These notes are collected from a number of sources, including my own notes from when I was an undergraduate, notes I made when I was a post-graduate, and more recently, notes I’ve written for lectures I have given.
Hopefully they’re of some use to someone.
You can find the git repository for these notes at
Feel free to leave an issue on that repository if you spot any problems in the notes.
Warning
It’s very likely that there are mistakes in these notes. Many of them were taken at some speed, so please be cautious while using them. I’m working to revise them, but this is slow work, and taken-on mostly in spare time.
Classical mechanics deals with the description of the motion of masses, and the time-evolution of systems of objects.
Classical mechanics can be approached in three different, but related ways; Newtonian mechanics, which formulates mechanics in terms of masses and forces; Lagrangian mechanics and Hamiltonian mechanics, which use generalised concepts such as energy, momentum, and generalised coordinates. The concepts of classical mechanics form the underpinning of many other areas of physics, including quantum mechanics, which is a generalisation of the theory.
Classical mechanics is a subject which is hundreds of years old, and despite its age continues to be an active research area.
When we think of classical mechanics we think of Newton’s Laws:
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
The alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d.
To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
These are easy to apply to simple systems, i.e. one or two particles with one or two forces. However, it is difficult to apply these laws in complicated systems, for example many-particle systems, and continuous systems. These difficulties led to the development of alternative formulations of classical mechanics, the Lagrangian and Hamiltonian formalisms, which are easier to apply to complex systems.
New structures become clear in this new approach which do not appear easily in the Newtonian approach.