1 Introduction

Kinematics is the branch of mechanics that deals with quantities involving space and time only. It treats variables such as displacement, velocity, acceleration, deformation, and rotation of fluid elements without referring to the forces responsible for such a motion. Kinematics therefore essentially describes the "appearance" of a motion. Some important kinematical concepts are described in this chapter. The forces are considered when one deals with the dynamics of the motion, which will be discussed in later chapters.

A few remarks should be made about the notation used in this chapter and throughout the rest of the book. The convention followed in Chapter 2, namely, that vectors are denoted by lowercase letters and higher-order tensors are denoted by uppercase letters, is no longer followed. Henceforth, the number of subscripts will specify the order of a tensor. The Cartesian coordinate directions are denoted by ( x, y, z), and the corresponding velocity components are denoted by ( u, v, w). When using tensor expressions, the Cartesian directions are denoted alternatively by ( x ₁, x ₂, x ₃), with the corresponding velocity components ( u ₁, u ₂, u ₃). Plane polar coordinates are denoted by ( r, ?), with u _r and u _? the corresponding velocity components (Figure 3.1a) Cylindrical polar coordinates are denoted by ( R, ?, x), with ( u _R, u _?, u _x) the corresponding...