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== Različiti aspekti „referentnog okvira” ==
 
ThePotreba needda tose distinguishrazlikuju betweenrazličita theznačenja various„referentnog meaningsokvira“ ofdovela "frameje ofdo reference" has led to a variety ofrazličitih termspojmova. ForNa exampleprimer, sometimesponekad theje typetip ofkoordinatnog coordinatesistema systempriključen iskao attached as a modifiermodifikator, askao inu ''Cartesiankartezijskom framereferentnom of referenceokviru''. SometimesPonekad these statenaglašava of motion isstanje emphasizedkretanja, askao inu ''[[Rotating reference frame|rotatingrotirajućem framereferentnom of referenceokviru]]''. SometimesPonekad theje waynaglašen itnačin transformsna tokoji framesse consideredtransformiše asu relatedokvire iskoji emphasizedse assmatraju inpovezanima kao u ''[[Galilean frame of reference|Galilejevom referentnom okviru]]''. SometimesPonekad framesse areokviri distinguishedrazlikuju bypo theobimu scalenjihovih of their observationsopservacija, askao inu ''macroscopicmakroskopskim'' andi ''microscopicmikroskopskim framesreferentnim of referenceokvirima''.<ref name=macroscopic>The distinction between macroscopic and microscopic frames shows up, for example, in electromagnetism where [[Constitutive equation|constitutive relations]] of various time and length scales are used to determine the current and charge densities entering [[Maxwell's equations]]. See, for example, {{cite book |title=Electromagnetic and Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media |author=Kurt Edmund Oughstun |page=165 |url=https://books.google.com/books?id=behRnNRiueAC&pg=PA165&dq=macroscopic+frame++electromagnetism|isbn=0-387-34599-X |year=2006 |publisher=Springer}}. These distinctions also appear in thermodynamics. See {{cite book |title=Classical Theory |author=Paul McEvoy |page=205 |url=https://books.google.com/books?id=dj0wFIxn-PoC&pg=PA206&dq=macroscopic+frame#PPA205,M1 |isbn=1-930832-02-8 |year=2002 |publisher=MicroAnalytix}}.</ref>
 
U ovom članku se termin ''referentni okvir posmatranja'' koristi kada je naglasak na ''stanju kretanja'', a ne na izboru koordinata ili karakteru posmatranja ili posmatračkog aparata. U tom smislu, referentni okvir posmatranja omogućava proučavanje uticaja kretanja na čitavu porodicu koordinatnih sistema koji bi mogli biti priključeni na ovaj okvir. S druge strane, koordinatni sistem se može koristiti u mnoge svrhe u kojima stanje kretanja nije glavni predmet interesa. Na primer, može se primeniti dati koordinatni sistem da bi se iskoristila simetrija sistema. Gledano sa još šire perspektive, formulacija mnogih problema iz fizike koristi ''[[generalized coordinates|generalizovane koordinate]]'', ''[[Normalni mod|normalne modove]]'' ili ''[[Sopstvene vrednosti i sopstveni vektori|sopstvene vektore]]'', koji su samo posredno povezani sa prostorom i vremenom. Stoga je korisno da se razdvoje različiti aspekti referentnog okvira radi diskusije u nastavku. Referentni okviri posmatranja, koordinatni sistemi i opservaciona oprema se uzimaju kao nezavisni koncepti.
In this article, the term ''observational frame of reference'' is used when emphasis is upon the ''state of motion'' rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a ''coordinate system'' may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs ''[[generalized coordinates]]'', ''[[normal modes]]'' or ''[[eigenvectors]]'', which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below:
 
* Okvir posmatranja (kao što je [[Инерцијални систем референције|inercijalni okvir]] ili [[Non-inertial reference frame|neinercijalni referentni okvir]]) fizički je koncept povezan sa stanjem kretanja.
* An observational frame (such as an [[inertial frame]] or [[non-inertial frame of reference]]) is a physical concept related to state of motion.
* Koordinatni sistem je matematički koncept, koji se sastoji od izbora jezika korištenog za opisivanje opažanja.<ref name =Pontriagin>In very general terms, a coordinate system is a set of arcs ''x''<sup>i</sup> = ''x''<sup>i</sup> (''t'') in a complex [[Lie group]]; see {{cite book |author=Lev Semenovich Pontri͡agin |title=L.S. Pontryagin: Selected Works Vol. 2: Topological Groups |page= 429 |year= 1986|url=https://books.google.com/books?id=JU0DT_wXu2oC&pg=PA429&dq=algebra+%22coordinate+system%22 |isbn=2-88124-133-6 |publisher=Gordon and Breach|edition=3rd }}. Less abstractly, a coordinate system in a space of n-dimensions is defined in terms of a basis set of vectors {'''e'''<sub>1</sub>, '''e'''<sub>2</sub>,… '''e'''<sub>n</sub>}; see {{cite book |title=Linear Algebra: A Geometric Approach |author1=Edoardo Sernesi |author2=J. Montaldi |page=95 |url=https://books.google.com/books?id=1dZOuFo1QYMC&pg=PA95&dq=algebra+%22coordinate+system%22|isbn=0-412-40680-2 |year=1993 |publisher=CRC Press}} As such, the coordinate system is a mathematical construct, a language, that may be related to motion, but has no necessary connection to motion.</ref> ConsequentlyShodno tome, anposmatrač observeru inposmatračkom anokviru observationalmože frameizabrati ofda referencekoristi canbilo choosekoji tokoordinatni employ any coordinate systemsistem (Cartesiankartezijanski, polarpolarni, curvilinearkrivolinijski, generalized,generalizovani …...) toda describebi observationsopisao madezapažanja fromsagledana thatiz frametog ofreferentnog referenceokvira. APromena changeizbora inovog thekoordinatnog choicesistema ofne thismenja coordinateposmatračevo systemstanje doeskretanja, noti changene anpodrazumeva observer'spromenu stateu ofreferentnom motion,okviru andposmatrača. soOvo doesgledište notse entailmože anaći changei indrugde.<ref thename=Johansson>{{cite observer'sbook ''observational''|title=Unification frameof Classical, Quantum and Relativistic Mechanics and of reference.the ThisFour viewpointForces can|author1=J beX foundZheng-Johansson elsewhere|author2=Per-Ivar asJohansson well|page=13 |url=https://books.<refgoogle.com/books?id=I1FU37uru6QC&pg=PA13&dq=frame+coordinate+johansson|isbn=1-59454-260-0 name|publisher=JohanssonNova Publishers |year=2006}}</ref> Neosporno je da su neki koordinatni sistemi bolji izbor za neka zapažanja od drugih.▼
* A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations.<ref name =Pontriagin>
* Izbor merene veličine i opservacionog aparata je zasebno pitanje od posmatračevog stanja kretanja i izbora koordinatnog sistema.
 
Brading i Kastelani su diskusiju odveli izvan jednostavnih sistemsko-vremenskih koordinatnih sistema.<ref name=Brading>{{cite book |title=Symmetries in Physics: Philosophical Reflections |author1=Katherine Brading |author2=Elena Castellani |page=417 |url=https://books.google.com/books?id=SnmBN64cAdYC&pg=PA417&dq=%22idea+of+a+reference+frame%22|isbn=0-521-82137-1 |year=2003 |publisher=Cambridge University Press}}</ref> Proširenje na koordinatne sisteme koristeći generalizovane koordinate u osnovi je [[Хамилтонов принцип|Hamiltonskih]] i [[Lagrangian mechanics|Lagranžovih]] formulacija<ref name=Johns>{{cite book |title=Analytical Mechanics for Relativity and Quantum Mechanics |page=Chapter 16 |author=Oliver Davis Johns |url=https://books.google.com/books?id=PNuM9YDN8CIC&pg=PA318&dq=coordinate+observer#PPA276,M1 |isbn=0-19-856726-X |year=2005 |publisher=Oxford University Press |nopp=true }}</ref> of [[quantum field theory|kvantne teorije polja]], [[classicalКласична mechanicsмеханика|classicalklasične relativisticrelativističke mechanicsmehanike]], andi [[quantumQuantum gravity|kvantne gravitacije]].<ref name=Greenwood>{{cite book |title=Classical dynamics |author=Donald T Greenwood |page=313 |year=1997 |edition=Reprint of 1977 edition by Prentice-Hall |publisher=Courier Dover Publications |url=https://books.google.com/books?id=x7rj83I98yMC&pg=RA2-PA314&dq=%22relativistic+%22+Lagrangian+OR+Hamiltonian#PRA2-PA313,M1 |isbn=0-486-69690-1 }}</ref><ref name=Trump>{{cite book |title=Classical Relativistic Many-Body Dynamics |author1=Matthew A. Trump |author2=W. C. Schieve |page= 99 |url=https://books.google.com/books?id=g2yfLOp0IzwC&pg=PA99&dq=relativity+%22generalized+coordinates%22#PPA99,M1 ▼
▲In very general terms, a coordinate system is a set of arcs ''x''<sup>i</sup> = ''x''<sup>i</sup> (''t'') in a complex [[Lie group]]; see {{cite book |author=Lev Semenovich Pontri͡agin |title=L.S. Pontryagin: Selected Works Vol. 2: Topological Groups |page= 429 |year= 1986|url=https://books.google.com/books?id=JU0DT_wXu2oC&pg=PA429&dq=algebra+%22coordinate+system%22|isbn=2-88124-133-6 |publisher=Gordon and Breach|edition=3rd }}. Less abstractly, a coordinate system in a space of n-dimensions is defined in terms of a basis set of vectors {'''e'''<sub>1</sub>, '''e'''<sub>2</sub>,… '''e'''<sub>n</sub>}; see {{cite book |title=Linear Algebra: A Geometric Approach |author1=Edoardo Sernesi |author2=J. Montaldi |page=95 |url=https://books.google.com/books?id=1dZOuFo1QYMC&pg=PA95&dq=algebra+%22coordinate+system%22|isbn=0-412-40680-2 |year=1993 |publisher=CRC Press}} As such, the coordinate system is a mathematical construct, a language, that may be related to motion, but has no necessary connection to motion.</ref> Consequently, an observer in an observational frame of reference can choose to employ any coordinate system (Cartesian, polar, curvilinear, generalized, …) to describe observations made from that frame of reference. A change in the choice of this coordinate system does not change an observer's state of motion, and so does not entail a change in the observer's ''observational'' frame of reference. This viewpoint can be found elsewhere as well.<ref name=Johansson>
|year=1999 |publisher=Springer |isbn= 0-7923-5737-X }}</ref><ref name=Kompaneyets>{{cite book |author=A S Kompaneyets |title=Theoretical Physics |url=https://books.google.com/books?id=CQ2gBrL5T4YC&pg=PA118&dq=relativity+%22generalized+coordinates%22|page=118 |isbn=0-486-49532-9 |year=2003 |publisher=Courier Dover Publications |edition=Reprint of the 1962 2nd }}</ref><ref name=Srednicki>{{cite book |title=Quantum Field Theory |page= Chapter 4|author=M Srednicki |publisher=Cambridge University Press |year=2007 |isbn=978-0-521-86449-7 |url=https://books.google.com/books?id=5OepxIG42B4C&pg=PA266&dq=isbn=9780521864497#PPA31,M1 |nopp=true }}</ref><ref name=Rovelli>{{cite book |title=Quantum Gravity |author=Carlo Rovelli |page= 98 ff |url=https://books.google.com/books?id=HrAzTmXdssQC&pg=PA179&dq=%22relativistic+%22+Lagrangian+OR+Hamiltonian#PPA98,M1 |isbn=0-521-83733-2 |year=2004 |publisher=Cambridge University Press}}</ref>▼
{{cite book |title=Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces |author1=J X Zheng-Johansson |author2=Per-Ivar Johansson |page=13
|url=https://books.google.com/books?id=I1FU37uru6QC&pg=PA13&dq=frame+coordinate+johansson|isbn=1-59454-260-0
|publisher=Nova Publishers
|year=2006}}</ref> Which is not to dispute that some coordinate systems may be a better choice for some observations than are others.
 
* Choice of what to measure and with what observational apparatus is a matter separate from the observer's state of motion and choice of coordinate system.
 
The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani.<ref name=Brading>{{cite book |title=Symmetries in Physics: Philosophical Reflections |author1=Katherine Brading |author2=Elena Castellani |page=417 |url=https://books.google.com/books?id=SnmBN64cAdYC&pg=PA417&dq=%22idea+of+a+reference+frame%22|isbn=0-521-82137-1 |year=2003 |publisher=Cambridge University Press}}</ref> Extension to coordinate systems using generalized coordinates underlies the [[Hamilton's principle|Hamiltonian]] and [[Lagrangian mechanics|Lagrangian]] formulations<ref name=Johns>{{cite book |title=Analytical Mechanics for Relativity and Quantum Mechanics |page=Chapter 16 |author=Oliver Davis Johns |url=https://books.google.com/books?id=PNuM9YDN8CIC&pg=PA318&dq=coordinate+observer#PPA276,M1
▲|isbn=0-19-856726-X |year=2005 |publisher=Oxford University Press |nopp=true }}</ref> of [[quantum field theory]], [[classical mechanics|classical relativistic mechanics]], and [[quantum gravity]].<ref name=Greenwood>{{cite book |title=Classical dynamics |author=Donald T Greenwood |page=313 |year=1997 |edition=Reprint of 1977 edition by Prentice-Hall |publisher=Courier Dover Publications |url=https://books.google.com/books?id=x7rj83I98yMC&pg=RA2-PA314&dq=%22relativistic+%22+Lagrangian+OR+Hamiltonian#PRA2-PA313,M1 |isbn=0-486-69690-1 }}</ref><ref name=Trump>{{cite book |title=Classical Relativistic Many-Body Dynamics |author1=Matthew A. Trump |author2=W. C. Schieve |page= 99 |url=https://books.google.com/books?id=g2yfLOp0IzwC&pg=PA99&dq=relativity+%22generalized+coordinates%22#PPA99,M1
▲|year=1999 |publisher=Springer |isbn= 0-7923-5737-X }}</ref><ref name=Kompaneyets>{{cite book |author=A S Kompaneyets |title=Theoretical Physics |url=https://books.google.com/books?id=CQ2gBrL5T4YC&pg=PA118&dq=relativity+%22generalized+coordinates%22|page=118 |isbn=0-486-49532-9 |year=2003 |publisher=Courier Dover Publications |edition=Reprint of the 1962 2nd }}</ref><ref name=Srednicki>{{cite book |title=Quantum Field Theory |page= Chapter 4|author=M Srednicki |publisher=Cambridge University Press |year=2007 |isbn=978-0-521-86449-7 |url=https://books.google.com/books?id=5OepxIG42B4C&pg=PA266&dq=isbn=9780521864497#PPA31,M1 |nopp=true }}</ref><ref name=Rovelli>{{cite book |title=Quantum Gravity |author=Carlo Rovelli |page= 98 ff |url=https://books.google.com/books?id=HrAzTmXdssQC&pg=PA179&dq=%22relativistic+%22+Lagrangian+OR+Hamiltonian#PPA98,M1
|isbn=0-521-83733-2 |year=2004 |publisher=Cambridge University Press}}</ref>
 
== Reference ==
Преузето из „https://sr.wikipedia.org/wiki/Referentni_sistem”