No Anome, what matters is the correct matching up of the maths to physical reality, and the polar coordinate system is the one that is tailor made to deal with concepts such as centrifugal force and Coriolis force.

The centrifugal force is a radial effect and the Coriolis force is a tangential effect.

But before we can use the expressions in polar coordinates we must construct a physical model of a real situation and then construct a differential equation around it, usually in the scalar variable of radial distance. 

If you were in the slightest genuine about this topic, you would have read the section which I added to the main article yesterday. You would have blocked PeR for vandalism and wikistalking for having erased it on specious grounds.

It hardly needed sourced since it is standard planetary orbital theory which obviously none of you know anything about. In fact I did mention Goldstein's Classical Mechanics.

The picture that I am getting here is that the article has been hi-jacked by a group who have had a basic introduction to circular motion but who would be incapable of handling elliptical or hyperbolic motion and so they will all make sure that no such generalizations appear in the main article.

Your group has indulged in a number of deceitful tactics which I will now list.

(1) Making arguments in polar coordinates but jumping into Cartesian coordinates to conceal the flaws. The main example is circular motion, which is all that you seem to be capable of considering. You accept one moment that there is a radially outward centrifugal force balancing a radially inward centripetal force. But as soon as the centrifugal force becomes inconvenient for you, you claim that it vanishes in the inertial frame, even though the centripetal force remains. That is just a nonsense.

(2) Trying to drag in the three body problem while totally sweeping the two body problem under the carpet. This is because you feel more comfortable in a field that nobody can understand. It is good cover for talking nonsense.

(3) Introducing Lagrangian mechanics.

(4) Introducing Hamiltonian mechanics.

(5) Introducing matrix algebra.

(6) Quoting Feynam.

We have seen all these tactics used in a pathetic attempt to deny the fact that centrifugal force only occurs when a particle actually possesses an angular velocity relative to a point.

The section which I put in yesterday contained partically all hat you need to know about centrifugal force. But that was too good for you. You much prefer that big mindless waffle of an introduction that tells us absolutely nothing about centrifugal force.