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 Earthís Motion†††††† Cross Product††††††††††††††† Problem 5.1

2.3 Accelerated Reference Frames†††† Transformation††††††††††††† Transformation(Ö)††††† Transformation Results

2.4 Einsteinís 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††††††††† Stokesí Theorem ††††††††††††† Problem 8.20 (own)

3.3 Gravitational Potential Energy Calculation††††††††††† Solid Sphere††† Sunís Self-Energy†††††††† Problem 8.4

3.4 Centre-of-Mass Theorem†††††††††††††††† Problem 9.1†††† Problem 9.6

3.5 Angular Momentum†††††††††††† Keplerís 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 axisRotational 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 Eulerís equations†††† Derivation††††††† Maple-demo

Tumbling textbookConservation 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