The convolution of two functions of x, f(x) and g(x), is defined by the definite integral Convolution is defined mathematically but it is possible to understand what it means in pictures. So, if you don’t like mathematics, ignore the next paragraph and the appendices. The definition of convolution can be extended into two, or more… Continue reading 22.20 Convolution

Before you read this, I suggest you read post 16.33. Stability is a more complicated idea than we often suppose. For example, a mechanical system can be stable but not in equilibrium because it is moving (with respect to an observer – see movement) on a stable path – it has dynamic stability. Similarly, a… Continue reading 22.19 Kinetic stability

Before you read this, I suggest you read post 18.11 The picture below shows an orthogonal Cartesian coordinate system in which the z-axis is vertical. We are going to think of two pendulums: one oscillates in the xz plane and the other oscillates in the yz plane. For small oscillations, we can consider that the… Continue reading 22.18 Coupled oscillators – Lissajou’s figures