pravaharesha, margaresha aanee margaresha

pravaharesha, margaresha aanee margaresha yaa dravachya pravahatil kshetra resha aahet.
jevha pravah kalanusar badalat rahato, mhanje jevha pravah sthir nasato tevhach teey badaltat.
satatya yantrikichya chaukatit trimiteey jaaget veg sadish kshetra vicharat ghetalyas, aamchyakade teey aaheh 
vyakhyenusar, pravahat ekach kshani vegvegalya pravaharesha chhedat naheet, kaaran drav kann ekach binduvar done bhinn veg asoo shakat naheet. tathapi, margareshanna swatahla kinwa itar margareshanna chhedanyachi parvanagi aahe (vegvegalya margareshanchya suruvatichya aanee shevatchya bindunvyatirikt, jeey vegale asane aavashyak aahe). resha swatahla aanee itar reshanna dekhil chhedu shakatat.
pravaharesha aanee kalresha kahee pravahakshetra vaishishtyancha eka snapshot pradan karatat, tarr pravaharesha aanee margaresha pravahachya-itihasavar avalambun asatat. tathapi, anekada vegvegalya kshanant kalresha (aanee resha) chey anukram-ektar ekach pratimet kinwa video pravahasah sadar kele jaatat-pravah aanee tyachya itihasachi antardrushti pradan karnyasathi vaparale jaau shakatat.
jarr ekhadi resha, vakr kinwa bund vakr reshanchya satatchya sanchasathi prarambh bindu mhanoon vaparali gelee tarr tyacha parinam mhanje pravahacha prushthbhag. sthir pravahat bund vakratechya babatit, pravahachya prushthbhagachya aat asalela drav tyach pravahachya prushthbhagachya aat kayamcha rahila pahije, kaaran pravaharesha pravah vegachya sparshika asatat. jyachya bahyaresha pravaharesha paribhashit karatat, teey scalar karya pravah karya mhanoon olakhale jaate.
rung resha ektar eka resha darshavu shakateh rung eka nishchit sthanavarun haloohaloo velenusar sodala jaato; kinwa tee kalresha darshavu shakateh rangachi eka resha eka vishisht kshani twarit lagoo kelee jaate aanee nantarchya kshani pahili jaate.
ganiteey varnan.
pravahit.
pravaharesha hya dware paribhashit kelya jaatat
jethe "sootra _ 2" heey vector cross product darshavate aanee sootra _ 3 heey eka velee "fakt eka" streamline parametric pratinidhitva aahe.
jarr vegache ghatak sootra 4 aanee pravaharesheche ghatak sootra 5 asey lihile asateel tarr aapan andaj lavto.
jeey darshavate qee vakr veg sadishala samantar aahet. yethe sootra _ 7 heey eka chull aahe jeey vakr sutrala parameters karate _ 8 pravaharesha twarit mojalya jaatat, mhanje eka velee tyaa tatkal pravah veg kshetratun sampoorn dravpadarthachi ganana kelya jaatat.
pravahanlikemadhye sanchar kebalpramanech pravahareshancha eka samooh asato.
ubhya pratalatil pravahasathi pravahareshevaril dravachya gatiche samikaran asey aaheh
sootra _ 9
pravahareshechya _ 7 yaa dishene asalelya sutratil pravahacha veg sootra _ 11 dware darshavila jaato. sootra _ 12 hii pravahareshechya vakratechi trijya aahe. dravachi ghanata sootra 13 dware aanee gatiman snigdhata sootra 14 dware darshavili jaate. sootra 15 heey daab pravan aanee sootra 16 heey pravahareshevaril veg pravan aahe. sthir pravahasathi, vegache vel vyutpann shoonya aaheh sootra _ 17. sootra _ 18 gurutvakarshanacha praveg darshavate.
margika.
margaresha hya dware paribhashit kelya jaatat
pratyay sootra _ 20 soochit karate qee aapan drav kananchya gatiche anusaran kareet aahot. 
lakshat ghya qee bindu sootra _ 21 varr vakr pravah veg vector sootra _ 22 laa samantar aahe, jethe veg vectorche moolyankan tyaa velee sootra _ 24 varr kann sootra _ 21 chya sthanavar kele jaate.
rekha.
resha asha prakare vyakt kelya jaau shakatatah
jethe, sootra _ 26 heey sthan sootra _ 28 aanee vel sootra _ 24 vareel kann sootra _ 20 chaa veg aahe. mapdand sootra _ 30, strickline sootra _ 31 aanee sootra _ 32 laa parameters karate, jethe sootra _ 24 hii swarasyapoorn vel aahe.
sthir pravah.
sthir pravahat (jevha veg vahak-kshetra velenusar badalat nahee), pravaharesha, margaresha aanee resha julatat. yache kaaran asey qee jevha pravahareshevaril kann eka binduvar pohochato, sootra 34, tyaa pravahareshevar pudhe pravah niyantrit karnari samikarane tyala eka vishisht dishene sootra 35 madhye pathvatil. jevha dusra kann sootra 34 paryant pohochato tevha pravah niyantrit karnari samikarane teech rahtil. jarr pravah sthir nasel tarr pudhil kann sthitee sootra 34 paryant pohochato tevha pravah badalala asata aanee kann vegalya dishene jaeel.
heey upayukt aahe, kaaran prayogat pravaharesha pahane sahasa khoop katheen asate. tathapi, jarr pravah sthir asel tarr streamline namunyache varnan karnyasathi ekhadi strickline vaparu shakate.
frame avalambitva.
pravaharesha chaukativar avalambun asatat. mhanjech, eka jadatviy sandarbh chaukatit chaukatit pravaharesha pravaharesha jadatviy sandarbh chaukatit pahilya pahilya pravahareshepeksha vegalya asatat. udaharanarth, vimanachya pankhambhovati havetil pravaharekha vimanatil pravashansathi jaminivaril nirikshakapeksha vegalya prakare paribhashit kelya jaatat. vimanachya udaharanat, jaminivarcha nirikshak asthir pravahache nirikshan karel aanee vimanatil nirikshak sthir pravahasah sthir pravahache nirikshan kartil. jevha shakya asel tevha drav gatishilatavadi eka sandarbh chaukat shodhanyacha prayatna karatat jyamadhye pravah sthir asato, jenekarun teey pravaharesha olakhanyasathi resha tayar karnyachya prayogik paddhatincha vapar karoo shaktil.
arj.
pravaharesheche dnyan drav gatishilatemadhye upayukt tharoo shakate. pravahareshechi vakrata hii pravahareshevar ubhya asalelya daab pravahashi sambandhit asate. pravahareshechya vakrateche kendra qamee hott asalelya trijya dabachya dishene asate. trijya daab pravahache pariman dravachi ghanata, pravahareshechi vakrata aanee sthanik veg yavarun thet mojale jaau shakate.
rung panyamadhye kinwa havet dhunyacha vapar keela jaau shakato, jyamule resha disatat, jyatoon patharesha mojalya jaau shakatat. sthir pravahasathi pravaharesha yaa pravahareshesarkhyach asatat. pudhe, rangsangaticha vapar kalmaryada tayar karnyasathi keela jaau shakato. dragg qamee karnyachya uddeshane, rachana badalanna namune margadarshan karatat. yaa karyala 'suvyavasthit karane' mhanoon olakhale jaate aanee parinami tayar kelelya aarakhadyala 'suvyavasthit' asey sambodhale jaate. havah-dravye, pravahit karnare, qaar aanee dolphin yasarkhya suvyavasthit vastoo aanee jeev anekada dolhyanna saundaryatmakdrushtya prasann karatat. 1930 aanee 1940 chya dashkatil aart dekochya shakhene, suvyavasthit aadhunik shailine tyaa kalatil vastukala aanee rachnet pravahit resha aanalya. suvyavasthit aakarache pramanit udaharan mhanje kombadiche andey jyacha bhola toke pudhe aahe. heey spashtapane darshavate qee samoril prushthbhagachi vakrata vastoochya mageel bhagapeksha khoop jaast asoo shakate. bahutek odhane odhane vastoochya mageel dravachya kadaa asalyamule hote aanee vastubhovati gelyanantar drav mand houu dene aanee kadaa naan tayar karata daab parat midvane haah uddesh asava.
operation suralit suralit konatyahi prakriyeche varnan karnyasathi tyach sandnya tevhapasoon samanya sthanik bhasha banalya aahet. udaharanarth, vyavasay paddhati kinwa karyapaddhati suvyavasthit karnyache sandarbh aikane samanya aahe.

