|
|
|
|
Non-inertial reference frame
|
| |
|
| |
A non-inertial reference frame is a reference frame that is not an inertial reference frame. As such, the laws of physics in such a frame do not take on their most simple form, as required by the special principle of relativity. 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.
inertial frames can be avoided.
Discussion
Ask a question about 'Non-inertial reference frame' Start a new discussion about 'Non-inertial reference frame' Answer questions from other users |
Encyclopedia
A non-inertial reference frame is a reference frame that is not an inertial reference frame. As such, the laws of physics in such a frame do not take on their most simple form, as required by the special principle of relativity. 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.
Avoiding fictitious forces in calculations
Non-inertial frames can be avoided. Of course, measurements with respect to non-inertial reference frames can be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration is 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. As pointed out by Ryder for the case of rotating frames as used in meteorology:
Detection of a non-inertial frame: need for fictitious forces
That a given frame is non-inertial can be detected by its need for fictitious forces to explain observed motions. For example, the rotation of the Earth can be observed using a Foucault pendulum. The rotation of the Earth causes the pendulum to change its plane of oscillation (fixed in space) with respect to its surroundings (moving with the Earth). The explanation of the apparent change in orientation from an Earth-bound (non-inertial) frame of reference requires the introduction of the fictitious Coriolis force.
Another famous example is that of the tension in the string between rotating spheres. In that case, prediction of the measured tension in the string based upon the motion of the spheres as observed from a rotating reference frame requires the rotating observers to introduce a fictitious centrifugal force .
In general, the identification of a frame as non-inertial is established by the presence of fictitious forces.
Arnol'd says:
As stated by Iro:
Fictitious forces in curvilinear coordinates
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 fictitious forces" to indicate their connection to the generalized coordinates of Lagrangian mechanics. The application of Lagrangian methods to polar coordinates can be found here.
See also
|
| |
|
|
