concepts

3.1 Work and Energy   Problem 8.6

3.2 Conservative Force Fields              curl F = 0          Stokes’ Theorem               Problem 8.20 (own)

3.3 Gravitational Potential Energy Calculation            Solid Sphere    Sun’s Self-Energy         Problem 8.4

3.4 Centre-of-Mass Theorem                 Problem 9.1     Problem 9.6

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         Demo1               Demo2

3.8 Classical Spin of a Rigid Body     Problem 15.1

 

 

4          Rotational Rigid-Body Motion

4.1 Rigid-body rotation basics              Rotational kinetic energy          Problem 11.20 (own)

4.2 Moments of inertia about different axes   

4.3 Torsion pendulum and physical pendulum              Problem 11.22 (own)

4.4 Arbitrary rigid body in rotation around fixed axis

4.5 Calculation of moments of inertia               Problem 11.21 (own)

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

4.7 Example: Atwood machine             Problem 11.23 (own)                 Problem 11.7

4.8 Example: when L and w are not aligned

4.9 Example: precession in the gyroscope      Demo   Demo

4.10 The Inertia tensor

4.11 Euler’s equations     Derivation        Maple-demo

Tumbling textbook Conservation laws Mathematical Detail

4.12 Principal axes determination example    General case

4.13 Gyroscope             Simple cases                  Maple-demo Problem 13.1; Problem 13.1(cont)

Nutation in the Gyroscope    Energy Consideration