anuchit rotation

jyaamiti mein, ack anuchit ghoornan, jise ghoornan-pratibimb, ghoornan-pratibimb, ghoornan-paraavartan yaa ghoornan-paraavartan bhee kahaa jaataa haye, euclidean sthaan mein ack samamit haye joe ack aksh key baare mein ack ghoornan aur usa aksh key lambavat ack samtal mein ack pratibimb kaa sanyojan haye. pratibimb aur vyutkram anuchit ghoornan key pratyek vishesh mamle hain. koee bhee anuchit ghoornan ack sambandh parivartan haye aur, una mamalon mein joe nirdeshank mool koo sthir rakhate hain, ack raikhik parivartan haye.
iska upayog jyaamitiya samroopata, aanvik samroopata aur chrystallography key sandarbh mein ack samroopata sanchaalan key roop mein kiya jaataa haye, jahaan ack vastu joe ghoornan aur pratibimb key sanyojan seey aparivartit haye, usey "anuchit ghoornan samroopata" kahaa jaataa haye.
teen ayam.
3 aayamon mein, anuchit ghoornan koo aksh parr ack bindu mein ack aksh key baare mein ghoornan aur vyutkram key sanyojan key roop mein samaan roop seey paribhaashit kiya jaataa haye. iss kaaran seey ise rotoinversion yaa rotary inversion bhee kahaa jaataa haye. donon paribhaashaaen samatulya hain kyonki ack konn dwara ghoornan θ key baad paraavartan θ + 180° dwara ghoornan key roop mein samaan parivartan haye jisake baad vyutkram (vyutkram key bindu koo paraavartan key tala mein lena) haye. donon paribhashaon mein, sanchaalan awagaman karate hain.
ack tri-ayami samroopata jisamen kewal ack nishchit bindu hotaa haye, anivarya roop seey ack anuchit ghoornan haye. 
iss prakaar kissy vastu kaa anuchit ghoornan usaki darpan chhavi kaa ghoornan utpann kartaa haye. aksh koo ghoornan-pratibimb aksh kahaa jaataa haye. ise "aine"-gunaa anuchit ghoornan kahaa jaataa haye yadi ghoornan kaa konn, prativartan seey pahale yaa baad mein, 360°/"aine" haye (jahaan "aine" summ honah chaahiye). vyaktigat anuchit aavartan key namkaran key liye kaee alag-alag pranaaliyan hainh
ack apratyaksh samamitika key roop mein.
vyaapak arth mein, ack anuchit ghoornan koo kissy bhee apratyaksh samamit key roop mein paribhaashit kiya jaa sakata haye; i.ee.ee (3) kaa ack tatva, ee (3) \ee + (3): iss prakaar yeh ack tala mein ack shuddh pratibimb bhee hoe sakata haye, yaa ack glide tala hoe sakata haye. ack apratyaksh samamitiyaan ack orthogonal matricks key saath ack affine parivartan haye jisamen −1 kaa nirdhaarak hotaa haye.
ack uchit ghoornan ack samanya ghoornan haye. vyaapak arth mein, ack uchit ghoornan koo ack pratyaksh samamit key roop mein paribhaashit kiya gayaa haye; i.ee.ee + (3) kaa ack tatvah yeh pehchaan, aksh key saath anuvaad key saath ack ghoornan, yaa ack shuddh anuvaad bhee hoe sakata haye. ack pratyaksh samamitita ack orthogonal matricks key saath ack affine parivartan haye jisamen 1 kaa nirdhaarak hotaa haye.
sankeern yaa vyaapak indriyon mein, dou anuchit ghoornan kii sanrachana ack uchit ghoornan haye, aur ack anuchit aur uchit ghoornan kii sanrachana ack anuchit ghoornan haye.
bhautik pranaaliyan.
anuchit ghoornan key tahat ack bhautik pranali kii samroopata kaa adhyayan karate samay (ee.jee.yadi kissy pranali mein darpan samroopata samtal haye), tou vactor aur chhadm-kaarak (saath hii scalar aur chhadm-kaarak, aur samanya roop seey tensor aur chhadm-sansoochak key beach) key beach antar karna mahatvapurna haye, kyonki baad vaalaa uchit aur anuchit ghoornan key tahat alag-alag roop seey parivartit hotaa haye (3 aayamon mein, chhadm-kaarak vyutkram key tahat aparivartaniya hotey hain).

