# Rotating coordinate system in Dynamical systems

Say I have a dynamical system on the disk in polar coordinates

$(\dot{r},\dot{\phi}) = f(r,\phi)(t)$

I'm interested in doing a bifurcation analysis of the system, but in a rotating coordinate system, where the disk turns with a fixed angular frequency $\omega$. How do I transform my Dynamical system?

Is it straightforward, and I just substract the frequency to my equation for the phase $\dot{\phi}$ and look at $(\dot{r},\dot{\phi}-\omega)$ ?

What if the system is coupled, then this model doesn't work, because $\dot{r}$ will be influenced by the rotation.

• Can you please share the equations for which you want to do a bifurcation analysis? It'll be probably much easier to help knowing the particular case. – Evgeny Jun 22 '18 at 15:17
• I don't have a specific problem in mind, it was more of a general question about rotating co-ordinate systems and their relation to dynamical systems – 1233023 Jun 22 '18 at 15:25