Differential Equations, 3rd Edition

3Some Applications of the First-Order Theory

DOI: 10.1201/9781003214526-3

• Hanging chain and pursuit curves

• Electric circuits

3.1 The Hanging Chain and Pursuit Curves

3.1.1 The Hanging Chain

Imagine a flexible steel chain, attached firmly at equal height at both ends, hanging under its own weight (see Figure 3.1). What shape will it describe as it hangs?

Figure 3.1 The hanging chain.

This is a classical problem of mechanical engineering, and its analytical solution involves calculus, elementary physics, and differential equations. We describe it here.

We analyze a portion of the chain between points A and B, as shown in Figure 3.2, where ...