References analysis of the Wikipedia article "چارچوب مرجع" in the Persian version

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The distinction between macroscopic and microscopic frames shows up, for example, in electromagnetism where constitutive relations of various time and length scales are used to determine the current and charge densities entering معادلات ماکسول. See, for example, Kurt Edmund Oughstun (2006). [[۱](https://books.google.com/books?id=behRnNRiueAC&q=macroscopic+frame++electromagnetism&pg=PA165) Electromagnetic and Optical Pulse Propagation 1: Spectral Representations in Temporally Dispersive Media]. Springer. p. 165. ISBN 0-387-34599-X. {{cite book}}: Check |url= value (help). These distinctions also appear in thermodynamics. See Paul McEvoy (2002). [[۲](https://books.google.com/books?id=dj0wFIxn-PoC&q=macroscopic+frame&pg=PA206) Classical Theory]. MicroAnalytix. p. 205. ISBN 1-930832-02-8. {{cite book}}: Check |url= value (help).

به‌طورکلی، یک دستگاه مختصات مجموعه‌ای از کمان‌ها x^i = x^i (t) در یک گروه لی پیچیده است. نگاه کنید به Lev Semenovich Pontri͡agin (1986). [[۳](https://books.google.com/books?id=JU0DT_wXu2oC&q=algebra+%22coordinate+system%22&pg=PA429) L.S. Pontryagin: Selected Works Vol. 2: Topological Groups] (3rd ed.). Gordon and Breach. p. 429. ISBN 2-88124-133-6. {{cite book}}: Check |url= value (help). به‌طور خلاصه‌تر، یک دستگاه مختصات در یک فضای n-بعدی بر حسب یک مجموعه پایه از بردارها {e1, e2,... en} تعریف می‌شود. به این ترتیب، دستگاه مختصات یک ساختار ریاضی، یک زبان است که ممکن است به حرکت مرتبط باشد، اما ارتباط ضروری با حرکت ندارد.

J X Zheng-Johansson; Per-Ivar Johansson (2006). [[۴](https://books.google.com/books?id=I1FU37uru6QC&q=frame+coordinate+johansson&pg=PA13) Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces]. Nova Publishers. p. 13. ISBN 1-59454-260-0. {{cite book}}: Check |url= value (help)

Jean Salençon; Stephen Lyle (2001). [[۵](https://books.google.com/books?id=H3xIED8ctfUC&q=physical+%22frame+of+reference%22&pg=PA9) Handbook of Continuum Mechanics: General Concepts, Thermoelasticity]. Springer. p. 9. ISBN 3-540-41443-6. {{cite book}}: Check |url= value (help)

Patrick Cornille (Akhlesh Lakhtakia, editor) (1993). [[۶](https://books.google.com/books?id=qsOBhKVM1qYC&q=coordinate+system+%22reference+frame%22&pg=PA149) Essays on the Formal Aspects of Electromagnetic Theory]. World Scientific. p. 149. ISBN 981-02-0854-5. {{cite book}}: |author= has generic name (help); Check |url= value (help)

Nerlich, Graham (1994). [[۷](https://books.google.com/books?id=fKK7rKOpc7AC&q=%22idea+of+a+reference+frame%22&pg=PA64) What Spacetime Explains: Metaphysical essays on space and time]. Cambridge University Press. p. 64. ISBN 0-521-45261-9. {{cite book}}: Check |url= value (help)

William Barker; Roger Howe (2008). [[۹](https://books.google.com/books?id=NIxExnr2EjYC&q=geometry++axiom+%22coordinate+system%22&pg=PA17) Continuous symmetry: from Euclid to Klein]. American Mathematical Society. p. 18 ff. ISBN 978-0-8218-3900-3. {{cite book}}: Check |url= value (help)

According to Hawking and Ellis: "A manifold is a space locally similar to Euclidean space in that it can be covered by coordinate patches. This structure allows differentiation to be defined, but does not distinguish between different coordinate systems. Thus, the only concepts defined by the manifold structure are those that are independent of the choice of a coordinate system." Stephen W. Hawking; George Francis Rayner Ellis (1973). [[۱۲](https://books.google.com/books?id=QagG_KI7Ll8C&q=manifold+%22The+Large+Scale+Structure+of+Space-Time%22&pg=PA59) The Large Scale Structure of Space-Time]. Cambridge University Press. p. 11. ISBN 0-521-09906-4. {{cite book}}: Check |url= value (help) A mathematical definition is: A connected فضای هاسدورف M is called an n-dimensional manifold if each point of M is contained in an open set that is homeomorphic to an open set in Euclidean n-dimensional space.

Granino Arthur Korn; Theresa M. Korn (2000). [[۱۵](https://books.google.com/books?id=xHNd5zCXt-EC&q=curvilinear+%22coordinate+system%22&pg=PA169) Mathematical handbook for scientists and engineers: definitions, theorems, and formulas for reference and review]. Courier Dover Publications. p. 169. ISBN 0-486-41147-8. {{cite book}}: Check |url= value (help)

Katsu Yamane (2004). [[۱۷](https://books.google.com/books?id=tNrMiIx3fToC&q=generalized+coordinates+%22kinematic+chain%22&pg=PA12) Simulating and Generating Motions of Human Figures]. Springer. pp. 12–13. ISBN 3-540-20317-6. {{cite book}}: Check |url= value (help)

Achilleus Papapetrou (1974). [[۱۸](https://books.google.com/books?id=SWeOggyp1ZsC&q=relativistic++%22general+coordinates%22&pg=PA3) Lectures on General Relativity]. Springer. p. 5. ISBN 90-277-0540-2. {{cite book}}: Check |url= value (help)

Wilford Zdunkowski; Andreas Bott (2003). [[۱۹](https://books.google.com/books?id=GuYvC21v3g8C&q=%22curvilinear+coordinate+system%22&pg=RA1-PA84) Dynamics of the Atmosphere]. Cambridge University Press. p. 84. ISBN 0-521-00666-X. {{cite book}}: Check |url= value (help)

A. I. Borisenko; I. E. Tarapov; Richard A. Silverman (1979). [[۲۰](https://books.google.com/books?id=CRIjIx2ac6AC&q=coordinate+metric&pg=PA86) Vector and Tensor Analysis with Applications]. Courier Dover Publications. p. 86. ISBN 0-486-63833-2. {{cite book}}: Check |url= value (help)

See Arvind Kumar; Shrish Barve (2003). [[۲۱](https://books.google.com/books?id=czlUPz38MOQC&q=%22characterized+only+by+its+state+of+motion%22+inauthor:Kumar&pg=PA115) How and Why in Basic Mechanics]. Orient Longman. p. 115. ISBN 81-7371-420-7. {{cite book}}: Check |url= value (help)

Richard L Faber (1983). [[۲۵](https://books.google.com/books?id=ctM3_afLuVEC&q=relativistic++%22general+coordinates%22&pg=PA149) Differential Geometry and Relativity Theory: an introduction]. CRC Press. p. 211. ISBN 0-8247-1749-X. {{cite book}}: Check |url= value (help)

Richard Wolfson (2003). [[۲۶](https://books.google.com/books?id=OUJWKdlFKeQC&q=%22gravitational+time+dilation+%22&pg=PA216) Simply Einstein]. W W Norton & Co. p. 216. ISBN 0-393-05154-4. {{cite book}}: Check |url= value (help)

See Guido Rizzi; Matteo Luca Ruggiero (2003). [[۲۷](https://books.google.com/books?id=_PGrlCLkkIgC&q=centrifugal+%22+%22+relativity+OR+relativistic&pg=PA226) Relativity in rotating frames]. Springer. p. 33. ISBN 1-4020-1805-3. {{cite book}}: Check |url= value (help).

Katherine Brading; Elena Castellani (2003). [[۲۸](https://books.google.com/books?id=SnmBN64cAdYC&q=%22idea+of+a+reference+frame%22&pg=PA417) Symmetries in Physics: Philosophical Reflections]. Cambridge University Press. p. 417. ISBN 0-521-82137-1. {{cite book}}: Check |url= value (help)

Oliver Davis Johns (2005). [[۲۹](https://books.google.com/books?id=PNuM9YDN8CIC&q=coordinate+observer&pg=PA318) Analytical Mechanics for Relativity and Quantum Mechanics]. Oxford University Press. Chapter 16. ISBN 0-19-856726-X. {{cite book}}: Check |url= value (help)

Donald T Greenwood (1997). [[۳۰](https://books.google.com/books?id=x7rj83I98yMC&q=%22relativistic+%22+Lagrangian+OR+Hamiltonian&pg=RA2-PA314) Classical dynamics] (Reprint of 1977 edition by Prentice-Hall ed.). Courier Dover Publications. p. 313. ISBN 0-486-69690-1. {{cite book}}: Check |url= value (help)

Matthew A. Trump; W. C. Schieve (1999). [[۳۱](https://books.google.com/books?id=g2yfLOp0IzwC&q=relativity+%22generalized+coordinates%22&pg=PA99) Classical Relativistic Many-Body Dynamics]. Springer. p. 99. ISBN 0-7923-5737-X. {{cite book}}: Check |url= value (help)

Alexander Solomonovich Kompaneyets (2003). [[۳۲](https://books.google.com/books?id=CQ2gBrL5T4YC&q=relativity+%22generalized+coordinates%22&pg=PA118) Theoretical Physics] (Reprint of the 1962 2nd ed.). Courier Dover Publications. p. 118. ISBN 0-486-49532-9. {{cite book}}: Check |url= value (help)

M Srednicki (2007). [[۳۳](https://books.google.com/books?id=5OepxIG42B4C&pg=PA266) Quantum Field Theory]. Cambridge University Press. Chapter 4. ISBN 978-0-521-86449-7. {{cite book}}: Check |url= value (help)

Carlo Rovelli (2004). [[۳۴](https://books.google.com/books?id=HrAzTmXdssQC&q=%22relativistic+%22+Lagrangian+OR+Hamiltonian&pg=PA179) Quantum Gravity]. Cambridge University Press. p. 98 ff. ISBN 0-521-83733-2. {{cite book}}: Check |url= value (help)

doi.org

Kovalevsky, J.; Mueller, Ivan I. (1989). "Introduction". Reference Frames. Astrophysics and Space Science Library. Vol. 154. Dordrecht: Springer Netherlands. pp. 1–12. doi:10.1007/978-94-009-0933-5_1. ISBN 978-94-010-6909-0. ISSN 0067-0057.

worldcat.org

Chris Doran; Anthony Lasenby (2003). [[۲۲](http://www.worldcat.org/search?q=9780521715959&qt=owc_search) Geometric Algebra for Physicists]. Cambridge University Press. p. §5.2.2, p. 133. ISBN 978-0-521-71595-9. {{cite book}}: Check |url= value (help).

چارچوب مرجع (Persian Wikipedia)

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