ABSTRACT
This chapter is mostly about classical mechanics. By `classical', I mean to indicate that we are not yet going to take any account of quantum mechanics. (In the literature, `classical' is sometimes used to mean that no account is taken of special relativity either, and sometimes also to describe any venerable theory that has been superseded by a more `modern' one.) I shall actually be assuming that readers already have a fair understanding of the elementary aspects of Newtonian mechanics: for example, we shall not spend time developing techniques for calculating the trajectories of projectiles or planetary orbits, important though these topics undoubtedly are. The aim of this chapter is to set out the mathematics of classical mechanics in a way that makes clear the nature of the basic physical laws embodied in it and which, to a large extent, will enable us to see the principles of general relativity and of the quantum theory as natural generalizations of these laws. In a later chapter, this mathematical description will also help us towards setting up a statistical description of the macroscopic behaviour of large assemblages of particles.
