Coordenadas Polares 2020 Conicas
August 23, 2022 | Author: Anonymous | Category: N/A
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Immrlbcklks Zmfkrbs? Fmc`htul lb Krim. Ybiihmcbs I¼ mchiks. mchiks.
Zrmd. Zrm d. Lhf Lhfihk ihk Z¼ brb z brbz
; Immrl Immrl.. Zmfk Zmfkrbs rbs?? Fmc` Fmc`htu htul l l lb b K Krim rim I I
I d x I y d d I I d x, x, y I
x g gt t λ, λ, α , λ 6 α,
∇
x ` `t
g ` g Lbchih¼ mc? ;.:. mc? ;.:.; ; Yh d d y ` ` smc ducihmcbs imcthcuks bc H H λ, α , λ 6 α , fks biiukihmcbs
I
x g gt t H H λ, λ, α , λ 6 α,
∇
x ` `t
sb lbcmnhck lbcmnhckc c biukihmcbs pkrkn¼ pkrkn¼btrhiks btrhiks lb I imc I imc pkr¼ knbtrm knbtrm t. K nblhlk qub t vkr¼ vk r¼Ļk Ļk bc bc H , fms puctms lbsirhabc uck iurvk I lbcmnhcklk I lbcmnhcklk Iurvk Iur vk pkrkn¼ btrh bt rhik. ik. Kf puctm puctm g gλ, `λ sb fb lbcmnhck puctm hchihkf5 nhbctrks qub, qub, g gα , ` α puctm puctm ckf.
IKZ ¼ H\RFM ;. IMMQL. ZMF ZMFKQBY? KQBY? FMC@H\RL FMC@H\RL LB KQI KQIM M
Bobnpfm ;.:.;
I ;
x t
, t H H , ϊ,
∇
t
:
x
;
y
:
t
:
x
:
y
;
ϊ
ϊ
<
1
ϊ<
ϊ
∟ / : ∑∟ / -; ∟ / ; ∟ / :
y t t
Bobnpfm ;.:.1
I 1
x t t
, t H H , , ϊ ,
∇
y t
ϊ
ϊ
<
1
ϊ<
ϊ
∟ / ; ∟ / : ∟ / : ∑∟ / -;
Immrlbcklks Zmfkrbs Bobnpfm ;.:.9 Yh r bctmcibs x d b y d pkrknbtrh r d d η, bctmcibs d η η b d η ηη bs uck pkrknbtrh-
zkih¼ mc lb fk iurvk lbsirhtk pmr fk biukih¼ mc bc immrlbcklks pmfkrbs rr d d η . Bc bf bobnpfm ,,, rη imc η
∇ , , ϊ . Zkrk bf iksm, rη ∑ η, η ∇ , , 1 , tbcbnms qub ϊ
I ;
η
ϊ
x
∑ η η , t H H , ϊ,
∇
y ϊ
<
1
∑ ∟ /∟ / ∟ ∟ ∑ / /
∑ η ηη
ϊ<
ϊ ϊ<
∑ ∑ ∟ /∟ / ∟ ∟ / /
∑ ∟ /∟ / ∑ ∟ /∟ /
ϊ1
Fmc`htul lb Krim
\bmrbnk ;.:.; Yh I
x g gt t H H λ, α , λ 6 α,
∇
bs tkf qub d d y y ` smc
x ` `t ducihmcbs imc lbrhvklks imcthcuks bc bc H H λ, α , X X I I bs trkzklk trkzklk bxkitknbctb bxkitknbctb uck vbz iukclm t iukclm t irbib lb λ λ k α, bctmcibs fk fmc`htul F F lb I vhbcb lklk pmr? α
F
lx lt
1
ly lt
∥ λ
1
lt.
IKZ ¼ H\RFM ;. IMMQL. ZMF ZMFKQBY? KQBY? FMC@H\RL FMC@H\RL LB KQI KQIM M
d H λ, α x d d η η y d H d d η η, r d η, r d η lx η r ims lη lt
ly η rsbc lη lt
lr lη
∑r ηη ∑r η
η
lr ηη lη
lx
1
lη ly lη
1
1
() lx lη
ly lη
1
r1 1 η
( )
1
1
r lr ηη η lr 1 η.
∑
r η
lη
lη
lr ηη η r lη
1
lr r1 1 η 1 η lη
)
(
lr 1 1 η. lη
1
1 η 1 η ,
)
(
d bs uck ducih¼ mc qub thbcb lbrhvklk imcthcuk bc H H λ, \bmrbnk ;.:.1 Yh d bs λ, α , tkf qub I bs lbsirhtk pmr bstk ducih¼ mc, fk iukf bs trkzklk bxkitknbctb uck vbz iukclm iukclm η irbib lb λ λ k α, bctmcibs fk fmc`htul F F lb I vhbcb lklk pmr?
∥ α
r1
F
lr lη
λ
1
lη.
Bobnpfm ;.:.< Ikfiufkr fk fmc`htul lb krim lb fk iurvk lklk pmr pmr r
d d d η d
∑ η
∑ η, d d
H H , , ϊ
∥ 1ϊ
F
r1
lr lη
:
1
ϊ
lη
∥ ∑
1
η 1 lη
:
ϊ
F
∥ ∟ ∑
∟
ηlη
:
ϊ
∥ ∟ ∑
:
∟
ηlη
∥ ∟ ϊ
:
η lη ..
Masbrvkih¼ mc mc
r d η x x r r η y r r d η η r ηη I d η I r d tgbtk, n tgbtk d d η, η ly nη lx
ly lη lx lη
d d η η d ηη d ‱ η ‱ d d η ηη d d η η
∑
Bobnpfm ;.:.2 Bcimctrkr fk pbclhbctb lb fk rbitk tkc`bctb k fk ihriucdbrbcihk rr η
bc bf puctm lmclb η η ϊ/ ϊ/. mc mc Ymfuih¼
d η, d ‱ η d d d η η, d
∑ η, η,
n ly 1 η 1 η lx η ηη
∑
∑
ηη ∑ ∑ η. η. ηη
η ϊ/ ϊ/ ϊ ly n lx
ϊ/ ϊ/ . . | > ∑ η
ϊ
<
η ϊ/ ϊ/
Bobnpfm ;.:.4 Gkffkr fms puctms bc fk iurvk iuyk biukih¼ mc bc immrlbcklks pmfkrbs vhbcb
lklk pmr r r η bc fk qub bxhstk uck rbitk gmrhzmctkf, uck vbrthikf m uc puctm shc`ufkr. Masbrvkih¼ mc mc
∑
• d d η: , η: ly/lη ly/lη | > lx/lη | > ̷
η η:
η η:
• lx/lη | >
η η:
ly/lη
| > ̷ η η:
d η: , η: d d η: , η: ly/lη d
•
η >η:
|
lx/lη
η>η:
|
IKZ ¼ H\RFM ;. IMMQL. ZMF ZMFKQBY? KQBY? FMC@H\RL FMC@H\RL LB KQI KQIM M
x ly/lη lx/lη
∑ ∑ η η y ∑ ∑ η η, η, 1 η ∑ η η 1 η η ∑ 1 η ∑ 1 η η ∑ 1 η ∑1 η η η η
∑ ∑ η ηη η η ∑
ly/lη ly/lη
η η
∑ ηη η ηη
⇜ ∑1 η η ⇜ η ; ∟ ;< 19 r imsη ,, 19ϊ ,, 19ϊ 19ϊ η
| ̷ ∑
1ϊ 9
ϊ
°
∑
, , ly/lη | > ̷ d d ∑ 9 , , 9 ° , 9 ° , 29 η
ϊ
η
ϊ
9
ϊ
ϊ
ϊ
9
ϊ
• ∑ ims ims, , , ly/lη ly/lη | >: lx/lη | >: η
η
Ksh`ckih¼ mc mc
nη, η↑:+ n
• η↑ 2
ϊ
9
+
n nη η↑ 2
ϊ
9
∑
nη , η↑ 9 + n nη , nη, η↑ 9 ∑ n η↑:∑ n ϊ
n nη ,
•
ϊ
IKZ ¼ H\RFM ;. IMMQL. ZMF ZMFKQBY? KQBY? FMC@H\RL FMC@H\RL LB KQI KQIM M
1 I¼ m mchiks? chiks? Yhstbnk Ikrtbshkcm
Kx1 Ay 1 I Ixy xy Lx By D . Lx By D
Ihriucdbrbcihk Ihriucdbrbcihk bf imcouctm lb tmlms fms puctms Z Z x, y qub smc bquhlhstkctbs lb uc puctm om I om I g, e bf g1 y y
x
∑
e 1 r 1 .
∑
r Z r Z I I
¼ IKZ ¼ H\ H\RF RFM M 1 1.. I MCHIKY? YHY\BNK IKQ\BYHKCM
Zk Zkr¼ r¼ ka mf ka mfk k kamfk kamfk f f D D Zkr¼
f f D D D D f
\bmrbnk ;
Bfhpsb
x, x, y ,
\bmrbnk 1
mc? 1.:. mc? 1.:.; ; Fk bxibctrhihlkl b Lbchih¼ b lb uck bfhpsb bst¼ k lklk pmr bf imihbctb b
i k
Ghp¼ p¼ br a mf bra mfk k Gh
x, x, y
¼ IKZ ¼ H\ H\RF RFM M 1 1.. I MCHIKY? YHY\BNK IKQ\BYHKCM
\bmrbnk 9
k k a a g, g, e a g, g, e a a g, e
\bmrbnk <
∑ a
Lbchih¼ mc? 1.:. mc? 1.:.1 1 Fk bxibctrhihlkl b b lb uck ghp¼bbramfk ramfk bst bst¼ k¼ lklk pmr bf imihbctb b ki
b b ki i 3 k b 3
\bmrbnk <
xy xy Kx1 Ay 1 LxBy LxBy D D K A K A K A L
̷
̷
x x K A L x
̷
K A B
̷
̷
y y B K A B y
̷
sh`cK sh`c sh`cA sh`c sh`cK sh`c sh`cA sh`c
̷
¼ IKZ ¼ H\ H\RF RFM M 1 1.. I MCHIKY? YHY\BNK IKQ\BYHKCM
9 I¼ m mchiks? chiks? Yhstbnk Zmfkr
\bmrbnk <
D Z D f Z Z D D b Z Z f f Z
|Z D | Zf
b
6 6 b 6 b b b 3
¼ IKZ ¼ H\ H\RF RFM M 9 9.. I MCHIKY? YHY\BNK ZMFKQ
Lbluiih¼ mc lb fks Biukihmcbs Zmfkrbs lb fks I¼ mc mchiks. mchiks.
|Z D | Zf
b
D D f l l l 3 D D x
∑l.l. Z Z r, r, η |Z D | r ∠ |Z f| l r r η °
°
r b l r r η
⇑ r ∑ bl b η
b \bmrbnk 2
b l
Bobnpfm 9.:.; Bf bdbitm lb vkrhks bxibctrhihlklbs
Gkffkr biukihmcbs pmfkrbs lb fks sbiihmcbs i¼ mchiks imc Dmim bc bf pmfm , lhrbitrhz rr η y bxibctrhihlklbs (k)b (k)b ,, (a) b ,, (i) b , (l) (l) b b , y (b) (b) b . Ymfuih¼ mc. mc.
b b b η
;,4 ;+:,
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