# Range of a heading angle [0,2π) or [−π,π)

Consider the unicycle dynamics in 2D plane:

$$\begin{array}{l} \dot x = v\cos \varphi \\ \dot y = v\sin \varphi \\ \dot \varphi = \omega \end{array}$$

What is the range of the heading angle $$\phi$$? Some texts say $$\varphi \in [ - \pi ,\pi )$$ and other use this convention $$\varphi \in [ 0 ,2\pi )$$. What is the reason for this difference?

## 1 Answer

No difference at all although φ∈[−π,π) is much more reasonable and intuitive. It is just a matter of system definition.