In Classical Mechanics, John R. Taylor defines generalized coordinates like so:
Consider now an arbitrary system of $N$ particles, $\alpha = 1, \dots , N$ with positions $\boldsymbol{r}_a$. We say that the parameters $q_1, \dots, q_n$ are a set of generalized coordinates for the system if each position $\boldsymbol{r}_a$ can be expressed as a function of $q_1, \dots, q_n$, and possibly the time $t$, ..., and conversely each $q_i$ can be expressed in terms of the $\boldsymbol{r}_a$ and possibly $t$.
Do the positions $\boldsymbol{r}_a$ have to be positions in an inertial reference frame?
