Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA
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1 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Rliisi Dnis n lonis in Unifol l n in Unifol Roin s-th Gnl ssions fo h loni 4-Vo Ponil in Sfi Unisi of Clifoni 387 So Hll UC Bkl Clifoni US Ri 5 h M 7; Ris 4 h Jn 7; 6 h Jn 7; Plish: 3 h Jn 7 s- In h n w sn nliion of h nsfos fo h f o-oin wih n l il fo ih ilin o il oion ino n inil f of fn. Th solion is of ins fo l i liions s h-on loois inil onl in oiion Th oiion is h h l lif liions inl lin n oin fs wih i oinion o ofn hn h ili s of inil fs; o il ins hn in h loois h o h oin h. O is ii ino wo in sions h fis sion ls wih nis i.. fos h son sion ls wih lonis i.. loni onils. K Wos: l oion Gnl ooin nsfoions l ils Unifo oion o-fo o o-loni o.. INTRODUCTION Rl lif liions inl lin n oin fs o ofn hn h ili s of inil fs. O il ins hn in h loois h o h oin h. Mn ooks n s h n i o nsfoions wn il ss of ilin lion no oion [] n o h liions of sh fols [-3 5]. Th is ins in oin nl solion h ls wih i oinion of lion in h s of ilin oion n fo i iion of nifo nl loi. Th in i of his is o n sn lin fo nl solion. Th lin lis on nsfoin h ol oill in h nonil fn f of [] follow h liion of h hsil nsfos i fo sh nonil oinions [-7] n nin wih h liion of h ins oil nsfoion: GoTnsfo > PhsisTnsfo >InsGoTnsfo W onl o wih il liion of iin h fol of h Lon fo in nifol oin f. Coih IJPOT ll Rihs Rs. DYNMICS IN CCLRTD RCTILINR MOTION L S sn n inil ss of ooins n S n l on. Moll [] onsis il s wh il os wih lion lin wih h -is. oin o fn [] h nsfoion fo h il s fo S ino S is: Ph ilin wh osh h Ph ilin 3 h osh Ph ilin Ph ilin Ph ilin Ph ilin 4 P 36
2 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 37 Thfo ilin Ph ilin Ph h osh osh h 5 wh ilin Ph os os 6 Th s s in h inil f ns oh on h s n h osiion s in h l f. If w onsi h s of h l f ooin wih h oj il n s hn: 7 n ilin Ph ilin Ph h osh osh h 8 In h followin sion w nli his iion fo h i s fo oinin h nl fos ooin nsfoions h k s fo S ino S. ss in ol ooins h lion hs h fo: n os os os θ θ θ 9 Th fis s os h ni o of lion 9 on h is h o oss-o sh s lin wih h -is i.. o his os w will ino h il. Th followin ssions hol [4]: Ro os os os9 9 9 os9 9 Ro Ro Ro 9 lins wih. Th son s is ois noh oion on h -is 9 h lins wih : 9 Ro Pin i ll oh: Ro Ro Ro R Th nl ooin nsfoion wn S n S is: 4
3 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 38 wh R ilin Ph R 5 Th nl loi nsfoion is hfo: wh R ilin Ph R 7 Th ins nsfo is: wh R ilin Ph R If w onsi h s of h l f ooin wih h oj il n s hn: n 8 silifis o: i. : i iion ilin l oion i. : Unifo oion wih i iion of nl loi 4 4 Th ooin lion n i iil s:
4 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 39 Th n-on nsfos h s w s h 4- ooins 4 i of in 4-o: 3 Thfo: Th ins nsfo fo h inil f S ino h l f S is: If w onsi h s of h l f ooin wih h oj il n s hn: 6 n 7 In his s: 8 3. DYNMICS IN UNIORM NGULR VLOCITY ROTTION In his sion w isss h s of h il oin in n i ln wih h nol in h onsn nl loi i.. oin o Moll [] h sil s whn is lin wih h -is os h nsfoion wn h oin f S h o h il n n inil non-oin f S h o h n of oion: oion Ph 9 wh os os os os os os os os os os oion Ph 3 3
5 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 4 Th nl s is nsfoin h ol ino h il s in [] hoh nsfoion ino h nonil s follow n liion of h nsfoion fo h l f ino h inil f nin wih h ins of h fis nsfoion s shown low R oion R 3 Ro Ro Ro R Ro Ro 9 lins wih. Th son s is ois noh oion on h -is 9 h lins wih : 9 Ro 34 ssion 3 is h solion fo h nl s of i nl loi iion. Th nl loi nsfoion is: Th nl fo nsfoion is: wh: R oion Ph R 37 Th s nsfoion is: wh: R oion Ph R W will s 38 in h n sion n liion h ins h ssion of h Lon fo in oin f. 4. PPLICTION-TH XPRSSION O TH LORNTZ ORC IN UNIORMLY ROTTING RM ss h w h il of h q n ss oin in h - ln n h infln of ni fil B lin wih h is. W know h in h f of h l h ssion of h Lon fo in on h il is B k j i q B q os 4 W wol lik o fin o h ssion of h fo in h f o-oin wih h h il. o his os w will so o W know h [56]: os 4
6 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 4 os os os B qb 45 Ssiin 4-45 ino 4 w oin: qb qb os os os os 46 To h o w n o [6] h f h: qb qb 47 In 47 is h iniil s of h il. wih h 46 s h sil fo: qb qb qb qb qb qb qb qb qb qb qb qb os os os os LCTRODYNMICS IN UNIORMLY CCLRTD RMS ND IN UNIORMLY ROTTING RMS TH GNRL XPRSSIONS OR TH LCTROMGNTIC 4-VCTOR POTNTIL Piosl [78] w h l wih h s of h nsfoion of Mwll qions fo h s of nifol l fs n nifol oin fs in i iions. Th folis i in his sion llows s o nl nsfoion wn h inil f S n S n h ins. Th loni onil nsfos h s w s h 4-ooins 4 i of in 4-o: 49 wh is in 5 fo nifol l fs n 37 fo nifol oin fs. In o o nsfo Mwll qions wn h fs w n h il iis wih s o. W will show how o ll wo of h s lin.
7 Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Coih IJPOT ll Rihs Rs P 4 5 Th ins nsfos : 5 6. CONCLUSIONS W ons h nl nsfos fo h f S o-oin wih n l il fo ilin o il oion ino n inil f of fn S. Th solion is of ins fo l lif liions s o h-on loois inil onl in oiion; in l lif h loois o n h l. W o lin fo nliin h solions fo h i s n w onl wih il liion of iin h fol of h Lon fo in nifol oin f. RRNCS [] C. Moll Th Tho of Rlii Ofo Pss 96. [] L. H. Thos Th oion of h nin lon N ol [3]. Bn-Mnh Wins oion isi. J. Phs. ol. 53 no [4] S. Bn-Mnh Th Thos ssion n lois J. Mh. Phs. ol. 7 no [5] H. Ko Th Thos ssion fo in oi inion J. Phsis. ol. 7 no [6] J.. Rhos n M. D. Son Rliisi loi s Win oion n Thos ssion. J. Phs. ol. 7 no [7] G. B. Mlkin Thos ssion: o n ino solions Phs. Us. ol. 49 no [8] M. I. Kiohnko Roion of h swin ln of ols nl n Thos ssion: Two fs of on oin Phs. Us. ol. 5 no [9]. Sfi Holi Moion Tn fo Bll s Sshi in iik ol. 8 no []. Sfi Cooin Ti Holi Moion fo Bll s Sshi in iik ol 9 no []. Sfi Rlii solion fo Twin o : ohnsi solion Inin J. Phsis ol. 86 no [] K. Rils Con on ln nlsis of h sil liisi oinion of loiis Win oion n Thos ssion. J. Phs. ol. 34 no. 3. L55 L6 3. [3] R.. Nlson Gnli Lon nsfoion fo n l oin f of fn J. Mh. Phs. ol. 8 no [4] h:lok.noo [5]. Sfi Th Gnl Tjois of l Pils in Sil Rlii J. li Phsil Sin Innionl ol. 5 no [6]. Sfi Th jois of h ils oin liisi ss insi il sos fll soli solion In. J. N. n Si. n Th. ol. 4 no [7]. Sfi lonis in Unifol lin s s Viw fo n Inil In. J. Pho. n O. Th. ol. 3 no [8]. Sfi lonis in Unifol Roin s s Viw fo n Inil In. J. Pho. n O. Th. ol. 3 no
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