You will find that this chapter is a sales pitch for the mathematics that will help you to understand and analyse the behaviour of rotating bodies, robot arms and complex vibrations. To reinforce this understanding, the book will introduce real-time simulations that you can react with and modify yourself. These run in any browser. Dynamics is the study of how things move. That seems fairly obvious. Our instincts and experience can confirm equations of linear motion, but as soon as solid bodies start to rotate, we bump into startling examples. Gyroscopes are regarded with mystique. So there are fundamental principles that have to be understood, and those are hedged around with some pretty forbidding mathematics. Just as Newton’s second law tells us to take account of linear momentum and forces, so we must additionally consider angular momentum and couples. This is where the lovers of mathematics can really come into their own! In the same way that electrical engineers cannot breathe without complex numbers, so you will have to learn to love vectors and matrices. They give strength to your elbow for analysing anything from a spinning asteroid, to a vibrating spin-drier or the reach of a robot arm.