In this connection, it may be noted that a change in coordinate system, for example, from Cartesian to polar, if implemented without any change in relative motion, does not cause the appearance of fictitious forces, although the form of the laws of motion varies from one type of curvilinear coordinate system to another.
==Fictitious forces in curvilinear coordinates==
{{see also|Mechanics of planar particle motion}}
A different use of the term "fictitious force" often is used in [[curvilinear coordinates]], particularly [[polar coordinates]]. To avoid confusion, this distracting ambiguity in terminologies is pointed out here. These so-called "forces" are non-zero in all frames of reference, inertial or non-inertial, and do ''not'' transform as vectors under rotations and translations of the coordinates (as all Newtonian forces do, fictitious or otherwise).
This incompatible use of the term "fictitious force" is unrelated to non-inertial frames. These so-called "forces" are defined by determining the acceleration of a particle within the curvilinear coordinate system, and then separating the simple double-time derivatives of coordinates from the remaining terms. These remaining terms then are called "fictitious forces". More careful usage calls these terms "[[generalized forces|<u>generalized</u> fictitious forces]]" to indicate their connection to the [[generalized coordinates]] of [[Lagrangian mechanics]]. The application of Lagrangian methods to polar coordinates can be found [[Mechanics of planar particle motion#Lagrangian approach|here]].
