While dealing with central force there is a known result: $$U_\text{eff}(r)=\frac{L^2}{2m r^2}+ U(r) \, $$
If I understand correctly the centrifugal potential term $l^2/(2\mu r^2)$ arises when you look at an orbit from $(r,\theta)$ perspective and just look at it in one dimension $r$. Is there also a coriolis potential that you can derive in a similar fashion? How would you interpret that?
Your guess in the comment seems correct: one can introduce a vector potential for the Coriolis force (American Journal of Physics 41, 585 (1973); https://doi.org/10.1119/1.1987297 , or https://arxiv.org/abs/2003.11359 )
The coriolis term in the equation of motion for a rotating coordinate system is proportional to velocity.
The convention is to define a potential when at each point in space the force exterted (for instance gravitational force) is a function of the position coordinate.
As we know: the potential difference between point A and point B is the negative of the work done in moving a test mass from point A to point B.
That is what allows the concept of centrifugal potential to be defined.
In the case of the coriolis term:
As we know: the coriolis term vector is perpendicular to the instantaneous velocity.
The definition of work done is displacement in the direction parallel to the force exerted.
That is: if a force is always acting perpendicular to the instantaneous velocity vector then the effect of that force does not fall in the category of work done.
As we know: the coriolis term vector is perpendicular to the instantaneous velocity.
