Chapter 7.2, Problem 4E

Interpretation Introduction

Interpretation:

To show that all vector fields on the line are a gradient system

Concept Introduction:

The system can be written in the form $\dot{\text{x}}\text{= -}\nabla \text{V}$ for some continuously differential, single-valued scalar function $\text{V(x)}$. Such a system is called a gradient system with potential function V. $\text{V(x)}$

Closed orbit is impossible in the gradient system.