, Ctfl<* COS^-tgA.5VHtf-tgAiSVH>ft-ctgal.<C03 y1
3 tgAcosvf-toA^osip+ ctooisiKtp+ctQ<i,1siHif1
, .
1. , .
2. , , ,
: , .
3.
. (
)
, .
,
, .
2.3. 2.3.1. ^2 ^-^ . Xw , , , .
^ Zv (. 2.10). , . , V, . . , X Z . -
. . (. 2.10,2.11).
. 2.10. |
. 2.11.
12.3.2. , . . ■ . .. - .
|
|
2.3.2.1. ,
(. 2.12), Zy, -
"'4.1 (0 i 0, Z)i () -
...... :
0M=(0-Xo; a-v, Z-Zo)=(0; 0;Z),
X0, 0, Z0 - 0. ^ 0 - , -=0; 90=0; Z0=O. , = ( ; 1).
2.3.2.3. ,
^ , . - , (. 2.13, ). . 2.13, :
. 2.12.
'_ , j. Xv , i= (1; ; ); f- (; 1; ).
2.3.2.2. ,
OZy (. 2.12). X, 0, Z. | oft. . 2.12 : X = C0s'4'0-; Z=C0St. ,
0B=tX-0-,0;Z-0)=(cosV0Bl0;coT!0BV
, OZy. :
!=(+; 0;-Z) =(cosV0E \ 0;cos<cOE)=(cosVOE';0;-coS^E).
X W (W); J () < ("") - , Z . .
, , , , , . . 2.12
' '
0B = Ccos4r, |
06 1 |
05;05( -
0ZV Zv
Dj -I |
. 2.13. : - ;
0,, :
. |
01 = 0 cos ,
(2.1) |
0,2 -~=02/cos ^; ^ OB cost
'
(2.1), :
cos<C0 = cosA,cos<f. (2.2)
Xv. D , :
,-* OB, = cos X;
0-0 = 0,51(; (2>3)
-*- OK = 0BcosYOB.
(2.4) |
(2.3) :
cosV = cosAsinip. cosP0. . 2.13, :
joe= 90-/; cosj90B=cosC90"-Jl) = sinX. (2.5)
, , :
0& = (.csA,3tKcp; stnA; eosA cosip). (2.6)
. . 2.13, :
|
|
1=(,,)=(;; ).
, = cos(90- ) sinA;
0B,=cosA.,' OB = 0B.cos<f = cosXcosif; 0K= 0B,simp = cosXsin<p.
OBe(cosXei.rttf, s-ihA^cosA, cosw). Oil, : ="_'.,cos^> '"^^ ' ^3 Z Xv0Zv(pnc. 2.13,6). OBI, D.:
021->.0 = 01/81;
aOD^-OD^QBj/coshv (2.7)
01)-*01}2 = ODcost'pj,; cos-c'a|= cos A,, cos(fr
:
cost; |
=-cost'; cost._ =-cosif,cos,.- (2.8)
AT) ' OD
cosBn-. . 2.13,6 :
ja0I= 90+ A,,;cos>pOIl=cos(fl00+A1)=-siKJl1.(2-9) I . QD^jD:
0JDD,-* = OBi/cos^; 0DI3-* ^= 0Ilcos4,0B i
,3- 03= OB,cos(90-,). (2.10)
cosY0B= cos A, sintf^. _^ (1.11)
, . , , :
bj = (cosA,1sih.ip1;-s{,HA1;-cosA1cosf>l).
. . 2.13,6 :
_ o5 = (x-,-9;-Z)=(oj3;-oi)1;-oii2).
- ,
OJ^cosA,; 01j= OD^iK^scosA^siHift; QB2= Oncost?, = cosAiCostp,; ,= sinA,;
= (cosA^inip, j- tinXi'1-coaX1cos<fi)
2.3.2.4. ,
, (. 2.14,):
(2.12) (2.13) (2.14) |
6c = (coSVoc;coSjDoc;coStoc). , 2 (. 2.14,) : = 00,/cos; 0=0, tp; 0 = cos Y0o;
0 "s^oc = COSif cos f'
cosJoc= cos(90+ y)=- sitty.
0,3 :
(2.15) (2.16) (2.17) |
0C3=0C,cos(9O-<p); 0C=0C,/cosj; 0C3= OCcosT^;
cosX^.= cosysi*<p; cosi;oc=-costjC; cosZ^-cosfsiny.
II _^
OC = (cosip.cosj;-stH,t";-cosy si<f)-
. , , ( Xv OZy, (. 2.14,): _^
, = (cosip \ 0 '■,- sin if). ) > -My[OC,|=cosy 00,= (cosycosip; 0;-cosy sirtip).
0 = , + , = (cosy cosif;-sin.v;-simpccsy), C^=(0',-siHy; 0)
, yaor-i |
. 2.14.
:
- ;
;
-
(2.18) (2.19) (2.20) |
= ^1 i fi = 90 if ', : = 0D*(cosX15itnf J-svitl,;-cosA,cosif,). , (. 2.14,6). . Xy0Zv. ,, :
0=,5>' , = .cos (.90-.1); 0 = OK cosYol<; cosY0K = cosif.svtt,oi.-, (0 = 180-;
cosPoK=_ cos*- ,, : OKj= OK^cos 130-ifV,
OK^OKcOSlSC-ot); 3=05;', COST'= Stasia if; (2.21)
(2.22) (2.23) |
cos'C0K=- COSir0K=-Sirt<*SvH,tf;
OK =(cosip siivoi-;-cosi.;-siito(,simp). : 0 = \+ ol^tOKj',-0^;- 0K3);0K=strtoc;0K2=sittAcos4-;flKJ-sitisk(p;0K^cos<t.
OK = (sictc03lf)-COS<i;-si(lcl Siltlf). , (. 2.14,). 03] , . - Xv0Zy.
(2.24) (2.25) (2.26) |
0= , cos 90-ip,); 0,= skd; 0=0;}
cosjdoh= cos 180-)=-C0Sdv
= O^cosip; 0;= OHstwi; 03= 0HcosY0H- |
(2.27)
,3-*
cosYOH= siito^cosi^;
|
|
(2.28)
OHstcosi^siturt,;-cosot1;st(tot1sittif1). (2.29)
. . 2.14, :
_ 0H = 0H1+0H^ = (+X;-9; + z)=(0H3;-0H4; 0);
0H, = sirt,o^; OHjsSlHdiCOS^; OH^siud^siKifi; OH^cosd,;
0H = (ein.<i1COSlf1-?- COSot,; sinij^ SV.Hcl,).
2.3.3. , ,
. , , .. 08 (. . 2.11):
0 = (cos X siittfy stn-A. J cos cos if);
= 0; |
(cosif cosy - siny;-cosy sitiif). - , , , - (X , Z) ' :
cosAsitvif; | svkX ', | cosA. cosip |
cos if cos v; | - it* J! | -cosy simp |
X | Z |
-cueist tt if stnvZ + cosif eosycosA cos if- XsinA, cosy stttip + +!)cosAstKif cosYsittif- Zcostpcosy siwl + XsiHrcosX cosip= 0.
:
X(taycosvf-toAsttvif)+ -Z. (tor stnif+ talcosip)=:0- (2'3) , taf =taX/tar, :
Xcos(if-f)+ ycbycosf-ZstnCip+fJsO. , , .. OK = (stwotcosif^- cosot;-3tnd, stn,^p)j
cosAsvnif, sin A; cosA cosif
= 0. |
(2.31) |
StWd, COSlf ', - COS*; - StHcisitHf
Z.
taQ^taX/., :
Xcos (.if+9)+ ytgd-cosQ- Zsin (if + Q). , , .. :
0H(cosif1 sitiot^-cosd,,', stud, simp,,).
cosA^inip,; -sinl,; -cos^cos^
cosif, sind,.,; - cosoc,; since, sinip,
* 0
X (tqlfSiittp,+ eta*, cosip,) + +Z CfetgX1sin.f1-tqX1cos<p1) = 0. , tgA^geCjs toe, :
^♦.^♦!)'; (2.32)
cose ' cose
, - . ^ , .. , 0 OZy
0 (. . 2.13_^ , 02(.. 0B/Xv0Zv) " 0,. (2.13,) :
0B/Xv 0ZV = OB^tcosAsihtp; 0; cosl cosip);
| OB, | = cosA.
0B1 ,
OB, = (sinif; 0; cos if). , OB, 0(0^ jZ.), :
aCX-X0)+e(y-90) + c(Z-ZQ) = 0,
a, , - _, ( 0 ,); Xfl, 0. Z 0 - , ' .
, (sitiif' Ojcosif). :
sinif (.- svttif)+ cos if (Z.-cos if)= 0; Xsinif +Z cos<f-t = 0. (2.33)
- 0(0; 0', 0), :
si.tnf(X-0) + cosif (JZ-0)=0; Xsinif + Zcostf =0. (2.34)
, - . (. . 2.13)
:
Btcos *; cos.?oe 1 C0S<C0B^= tc0sJl slue; sin A- cosAcos(p). , OB, :
(; ; ) = (cosY^^tos^; costgg) _ ; X 0 S. i Ze - . :
|
|
XcosAsini? + 9si/nA< + cosXcospZ=H; (2.35)
Xsinif + tgA,9 + eosifZ^'l/cosA.. , OB, , :
Xsintft + = 0. (2.36)
, ..
,
XyOZy. . 2.13,6 01 -
,
XyOZy. _^
, (sin ^; 0 Jr. cos ip,) j ((.^; Oj-cos?,). , 0D1, 1,
:
aU-X0) + 6(9-90HcU-Z0)=0;
sitv^CX-sin^^ + O+tcosvp^Z + cos^^O; (2.37) Xsin^-Zcos^ - 1 =0.
, , :
Xsitv^- Z,cos^=.0. (2-38)
(2;35) (2,36) ,
,
X si tup - ٧ -Zcos , 1/coei,; (2.39)
xein^-atg^-Zcos^eO. (2-40)
(2.39) J, (2.40) - (.. 2.13,6)
. , 0D XyOZy. *. (. . 2.14,).
,
.
. _.
OJ^cos^SiKcp }- sinX,; - cosl^ostft);
OB^cosl^slivift; O^-cosA, cos<f,).
A, 01, -Ite :
XcosA^sinip -Zcos^cos^ = 0.
XyOZy QH^ (Xj Oj Z) (cosA.COSif. '.0', cosX. Svnif.). QH , ■ ' .. ^ , ' + /] = \ ( ' 01). |0/| = cosd ■ 0 j * I sii-vol,. , . sind|/cosA.B :
'- (sinoL^osip,; 0; slKot^inif,).
il _.-*.-
= ' +■ .= (cosvf sinot^-cosot,'siivaCjSitnf,).
, '" iro .
2.3.4. ,
, , i 1 - 1, .
I ( (. . 2.13). , -||' il , :
0 = (cos A, simp; sinl; cos A, cos f); j= (0; 1; 0).
10: |
12.^* 12. 1 ** 2.
sin, X |
^\^;^
cos |
llcos^sin^p + si .2 + cos*A cos4p COS 8 = cos (.90-,), = 90- X. |
1) : XyOZy (.. 2.13): |
;= si .;
0B, = (situp; 0", cosif); Sl^aCsift^' 0;-cosif,);
Sinip sittip -cosipcostp.
Y |
COS 9 =
sin\ + cos2ip ys-2' J-"1*1'
: sin If sin if ~ cos ip COS If = - COS (If +tp.)-
2.4.
XvyvZy (, , , - ).
2.4.1. (.. 2.11) X(tajpcos(f-tolsi.Kip)+ -Z.(tqj svnip + toXcos *f) = XyOZy X sin^p t Z cos if = 0. :
t |
X sintf + Zcos ip =0; X(tcgcosip - ttj A.sinif)+ y-Z(tg3fsin<f+tgA,cos<p)=0. ,!
X - X |
Z - Z, |
_____ |
V V
COS if |
SVHlf |
COS if |
Jtayjitvi) \+t|^C0Stf / |
sinip
/tgjfHnvpA /tjfcosiM \ t|Xcos*f ) ^tjjAsinip/ |
tolsiaif /
X- x( -cos If |
Si n tf |
+ t |
-,
|
|
, 1= (-cosip; + tay; + sinsj>).
0ZV |
X simp + Z cos ip s 0, =0.
_ | z - Z 0 |
sin if 0 0 1 |
cos if 0 |
:
- Մ - _
Svn<f |
COS vf
- 0
cos > |
S itv ip
, -
- (-cosif; 0; siw if).
... ( ( .):
1 2 cos > t -sJH |
0056,=: |
cos > t u + sm > _____ 1 1
a: I COS'J-
, ,
, -m II V.
1 , I . , -^ I . -" I in.li!. [|| .
f |
QZy (. . 2.14,6). : )
XstHip +Zcos f = 0;
fl)
XUtoAeosif-toAsiHipJ+y- Z(ctQqtsiH^+tgXcostp)=0^ ill yv0Zy; X - .