It is not the purpose here to outline how Lagrangian mechanics works. The interested reader can look at other articles explaining this approach. For the moment, the goal is simply to show that the Lagrangian approach can lead to "generalized fictitious forces" that do not vanish in inertial frames. What is pertinent here is that in the case of a single particle, the Lagrangian approach can be arranged to capture exactly the "coordinate" fictitious forces just introduced.