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