What do you mean?
It may be safe to ignore the poles.
You may be able to subtract out the poles and handle them analytically.
You might use some asymptotic method.
Some transformation might eliminate the pole or make it insignificant.
It is hard to handle such things in general.
There are many different situations.
I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr:
$$
\mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}}
$$