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~ = _2 Htga



Ec


= ~+ K1 Pt~ + K2ptg 2e, y

(1 - tg(3tgJ)(AtgfJ + B)



'(



_K



= .e. (H - h n ) +



p



y



+



KO;l



= Ko + i.lKop



2 Htg::ttg
Y



K2p =-



ey (H -



hn) ' gil'



Hinh XI1I-2-6



Ko. K 1. K2 Iheo SCI



--,K IP



=2 (H y



hn ) +



do 2-3



Kop = K.:J + I1Kop



- 2. L(lg(} + tgUl)

-f



e (H -



LtgP) t9(j1



hn +



'(



Hillll XIII-2-7



Ko. K\, K2 theo SCI do 2-1

II



=e (HlgCJ. -



L)



2

Ecd -- -Kop + K, pt!tl + K2ptg e , y



(1 - tgPtg':!}(Alg8 + B)



Y



~K l p



=.e..( (H -



hn) -



- .e Ht g:ttglj'l +.e. l(tgl + t9'P)



KIp



= K, + I1K,p



=- 2 (H - h" + Ltg(3) tgp K2p



= K2 + I1K2p



.,



2p



Kop = Ko + I1Kop



Y



y



Hillll XIII-2-8



Ko. K, . K2 theo SCI do 2-2



= Kop + K1plg8 + f<2p1g2fl



~Kc;>



=- e (Htga + L)



Ecd



.~K lp



= e (H -



Kop



= Ko + I1Kop



Ko.



K,. K2 theo ScJ



h n) +



. '(



(1 - tgPtg8)(Atgtl + B)



y



'(



_iK2p =-



e (H -



hn + LtgP) tgp



'(



Hinh XIII-2-9



do 2-3

265



E~d



Kop + Kl ptg0 + Kzptg2e y



=.







Kop



K2p =



ey B



0



.



(1 - tgj3tgS)(Atg9 + B)



= Ko + .1Kop



tgptg
Ko. K, . K2 theo set



Ecd



L'.Kop



=..e.y B



=



db



2-1



Kop + K, plg8 + K2p1gz8

(1 - Igj3tgS)(Atg9



+ B)



Ko. K 1. K2 thee set d6 2-2



t.Kop



=..e.y B



Hill" XllI-2-12



Ecd



+ K, ptga + K2p1g2e

= Kop

(1 - Igj3tg8)(Atg0 + B)



Kop



=Ko + L'.Kop



0



y



Ko , K,. K2 theo sd do 2-3



t.Kop



= P1

O(



Ecd -_ Kop + Klptge + K2plWS



8 - P2 L

Y



(1 - tgPIg0)(Atg9 + B)



Kop = Ko + liKop

)( (191 + tgc,~) + P2 (H - hn)

0



y



t.K2p = p, BIg3lglp - P2 )(



y

XlIl~ 2-13



y

0



Kop = Ko + t.Kop



Hill" XIIl-2-11



Hillh



.



x (H - hn



Y



K,p



=K,



+



L'.K,p



K2P = K2 + L'.K2p



+ ltgl)lgr,p \ K o , K,. K2 thee set d6 2-1



.Y



=E- 8 + P2 (Htip -



~Ko p



Y



L)



Ecd



= Kop + KlptgS + K2plg2a , y

(1 - 19j3tg3)(Alg9 + 8)



Y



ilK,p =



- ( £.!. B - P2 L )(tgj3 + tg
Y



Kop = Ko +



~f


Y



+ P2 (H _ hn) _ P2 tgotgp

y

y



~K2p = E.!. Blg13tg
Y

y



Hill" XIII-2-/4



(H - hn + Lt~)tg


x



.6.Kop = £.!. 8 - P2(HIg::t + L)

y



y



Ko . K 1, K2 theo sd d6 2-2



Ecd -- Kop + K,ptg8 + K2 ptg2a - .(

(1 - !g13tgfl)(Atgf) + 8 )



.6.K l p =



P2 \

- (.yp, 8 - Y

L l'gJ + tg
P2



P2



y



y



+-(H-hn)+-tgClt~



Hinlr XIII-l-15



- E. (H - hn + Ltgp)tg


Kep



=Ko + .6.Kop



K,p=K,+



K,p



Ke. KI. K2 theo sd db 2-3



.(



Ecd -_ Kop+K iPtgO+K2P~ . .!

(1 -tg(3lg8)(A!gE)



K o?



Hi,," XIII-2-16

=



f



E cd =



y



P



~K,P = - Y



Hiuh XIII-2-l7



=Ko + sKop



Ko. K,. K2 thea



Ko?



(Igp + Ig


B)



SCi



d6 2-1



Ko? + K, P!



(1 - tgPlgO)(AtgE) + 8 )



-1



Kop = Ko + .6.Kop



Ko. Kl , K2 theo sdd 2-2



267



t.Kop =



f



ho



f



6K1P = H



E



_ Kop + K1pigS + K2Pt9 e

(1 - IgPtgO)(AtgO + B)



Kop



= Ko + ~Kop



K,p



= K,



2



cd -



y



y



(lg0 + t9tjll



Ha



P



K2P = K2 + I'1K2P



I'1 K 2P = - Igl3lgcp



Y



Hinh X/lJ-2-l8



Ko. KI. K2 Ihea sd do 2-3



S = tgp + Igtp



..-::



Ecd =

-lgPtg~1)



V= 1

h"



H



+ I'1K,p



il~q



Hg



=0



Kog + Klqtgf) + K2glg2e



(1 - IgPlg9)(Atgf) + Bl



Koq = Ko + l'1Koq



ilK,q = 9 (H -h n) . S



K'q



=K, + t.K,q



=.9. (H -



K2Q



= K2 + I'1K2q



y



ilK2q



Y



hn) . V



Hi,," XlII-1-19



Ko . K" K2 thea SCi



--



do 2-1



Ecd -_ Keg'" Klgtg3 + K2gtg 2a .



I'1KOq = 9 Higo. . S

y



(1 - tgptg0)(Atge + B)



I'1K'q = 9 Htga.. V +



Koq



Y



+



9. (H

y



= Ko + I'1Koq



- h n) . S



ilK2q = .9. (H - h n) . V

Y



Hinh XIIJ-2-20



Ke. K,. K2 thea sd do 2-2

AKoQ = -



9. Higo. . S

y



Ecd



_ Koq + Kl qtg3

-



-4-



K2qtg :2a



(1 - tgptgO)(Alg6 + B)



I'1KIQ = 9. Htg::t . V +

y



+



KOQ = Ko + I'1KOQ



.9. (H - hn) . S

y



I'1K2q = 9. (H - h n) . V

Y



Hinl! XIII-2-21



Ko, K1. K2 Ihea



sa db



2-3



S



= Igp + Ig4~



V = 1 - IgPIg(l>



=- 9. L. S



Koq



KOQ = Ko ... sKoo



'(



LlKlq



=9. ( H y



+



h n) . S +



9. L . S . Ig~ - 9. L . V

Y



LlK2q



Hill/r XlII-2-22



K2Q



=K2



Ko .



K1. K2 Iheo SCi db 2·1



Ecd



= Kog + K1gtg3 + K2gtg2e . '{



+ ~K2



"t



=



9. (H - hn) . V +.9. L . V . Igp

Y



~Koq = 9. Higa . S - 9. L . S

Y

LlK1Q



'/



(1 - Ig(3Ig»(Alg8 + B)



=



9. HI~



. V + 9. (H _ hn)S +

Y



Y



Koq



= Ko + LlKoQ



llK2q = 9 (H - hn)V + 9 L . V .1913

"t

Y



Hi,,/r XIII·2·23



Ko. K 1, K2 theo SCi

LlKoQ



=- 9y Hlga , S -



9.



y



L.S



=

_ 9. HI9X . V + 9. (H _ hn)S +



db



2·2



E



KOQ + K,glg3 + K2gtg2e

cd = (1 _ tgl3tg3)(AlgO + B) . Y



LlK'q



Koq



+9L . Slgp - 9.L,V

y

Y

LlK 2q



y



K'Q=Kl+~K,q



=



9. {H -



hn)V + 9. L . V . Iga

y



Hillh XIll-2·24



Ko. Kt. K2 theo set db 2·3

S



=Igl3 + tg


Ecd



L\Koq



=9. B . S



Koq



= Ko + L\KOq



Klq



= K, + ~K1Q



Y



L\K1Q



=_.9. 8. Slgp+9 B . V

Y



6K2q



= Keg + Klglg8 + K2glg20

(1 - Ig(3lgO)(Alge + B) . Y



V = 1 - IgPlg


Hinh XIII·2-25



= Ko + ~ KoQ



Y



'I



Y



=- .9.Y B. V 1913

Ko. K" K2 thea set



do 2·1

~69



Ecd -- Kog + K'Qt~ + K2gt~

(1 - tgj3t~)(Atge + 8 )

liKoq



=gy B . S



KOQ = Ko + liKoq



liK,q = - 9 B. Slgp +.9. 8 V

y

Y



Klq = K, + 6.Klq



= - 9. B . V . Ig/3



K2Q = K2 + liK2Q



\K2q



.



'(



Hinlr XlIl-2-26



Ko. K, . K2 Ihee sa

liKoq



=.9. B . S



Ecd



db



2-2



+ K2 qtg2a

_ Koq + Klqtge

-



-



_



(1 - 193t~)(Atge + 8)



Y



liK1Q = _.9. B . Slg/3 + 9. 8 . V

Y

y



liK2q



-



KOQ = Ko + 6K oQ



=- .9. B . V . tgp

'(



Hillh XIII-2-27



Ko. K1. K2 theo sa



db



2-3



Ecd -- Ko9 + Klgtge + K2qlg2a

(1 - Igpt g))(Atg9 + B)



6Koq = T.5



Koq = Ko + liKoQ



liK'Q = q2 (H - hn)Sy



- T.SIg/3 + TV

liK2q



=q2 (H -



hn)V - TVlgp



K.2Q = K2 + 6K2q



'1<0. K,. K2 theo sa d6 2-1



Y



Hinh XIIl-2-28



liKoq = q2 H Igy . S + T . S

y



Koq



= Ko + liKoq



q2 (H - hnjV - T . Stg3 + T. V K1Q= K, + liKlq

'(



liK2q = q2 (H - hn)V - T.V.tgp K2Q = K2 + 6K.2q

Y



Hi,," XlIl-2-29



Ko. K,. K2 theo sa



d6



2-2



.



=-



tlKoq



q2 H tget . S + T.S



E



_ Koq +



cd -



(1 - IgPt~)(Atg8 + B)



y



~ K1Cl:= - q2 HI~ V+



Koq



K1 9t~ + K2gt9 2e . ,r



= Ko + ~KoCl



Y







+ q2 (H - ho}V - T.Stgp + T.V



K1Q = K, + lIK'q



Y



H

Ha



=q2(H -



lIK2q



ho}V - T.Stgp



K2Q



= K2 + l1K2Q



Y



Hi,," XI1l-2-30



K o • K 1. K2 theo sa do 2-3

lIKoo



=.Q cosp . S



E



cd



(1 - tg3t\t) Alga + B)



Y

h



t-K'Q



2



= Koo + K,otg8 + K2Qtg e . Y



=- -Qy CO$. tgp S + -a cosp.V



Koo



=Ko + lIKoo



Y



H

Ha



KIO = K, + lIK,O

lIK20 = -



9 CO$. tgp .V



K2Q := K2 + lIK2Q



'(



H11I/J XIII-2-31



Ko. K" K2 theo sa do 2-1



~Koo = .Q COSP . V



Ecd = KoQ + K 1OIg9 + K2Qtg20 . '(



y



(1 - tgPtgO)(AtgO + B)



hn



ho



Q

Q

t'.K1Q = - - co$ .tgJ S + - cosp.V

y

y



KoQ



= Ko + ~Koo



K,O



= K,



H

H



K2Q



=- Qy cO$ . V . tg3



Hinh Xlll.2-32



+ lIKlO



K2Q = K2 + l1K20

Ko• K I. K2 theo sC! db 2-2



Koo



=Q cosp . V



Eed



Y



KoQ + KlOtge + K2atg

:=



K



Q



.(



H



Q



CO$. Stgj3 + - CO$.v

y



Ha



Koo = Ko + ~Koo

K,o = K, + t'.KlO



lIK20



=- -Q co~ . V . tgJ



K2Q = K2 + I1K20



Y



Hinh XIIl-2-33



e.y



(1 - tgptgO)(Atg8 + B)



ho



t'. 10:= - -



2



Ko• K, . K2 theo sa db 2-3



B. cOS


nKoR =



+ Igolgtp)



y



AK1R



E c


_ KoR + K1RtgfJ + K2Rtifo



-



.



Y



(1 - tgPtgO)(Atge + B)



=£! COllJ)(lgu -



t~­



KoR = Ko + AKoR



Y



- tgq, - Igoo tgPlgq,)



R



LlK2R = - - cos!> (Igoo - Igtp)lg(3

Y



Hi,,11 Xlll-2-34



Ko, K" K2 Iheo sO'dO 2- 1

LlKoR



=£! cosw(1 + Igwlglp)



i



t

Ecd _- KoR + K1RIge + K2R e



LlK1A =



. y



(1 - tgptgtl)(Atge + B)



"(



B. CO~lJ)(t9J) - t~­



KoR



Y



=Ko + Il KoR



- tgql - tgwtgBtgql)



~K2R



= -



B. COSc.l (Igm - Igtp)lg~

'f



Hinh XIll·2-35



Ko. Kl , K2 Iheo sO'do 2-2

IlKoR



=-R cost,)(1 + Ig(c.ltgtp)

y



LlK 1R =



Ecd. _- KoR + K1RIge + K2Rlife . .(

(1 - tgptgtl)(AlgO + 8)



f!. C09:l)(19lJ -



tgl -



Y



KoR = Ko + AKoR



- Igtp - tgwtgJ}tgq»



~K2R = - .B COSil (Igm y



tgtp)lg(3



Hillh XTTl·2·36

u . cAe so



D6 vA



K o, K 1, K;? theo sO'



do 2-3



C6NG THUC TfNH TOAN THEO BAl ToAN CO BAN THU BA



1. Bai toan eO' ban thti' ba

2



S = !.. Ig(900 - Po)



ECd



= Ko + K,lge + K2tgZe . y

Atge



2



ai -



(H +

h~

Ao = -'--~'---~



2



Kl = Ao



Do = coHa



K2 = -Aotgtp - On



y



.Pc~



272



Ko = - On - 00



Bo =-S

~-+~--~~--~=-~---+--~~



Hillil XIII-3-I



+



On



=c(H + a y



h n)



'I-



Dotglj)



B



S :: -a2 [190. + Ig(900 - rIo»)

2



h~



Ko



=Bo -



Bo :: ~ tgl- S

2



Kl



= Ao - Botglp + Do(lga. + Ig(0 )



Do = coHa

y



K2 :: -Aotg(p - On



Ac, :: (H + a}2 -



On - 0 0 (1 - Igalgcp)



2

2



~~~~--~------------~---p~

oo~



Dn = c(H + a - hn)



Hit,,, XII/·3·2



y



a



a/- h~



A0 -- (H +



Ko = Bo - On - Do(l + tgutg41l



2



=_ (H + a)2 tgl _ S



Bo



K,



=Ao -



Bolgcp + DoHga +tg


2

-t--.,fo-........----":....-----------f-------'-~ Do = coHa



K2 = -AotgQ) - On



"(



Dn = c(H + a - hn)



Hilllt X/II·3·3



y



2. SO' do Hnh toan theo bai toan coo ban thli' ba

Ecd =



Ko p + K1PlgO + K2ptg2e



.y



Atrj3;- B

Kop = _.E. b



Kop = Ko +



Kop



'(



t. K,p = .E.(H - hn)

K2p



=-



+



Q btg(j)



Y



Y



e. (H y



h n) tgq>



Hi.1l1t XII/·3·4

p



ilKop ::



e. (Htga - b)

y



2



Ecd = Kop+ Klpl!;tl + K2ptg 8. Y



AtifJ + B

Kop = Ko + flKop



n



1"1



l:.(H - hn) - r::. (Htgu - b)tgp

y

y



ilK2p = -



K,p=Kl+flKlp



e. (H - h n) tgq>

y



Hillh XlII·3·S



Ko, K f, K2 theo set db 3-2



273



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