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Non-inertial reference frame
A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will in general detect a non-zero acceleration. In a curved spacetime all frames are non-inertial. The laws of motion in non-inertial frames do not take the simple form they do in inertial frames, and the laws vary from frame to frame depending on the acceleration. To explain the motion of bodies entirely within the viewpoint of non-inertial reference frames, fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) must be introduced to account for the observed motion, such as the Coriolis force or the centrifugal force, as derived from the acceleration of the non-inertial frame.
As stated by Goodman and Warner, "One might say that F ''m''a holds in any coordinate system provided the term 'force' is redefined to include the so-called 'reversed effective forces' or 'inertia forces'."
==Avoiding fictitious forces in calculations==
In flat spacetime, the use of non-inertial frames can be avoided if desired. Measurements with respect to non-inertial reference frames can always be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration as seen from the inertial frame. This approach avoids use of fictitious forces (it is based on an inertial frame, where fictitious forces are absent, by definition) but it may be less convenient from an intuitive, observational, and even a calculational viewpoint.〔“The inertial frame equations have to account for ''VΩ'' and this very large centripetal force explicitly, and yet our interest is almost always the small relative motion of the atmosphere and ocean, ''V' '', since it is the relative
motion that transports heat and mass over the Earth. … To say it a little differently—it is the relative velocity that we measure when () observe from Earth’s surface, and it is the relative velocity that we seek for most any practical purposes.” (MIT essays ) by James F. Price, Woods Hole Oceanographic Institution (2006). See in particular §4.3, p. 34 in the (Coriolis lecture )〕 As pointed out by Ryder for the case of rotating frames as used in meteorology:
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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