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Homotetik hareketler için cayley formülü, euler parametreleri ve uygulamaları

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(329) YH f S

(330) PDWULVOHULGH÷LúPHOLGLU>@ .  7HRUHP . f x

(331). an x n  an  x n     a x  a  ai     d i d n  YH  u  . WLSLQGHNL S DQWLVLPHWULNELUPDWULVROPDN]HUH  A. ª f S T

(332) º ¬ ¼. . f S

(333) . . LVH A  SO 

(334) RODUDNHOGHHGLOLU>@  7HRUHP A. ª f S T

(335) º ¬ ¼. PDWULVLVH ª¬ f S T

(336) º¼. . f S

(337). . f S

(338) úDUWÕQÕVD÷OD\DQ A PDWULVLSR]LWLIRUWRJRQDOELU. f S

(339) ª¬ f S T

(340) º¼ ¶GLU>@ . . . .

(341) . . 6RQRODUDN f S

(342) ¶QLQIDUNOÕGXUXPODUÕQÕHOHDODOÕP . L

(343)  f S

(344).  A. I   S VHoLOLUYH 

(345) GHQNOHPLJ|]|QQGHEXOXQGXUXOXUVD. I   S

(346) I   S

(347)  

(348)  . . HOGHHGLOLU%|\OHFH f ¶\HHQEDVLW&D\OH\G|QúPGHQLU>@ . LL

(349)  f S

(350).  A. I. . I   mS  nS  VHoLOLUYH 

(351) GHQNOHPLJ|]|QQGHEXOXQGXUXOXUVD.  mS  nS 

(352). . I. .  mS  nS 

(353)  

(354) . . EXOXQXU%|\OHFH f ¶\HJHQHOOHúWLULOPLú&D\OH\G|QúPGHQLU%XUDGD . f S

(355). an S n  an S n     aS  a , ai    a z   d i d n . . ROGX÷XQGDQ YH S  n . 

(356). n. 

(357). S  S  n . n. S n.    ROGX÷XQGDQ A . &D\OH\ IRUPOQQ \XNDUÕGD YHULOHQ LNL IRUPGDQ IDUNOÕ ELU KDOGH ROPDVÕ PPNQ GH÷LOGLU>@ . gWH\DQGDQ S PDWULVLQLQ|]GHQNOHPL O   s O.  ROPDN]HUH|]GH÷HUOHUL  is is . úHNOLQGH HOGH HGLOLU 2 KDOGH A  PDWULVLQLQ |] GH÷HUOHUL  p  iq

(358) p  iq

(359)  YH. p  iq

(360) p  iq

(361) RODUDNEXOXQXU z. p  iq. reiI VHoLOLUVH z z

(362). . z

(363). . z. e  iI YH. Ss  As s  ROGX÷XQGDQ A  SO 

(364)  JHQHOOHúWLULOPLú &D\OH\ PDWULVL JHRPHWULN G RODUDN R s I G|QPHKDUHNHW൴Q൴WHPV൴OHGHU>@.

(365).  . . .

(366) . . /RUHQW] 8]D\GD 3DUDPHWUHOL +DUHNHWOHU LoLQ &D\OH\ )RUPO (XOHU  5RGULJXHV3DUDPHWUHOHULYH&D\OH\'|QúP. . G G 7DQÕP x  y   VSDFHO൴NH W൴PHO൴NH

(367) YHNW|UOHUYH A  SO 

(368) ROPDN]HUH. /RUHQW]X]D\GDRU൴M൴QHWUDIÕQGDE൴UG|QPHKDUHNHW൴ . y. Ax  

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G]H\GH \HWHUOL YH JHQHO RODUDN |÷UHQFLOHULQ ELOLúLP WHNQRORMLOHULQH \|QHOLN \HWHUOLOLNOHULQLQ \HWHUOL G]H\GH ROGX÷X VRQXFXQD YDUÕOPÕúWÕU $\UÕFD DQDOL] VRQXoODUÕ