Угаона брзина — разлика између измена
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{{Short description|Псеудовектор који представља промену оријентације објекта у односу на време}}{{rut}}
{{Infobox physical quantity
| name = Угаона брзина
| unit =
| otherunits =
| symbols = '''{{math|ω}}'''
| baseunits = s<sup>−1</sup>
| dimension = wikidata
| extensive = yes
| intensive = yes (for [[rigid body]] only)
| conserved = no
| transformsas = псеудовектор
| derivations = {{math|1='''''ω''''' = d'''θ''' / d''t''}}
}}
[[Датотека:Angularvelocity.png|мини|Угаона брзина описује брзину ротације неког тела. Правац [[вектор]]а угаоне брзине подудара се са осом ротације, а смер joj је у овом случају (ротација супротно од смера кретања казаљки на [[часовник]]у) усмерен ка посматрачу]]
'''Угаона брзина''' или ''ротациона брзина''' ('''{{math|ω}}''' or '''{{math|Ω}}'''), такође позната као '''вектор угаоне фреквенције''',<ref name="UP1">{{cite book
| last = Cummings
| first = Karen
|author2=Halliday, David
| title = Understanding physics
| publisher = John Wiley & Sons Inc., authorized reprint to Wiley – India
| date = 2007
| location = New Delhi
| pages = 449, 484, 485, 487
| url = https://books.google.com/books?id=rAfF_X9cE0EC
| isbn =978-81-265-0882-2 }}(UP1)</ref> [[вектор]]ска је [[физичка величина]] која описује брзину и смер ротације неког тела. Њен интензитет бројно је једнак [[угао|углу]] (Θ) (израженом у радијанима) који тело у току своје ротације опише у [[јединица времена|јединици времена]] (t). У складу с тим, јединица угаоне брзине у [[СИ изведене јединице|СИ систему]] је [[радијан]] у [[секунд]]и. Правац угаоне брзине поклапа се са правцем осе око које тело ротира, а смер је одређен правилом „казаљки на [[часовник]]у" (или правилом [[правило десне руке|десног завртња]]).<ref name= EM1>{{cite book
| last = Hibbeler
| first = Russell C.
| title = Engineering Mechanics
| publisher = Pearson Prentice Hall
| year = 2009
| location = Upper Saddle River, New Jersey
| pages = 314, 153
| url =https://books.google.com/books?id=tOFRjXB-XvMC&q=angular+velocity&pg=PA314
| isbn = 978-0-13-607791-6}}(EM1)</ref> Према овом правилу, ротација тела посматрана са врха вектора угаоне брзине супротна је смеру кретања казаљки на часовнику (или ако десни завртањ паралелан са осом ротације обрћемо у смеру ротације тела, смер његовог „напредовања“ (или „назадовања") једнак је смеру вектора угаоне брзине; нпр. ако чеп на флаши обрћемо у истом смеру као што тело ротира он ће „напредовати“ ка флаши или „назадовати“ од флаше, што ће бити у оба случаја једнако смеру угаоне брзине тела, као и чепа, наравно). Угаона брзина је у вези и са [[брзина револуције|брзином револуције]] небеских тела која се мери у јединицама као што је [[револуција (астрономија)|револуција]] у [[минут]]у.
Ознака за угаону брзину је [[Грчки језик|грчко слово]] [[омега]] ('''ω'''). Угаона брзина астрономских објеката обично се означава великим словом омега '''Ω'''.
There are two types of angular velocity.
* '''Orbital angular velocity''' refers to how fast a point object [[Rotation around a fixed axis|revolves about a fixed origin]], i.e. the time rate of change of its angular position relative to the [[Origin (mathematics)|origin]].
* '''Spin angular velocity''' refers to how fast a rigid body rotates with respect to its [[centre of rotation|center of rotation]] and is independent of the choice of origin, in contrast to orbital angular velocity.
In general, angular velocity has [[dimension (physics)|dimension]] of angle per unit time (angle replacing [[distance]] from linear [[velocity]] with time in common). The [[SI unit]] of angular velocity is [[radians per second]],<ref>{{cite book |title=International System of Units (SI) |edition=revised 2008 |first1=Barry N. |last1=Taylor |publisher=DIANE Publishing |year=2009 |isbn=978-1-4379-1558-7 |page=27 |url=https://books.google.com/books?id=I-BlErBBeL8C}} [https://books.google.com/books?id=I-BlErBBeL8C&pg=PA27 Extract of page 27]</ref> with the [[radian]] being a [[dimensionless quantity]], thus the SI units of angular velocity may be listed as s<sup>−1</sup>. Angular velocity is usually represented by the symbol [[omega]] ('''{{math|ω}}''', sometimes '''{{math|Ω}}'''). By convention, positive angular velocity indicates counter-[[clockwise]] rotation, while negative is clockwise.
For example, a [[Geosynchronous orbit|geostationary]] satellite completes one orbit per day above the [[equator]], or 360 degrees per 24 hours, and has angular velocity ''ω'' = (360°)/(24 h) = 15°/h, or (2π rad)/(24 h) ≈ 0.26 rad/h. If angle is measured in radians, the linear velocity is the radius times the angular velocity, <math>v = r\omega</math>. With orbital radius 42,000 km from the earth's center, the satellite's speed through space is thus ''v'' = 42,000 km × 0.26/h ≈ 11,000 km/h. The angular velocity is positive since the satellite travels eastward with the Earth's rotation (counter-clockwise from above the north pole.)
== Референце ==
{{Reflist}}
== Литература ==
{{Refbegin|30em}}
* {{note_label|Symon1971||}}{{cite book|last=Symon | first=Keith |title=Mechanics|publisher=Addison-Wesley, Reading, MA|year=1971|isbn = 978-0-201-07392-8 }}
* {{note_label|LL||}}{{cite book |last=Landau |first=L.D. |author-link=Lev Landau |author2=Lifshitz, E.M. |title= Mechanics|year=1997 |publisher=Butterworth-Heinemann |isbn=978-0-7506-2896-9 |author2-link=Evgeny Lifshitz }}
* {{Cite book|ref=harv|last=Keith|first=Symon|title=Mechanics|publisher=Addison-Wesley, Reading, MA|year=1971|isbn=978-0-201-07392-8|pages=}}
* {{Citation
| last=Arvo
| first=James
| year=1992
| contribution=Fast random rotation matrices
| title=Graphics Gems III
| editor=David Kirk
| publisher=[[Academic Press]] Professional
| place=San Diego
| pages=[https://archive.org/details/isbn_9780124096738/page/117 117–120]
| bibcode=1992grge.book.....K
| isbn=978-0-12-409671-4
| url=https://archive.org/details/isbn_9780124096738/page/117
}}
* {{Citation
| last=Baker
| first=Andrew
| title=Matrix Groups: An Introduction to Lie Group Theory
| year=2003
| publisher=[[Springer-Verlag|Springer]]
| isbn=978-1-85233-470-3
| url-access=registration
| url=https://archive.org/details/matrixgroupsintr0000bake
}}
* {{Citation
| last=Bar-Itzhack
| first=Itzhack Y.
| date= 2000
| title=New method for extracting the quaternion from a rotation matrix
| journal=Journal of Guidance, Control and Dynamics
| volume=23
| issue=6
| pages=1085–1087
| issn=0731-5090
| doi=10.2514/2.4654
| bibcode=2000JGCD...23.1085B
}}
* {{Citation
| last1=Björck
| first1=Åke
| last2=Bowie
| first2=Clazett
|date=June 1971
| title=An iterative algorithm for computing the best estimate of an orthogonal matrix
| journal=SIAM Journal on Numerical Analysis
| volume=8
| issue=2
| pages=358–364
| issn=0036-1429
| doi=10.1137/0708036
| bibcode=1971SJNA....8..358B
}}
* {{Citation
| last=Cayley
| first=Arthur
| author-link=Arthur Cayley
| year=1846
| title=Sur quelques propriétés des déterminants gauches
| journal=[[Journal für die reine und angewandte Mathematik]]
| volume=1846
| issue=32
| pages=119–123
| issn=0075-4102
| doi=10.1515/crll.1846.32.119
| s2cid=199546746
| url=https://zenodo.org/record/1448846
}}; reprinted as article 52 in {{Citation
| last=Cayley
| first=Arthur
| author-link=Arthur Cayley
| year=1889
| title=The collected mathematical papers of Arthur Cayley
| publisher=[[Cambridge University Press]]
| volume=I (1841–1853)
| pages=332–336
| isbn=<!-- none given -->
| url=http://www.hti.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=ABS3153.0001.001;didno=ABS3153.0001.001;view=image;seq=00000349
}}
* {{Citation
| last1=Diaconis
| first1=Persi
| author1-link=Persi Diaconis
| last2=Shahshahani
| first2=Mehrdad
| title=The subgroup algorithm for generating uniform random variables
| journal=Probability in the Engineering and Informational Sciences
| volume=1
| pages=15–32
| year=1987
| issn=0269-9648
| doi=10.1017/S0269964800000255
}}
* {{Citation
| last=Engø
| first=Kenth
|date=June 2001
| title=On the BCH-formula in '''so'''(3)
| journal=BIT Numerical Mathematics
| volume=41
| pages=629–632
| issn=0006-3835
| doi=10.1023/A:1021979515229
| url=http://www.ii.uib.no/publikasjoner/texrap/abstract/2000-201.html
| issue=3
| s2cid=126053191
}}
* {{Citation
| last1=Fan
| first1=Ky
| last2=Hoffman
| first2=Alan J.
|date=February 1955
| title=Some metric inequalities in the space of matrices
| journal=[[Proceedings of the American Mathematical Society]]
| volume=6
| issue=1
| pages=111–116
| issn=0002-9939
| doi=10.2307/2032662
| jstor=2032662
| doi-access=free
}}
* {{Citation
| last1=Fulton
| first1=William
| author1-link=William Fulton (mathematician)
| last2=Harris
| first2=Joe
| author2-link=Joe Harris (mathematician)
| year=1991
| title=Representation Theory: A First Course
| publisher=[[Springer-Verlag|Springer]]
| place=New York, Berlin, Heidelberg
| isbn=978-0-387-97495-8
| series=[[Graduate Texts in Mathematics]]
| volume=129
| mr=1153249
}}
* {{Citation
| last1=Goldstein
| first1=Herbert
| author1-link=Herbert Goldstein
| last2=Poole
| first2=Charles P.
| last3=Safko
| first3=John L.
| year=2002<!-- January 15 -->
| title=Classical Mechanics
| edition=third
| publisher=[[Addison Wesley]]
| isbn=978-0-201-65702-9
}}
* {{Citation
| last=Hall
| first=Brian C.
| title=Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
| year=2004
| publisher=[[Springer-Verlag|Springer]]
| isbn=978-0-387-40122-5
}} ([[Graduate Texts in Mathematics|GTM]] 222)
* {{Citation
| last1=Herter
| first1=Thomas
| last2=Lott
| first2=Klaus
| date= 1993
| title=Algorithms for decomposing 3-D orthogonal matrices into primitive rotations
| journal=Computers & Graphics
| volume=17
| pages=517–527
| issn=0097-8493
| doi=10.1016/0097-8493(93)90003-R
| issue=5
}}
* {{Citation
| last=Higham
| first=Nicholas J.
| date=October 1, 1989
| contribution=Matrix nearness problems and applications
| title=Applications of Matrix Theory
| editor1-last=Gover
| editor1-first=Michael J. C.
| editor2-last=Barnett
| editor2-first=Stephen
| pages=[https://archive.org/details/applicationsofma0000unse/page/1 1–27]
| publisher=[[Oxford University Press]]
| isbn=978-0-19-853625-3
| url=https://archive.org/details/applicationsofma0000unse/page/1
}}
* {{Citation
| last1=León
| first1=Carlos A.
| last2=Massé
| first2=Jean-Claude
| last3=Rivest
| first3=Louis-Paul
|date=February 2006
| title=A statistical model for random rotations
| journal=Journal of Multivariate Analysis
| volume=97
| pages=412–430
| issn=0047-259X
| doi=10.1016/j.jmva.2005.03.009
| url=http://www.mat.ulaval.ca/pages/lpr/
| issue=2
| doi-access=free
}}
* {{Citation
| last=Miles
| first=Roger E.
|date=December 1965
| title=On random rotations in ''R''<sup>3</sup>
| journal=[[Biometrika]]
| volume=52
| pages=636–639
| issn=0006-3444
| doi=10.2307/2333716
| issue=3/4
| jstor=2333716
}}
* {{Citation
| last1=Moler
| first1=Cleve
| author1-link=Cleve Moler
| last2=Morrison
| first2=Donald
| title=Replacing square roots by pythagorean sums
| journal=IBM Journal of Research and Development
| volume=27
| pages=577–581
| year=1983<!--
| month=November-->
| url=http://domino.watson.ibm.com/tchjr/journalindex.nsf/0b9bc46ed06cbac1852565e6006fe1a0/0043d03ee1c1013c85256bfa0067f5a6?OpenDocument
| issn=0018-8646
| issue=6
| doi=10.1147/rd.276.0577
}}
* {{Citation
| last=Murnaghan
| first=Francis D.
| author-link=Francis Dominic Murnaghan (mathematician)
| year=1950<!-- November 15 -->
| title=The element of volume of the rotation group
| journal=[[Proceedings of the National Academy of Sciences]]
| volume=36
| issue=11
| pages=670–672
| issn=0027-8424
| doi=10.1073/pnas.36.11.670
| pmid=16589056
| pmc=1063502
| bibcode=1950PNAS...36..670M
| doi-access=free
}}
* {{Citation
| last=Murnaghan
| first=Francis D.
| author-link=Francis Dominic Murnaghan (mathematician)
| year=1962
| title=The Unitary and Rotation Groups
| series=Lectures on applied mathematics
| publisher=Spartan Books
| place=Washington
| isbn=<!-- none -->
}}
*{{Citation
| last=Cayley
| first=Arthur
| author-link=Arthur Cayley
| year=1889
| title=The collected mathematical papers of Arthur Cayley
| publisher=[[Cambridge University Press]]
| volume=I (1841–1853)
| pages=332–336
| isbn=<!-- none given -->
| url=http://www.hti.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;cc=umhistmath;rgn=full%20text;idno=ABS3153.0001.001;didno=ABS3153.0001.001;view=image;seq=00000349
}}
*{{Citation
| last=Paeth
| first=Alan W.
| year=1986
| title=A Fast Algorithm for General Raster Rotation
| journal=Proceedings, Graphics Interface '86
| pages=77–81
| url=https://graphicsinterface.org/wp-content/uploads/gi1986-15.pdf
}}
*{{Citation
| last1=Daubechies
| first1=Ingrid
| author-link1=Ingrid Daubechies
| last2=Sweldens
| first2=Wim
| author-link2=Wim Sweldens
| year=1998
| title=Factoring wavelet transforms into lifting steps
| journal=Journal of Fourier Analysis and Applications
| volume=4
| issue=3
| pages=247–269
| url=https://cm-bell-labs.github.io/who/wim/papers/factor/factor.pdf
| doi=10.1007/BF02476026
| s2cid=195242970
}}
* {{Citation
| last=Pique
| first=Michael E.
| year=1990
| contribution=Rotation Tools
| title=Graphics Gems
| editor=Andrew S. Glassner
| publisher=[[Academic Press]] Professional
| place=San Diego
| pages=465–469
| isbn=978-0-12-286166-6
| url=http://www.graphicsgems.org/
}}
*{{Citation
|last1=Press |first1=William H.
|last2=Teukolsky |first2=Saul A.
|last3=Vetterling |first3=William T.
|last4=Flannery |first4=Brian P.
|year=2007 |title=Numerical Recipes: The Art of Scientific Computing |edition=3rd |publisher=Cambridge University Press |location=New York |isbn=978-0-521-88068-8 |chapter=Section 21.5.2. Picking a Random Rotation Matrix |chapter-url=http://apps.nrbook.com/empanel/index.html#pg=1130 }}
* {{Citation
| last=Shepperd
| first=Stanley W.
| date= 1978
| title=Quaternion from rotation matrix
| journal= Journal of Guidance and Control
| volume=1
| issue=3
| pages=223–224
| doi=10.2514/3.55767b
}}
* {{Citation
| last=Shoemake
| first=Ken
| year=1994
| contribution=Euler angle conversion
| title=Graphics Gems IV
| editor=Paul Heckbert
| publisher=[[Academic Press]] Professional
| place=San Diego
| pages=[https://archive.org/details/isbn_9780123361554/page/222 222–229]
| isbn=978-0-12-336155-4
| url=https://archive.org/details/isbn_9780123361554/page/222
}}
* {{Citation
| last=Stuelpnagel
| first=John
|date=October 1964
| title=On the parameterization of the three-dimensional rotation group
| journal=SIAM Review
| volume=6
| pages=422–430
| issn=0036-1445
| doi=10.1137/1006093
| issue=4
| bibcode=1964SIAMR...6..422S
| s2cid=13990266
| url=https://semanticscholar.org/paper/740c8c9c6b32bf2ca583009ac4cf495c417c6b75
}} (Also [https://ntrs.nasa.gov/search.jsp NASA-CR-53568].)
* {{Citation
| last=Varadarajan
| first=Veeravalli S.
| title=Lie Groups, Lie Algebras, and Their Representation
| year=1984
| publisher=[[Springer-Verlag|Springer]]
| isbn=978-0-387-90969-1
}} ([[Graduate Texts in Mathematics|GTM]] 102)
* {{Citation
| last=Wedderburn
| first=Joseph H. M.
| author-link=Joseph Wedderburn
| year=1934
| title=Lectures on Matrices
| publisher=[[American Mathematical Society|AMS]]
| isbn=978-0-8218-3204-2
| url=https://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3AWedderburn+intitle%3ALectures+on+Matrices&as_publication=&as_ylo=1934&as_yhi=1934&btnG=Search
}}
{{Refend}}
== Спољашње везе ==
{{
* [http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_triganglinvelocity.xml Угаона и линеарна брзина]
* [https://archive.org/details/acollegetextboo01kimbgoog/page/n103 <!-- pg=88 --> A college text-book of physics] By Arthur Lalanne Kimball (''Angular Velocity of a particle'')
* {{cite web|last=Pickering|first=Steve|title=ω Speed of Rotation [Angular Velocity]|url=http://www.sixtysymbols.com/videos/angularvelocity.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|year=2009}}
{{нормативна контрола}}
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