This chapter develops some basic techniques for describing the motion of a point and therefore of a particle. The procedures we follow are driven not merely by how the point s motion is described, but also by the information we seek. Each formulation is based on describing vector quantities with respect to a different set of unit vectors. Which description is best suited to a particular situation depends on a variety of factors, but a primary consideration is whether the associated quantities, such as the coordinates, naturally fit the known aspects of the motion. Ultimately we will find that it might be beneficial to combine a variety of descriptions.

The various kinematical description that we use fall into two general classes. The one that might seem to be the most natural is extrinsic coordinates, which means that the description is extrinsic to knowledge of the path followed by the point. A simple case is rectangular Cartesian coordinates, for which the position is know in terms of distances measured along three mutually orthogonal straight lines representing reference directions. A variety of other extrinsic coordinate systems are in use. However, we begin by studying intrinsic coordinates, in which knowledge of the path is fundamental to the description of the motion. For example, the unit vectors for intrinsic coordinates are defined in terms of the properties of the path. For this reason, intrinsic coordinates are more commonly referred to as path variables.