Non-inertial reference frame: Difference between revisions

Revision as of 16:47, 19 September 2022

Revision as of 20:01, 2 November 2022

Line 4:

A '''non-inertial reference frame''' is a [[frame of reference]] that undergoes [[acceleration]] with respect to an [[Inertial frame of reference|inertial frame]].<ref name=Tocaci>{{cite book |title=Relativistic Mechanics, Time, and Inertia |author=Emil Tocaci, Clive William Kilmister |page=251 |url=https://books.google.com/books?id=7dVRL51JRI0C&pg=PA251 |isbn=90-277-1769-9 |year=1984 |publisher=Springer }}</ref> An [[accelerometer]] at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration.<ref>{{cite book |title=Essential Relativity |author=Wolfgang Rindler |page=25 |url=https://books.google.com/books?id=0J_dwCmQThgC&pg=PT43 |isbn=3-540-07970-X |year=1977 |publisher=[[Birkhäuser]]}}</ref><ref>{{cite book |title=Basics of Space Flight |author= Ludwik Marian Celnikier |page=286 |url=https://books.google.com/books?id=u2kf5uuaC6oC&pg=PA286 |isbn=2-86332-132-3 |year=1993 |publisher=Atlantica Séguier Frontières}}</ref>

In [[classical mechanics]] it is often possible to explain the motion of bodies in non-inertial reference frames is modeled by introducing additional forces ([[D'Alembert's principle|d'Alembert forces]]) to inertial reference frames in order to account for the inertia effects that are appearing in this situation. Because in principle they don't belong to the modeling of an inertial frame in terms of [[Newton's laws of motion|Newton's second law]] such inertial effects are called [[fictitious forces]]. (alsoThey might be called inertial forces, or pseudo- forces, too. <ref name=Iro>{{cite book |author=Harald Iro |title=A Modern Approach to Classical Mechanics |page=180 |url=https://books.google.com/books?id=-L5ckgdxA5YC&pg=PA179 |isbn=981-238-213-5 |year=2002 |publisher=[[World Scientific]] }}</ref> and [[D'Alembert's principle|d'Alembert forces]]) to [[Newton's laws of motion|Newton's second law]]. Common examples of this include the [[Coriolis force]] and the [[centrifugal force (fictitious)|centrifugal force]].

In general, the expression for any fictitious force can be derived from the acceleration of the non-inertial frame.<ref name=Shadowitz>{{cite book |author=Albert Shadowitz |url=https://archive.org/details/specialrelativit0000shad |url-access=registration |title=Special relativity |isbn=0-486-65743-4 |page=[https://archive.org/details/specialrelativit0000shad/page/4 4] |publisher=[[Courier Dover Publications]] |edition=Reprint of 1968 |year=1988}}</ref>

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'."<ref name=Goodman>{{cite book |title=Dynamics |author=Lawrence E. Goodman & William H. Warner |url=https://books.google.com/books?id=2z0ue1xk7gUC |isbn=0-486-42006-X |publisher=Courier Dover Publications |year=2001 |edition=Reprint of 1963|page=358}}</ref>

In the theory of [[general relativity]], the curvature of [[spacetime]] causes frames to be [[Local reference frame|locally]] inertial, but globally non-inertial. Due to the [[Introduction to the mathematics of general relativity|non-Euclidean geometry of curved space-time]], there are no global inertial reference frames in general relativity. More specifically, the fictitious force which appears in general relativity is the force of [[gravity]].