Rotation Dynamics  

Gyroscopic Motion

Equations of motion for a gyroscope are derived by considering the torques.

Rotation Dynamics  

Rotating coordinate system

In a rotating coordinate system, a free particle moves in a way that appears to be affected by three forces: the centrifugal force, the Coriolis force and the Euler force. These forces arise only from the rotation of the coordinate system.

Rotation Dynamics  

2D Rotational Dynamics

The description of 2D rotational motion is further developed in analogue to linear dynamics by introducing the rotational equivalents of force, momentum and mass.

Rotation Dynamics  

2D Rotational Kinematics

The description of 2D rotational motion is developed in analogue to linear kinematics.

Linear Motion  

Review of Linear Motion

A simple review of the notation and some of the expressions for kinematics and dynamics along a line, for classical physics.

Linear Motion  

Centre of Mass

The centre of mass of a system of particles is derived as a fictitious point that behaves as if the mass of the entire system where concentrated there. Tricks for finding it are discussed.

Oscillators  

Dynamical system maps

The map of phase space of a dynamical system is a really convenient way of summarising the behaviour of a system. In particular it doesn't require a solution to the equations of motion.

Coupled Oscillators  

The Loaded String

The loaded string is a classic problem of coupled oscillators where \(N\) small masses are threaded onto a light string. It makes a nice transition for considering the continuum case and waves.

Coupled Oscillators Waves  

Continuum Limit of the Loaded String

The continuum limit of the loaded string is derived, arriving at the one dimensional wave equation.

Coupled Oscillators  

Coupled Oscillators

Coupling together two or more oscillators introduces a whole new level of complexity. It turns out that there is a particular way of looking at the system that makes it simple to solve the motion.