It i i i-i, w ^ -
...... it, , ,
Mv (. . 2.15,).
I :
1) ;
2) ;
3) .
, ӄ ,
X yQZ :
1. X sin - Z cosu = 0;
2. f[cos&cosX cosy; - (.- sinAstnA'Cosi' + cosucosAsLn.ipjsiftAcosJlcosy],
LCcosu; 0; sin );
(2.53) |
HI |
f |
cos tqv - sin tq X.
= toy = tav ,. ..
, OF (. . 2.12). OF XyOLy
:
X(ctoetcostp-toJCsvH(f)+ y-Z,(ctQotsin^ + toA.cos4f) =
, + 9 - / = 0.
: X (taA.1sinif1+ cto<i1c05qj1)+ + ZCctQcLlsiH43-t<iA,1cos<f,) = 0
+ + % 0
:
DF = [,+ );- (^o^ajC,); (a, - )]. OF XyOZy".
QF/Xv0Zv= [(,+ ); 0; (,- )]. OF/Xy 0Z :
",+ + ,-)' |
cos (
U2 |
, -
SttvOJ =
^+^,- ) "
a,-cu ctaAcosq>- tgXsvnip-tg AjStnq^-ctgdycosify 3 \ + 1 ctqAsinif +toA,cos4?+ctq4*in4>1- to^ cos'tp.,
2.5.
2.5.1.
I '.' , |, . '
, 'I ( , ,
., (. . 2.13,), , :
____ ob=ob/xoz + ^/ = oS/xoa + o5/z = OB/yoz+ /.
| |
|'
i , -
""...... .
, , , -, .
|
|
- 9. (. 2.16,) X0Z 0' = (; 0; Z0) 0B.j= (X^OJZ,). * (.; ӄ^ % 0) 0*= (X; ; Z, ). - | 0. 0 I i J3 -i *"| :
0; |
X. = R cos (. |
: |
Z, = R sin (, -J3).
■; sin^s |
__ ___,.------------ *___ sl.A.=--------- -
tx> |
U
B'Uo.O'.Zo) |
(0;') |
B4o;y.;z<) |
Bcm(Xi'.o;zi) |
B4Xo;o;zo) |
;£
'(;2',)\ | 2 | ""\ | /ӻ |
))\ | %/ |
. 2.16. : - ; - ; X ; Z.
:
%*%', Xt=Xgco3j> + Zeitn$; U,sZ0cos-j-XeelKj.' (2.55) (.
2.16,6):
X, = Rsltv (, + JJ)= Z0cosj + X0sinja. ivt.56)
(2.56) , ,
(2.55).
(2.55) (2.56), ,
■ X < (. 2.16,):
t =$1 (+ ) = U,cosS + Z,siHQ';
-*%=- Rcos(iz + )= 1ttosS - 9, svnff. (2.57)
OB Z X (. 2.16,):
£j * 2; (l)tXjs Rsih, (3 + )= 5<+ *,;
S 9j = Rcos (3 + )= 5: - 1. (2.58)
(2.56)-(2.58) , .
, , j, tr (2.56)-(2.58) ,
■ , .
■ in ,
X 2..
ӗ X ', , X % , , , .
- X *.
(8 9 ( X9Z , ) :
"i = 1 -*■ 1= X0co3j3-Z0stnja |
t I. |
COS |
- |
(2.59) |
X <5 |
,SiHjD + £0
w |
X0cosjd - 10 sinja;
-*■ 2= Z,cos6- y^eiri.6 = (X0siH.J3 + Z0cosj3)cosS'- 90siH(o; t 9z=Z.,sin<5 + b1cos6' = (X0sin.p+20cosj))sinG+ ӄcos.(2.60)
|
|
1 Z V:
f = "- z"siv<?. Z *■■ Z"1; I X"=Xmco-c-ymsivc; |
(2.64) |
(2.63) |
SL = ^* - ,*1 = [(20cosj!> + Xosi,tiJi))$vn^+ yocosS3cost-(Xecosj3-
-Iesir,j5)SiK<t; (2.6.1)
Xj= XjCost; + aj9v,(C = (X0cosjs-Z0sltvJ>)costi-[Czocosja + X0in,p)sinS +
+ yocos(s]svn.<C,
X Z :
, = =X0(.cospcos'S+sin,p6iH'B')+ Ujcosefsinli 4
(2.62) |
+ Z0{tosp *{,*,<$ tint - siKjacost); }= y'=X0(slnp sin.Scos'B-cosp stu<o)+ yoeos6cos<C +
+ Z,o(coeipin.fcosc3+ sitvpitvt); Z =Z a Z0coejs cos£ + X.sCttj9co6(if- <3,
X., , %.
X Z > X'" i . X1"- X !,_. -
. X Z (. 2.1
,,).
1. +jj:
/ |
0=;
t |
i,Z0=X'co5js- x'siwp;
_ =X'cos^ + Z'siHja.
2. X +6:
'=" | /
7 (2.65) |
/
~
"='"< <-X'"svni!.
T
Xui
1> - X Z :
>'="5- Z"siH<?ty"Wt + X",Stne)cosS- Z'"in<J;
Z,0=Z'coeja- X'vnj3=(.Z"eo<?+y"in(5)co4j>- XHiiWjp = [> + ty"li t ,*1*.1ϻin]cosj3-(X,,'cos'E-y,,,siH/!r)sifvp =
X"eos(ocosp+ 9mcos'CcospSia^ + Xsvn'Scospei<it(J-XmcoS'o eitvj> + + 151! stnjs = X"1Cin'Coosp9in6'-coe4JsiKj)+ymCcoT;cotjscoff +
+ sim;*<,nj5)+ z'"coS cosj; X0-X'cosja+5t19inj = X,,coeja + (Xllc(JS<3+ y"9inef)8ittjs =
= (Xmcos'D- 9"'siw,<Oco4p + [z'"cos(S + (y'"costitX",iH<c)vtv^]sUj3 = = Xcostcosp- y'"stn.T;co,p-t-Z"ko9<5inp+ y"cos<Bitii,_p + +Xll,sin1svu<Sl,j = X' (costeoep+ sin's Si SiHp) +
+ yl"tcos,esiH(JsiH(S-Si.n'C tosja)+Z oosSsinp. (2.66)
-0 3, , 2, X'", "', Z'" -
.
. , X, X Z $ - X, - X - .
(2.56)-(2.58) :
_^'=1*5+ y"si,<a;
0C<(.n-af^i=cos6sin-!8' 9=1^; ^). , 1, ; i , ( ).
2.5.2.
. X J Z, , £.
, , , , .
2.5.2.1. ' +ja.
:
1. :
X cos(.if + )+ cose- Z siu tf + t),
|
|
v^irV-
2. ,
:
* XXX = (cos A. svntp; si.fi A; cos X cosif).
OB +jj (0 = 1 * ) (2.62) :
X.= coslstH((!cosij>-cosl<uOS^ siup = cos J, siuC^- J3)',
4,= sin X;
X, = cosAcosipcos,p + M>sA.si'H,ip sin.j=oosA,cos Cif-J);
OB. tX^X = [cosAsi-tvOf-p^sinV, cos A. cos (.if-ja)].
> , :
£ = [cos (if + ty, ctoj cosf,-sinlip + E)]= (; ,- ). X Z +js tt. :
)= <% 6-<>;
a1=cos(4,+ e)cosjs+ Svh ce+(p)siHjs = (>+ e-j) = cosCP-f-e); f^ctgycoee;
c1= coscif+eisitt-j -sinc*f + e)cosj = sincja-f - e)-
2.5.2.2. X
(2.62).
:
a^= cosCif+E);
, = cto cos - sin + ) silts';
, =- sin Ctf+e) costf - ct<jj- cos £ si,e\
-
XcosC(f+e)+ [cto cosecos<5-aittC(p+e)&i.n6]--Z [ei,HCif+t)cos6+ cta^cose sin <] = 0
2.5.2.3. V - X -Z
QB, :
X, = coslsinif:osjacos't + Si/Uj9si,u6 st*U)+ sln.A.cosdsin(o + + oos^cosi^(,-svtvj cosTi+ cosjssinS sitvt) = = cosJlsirtu>cos<peostC -cos^sltup sin. <3 s^"-^ sittja +
+ Sin , COS ^Sin<C-C0sXcOSip StttjD COS'S + cosJ.coefpcosjOsitidsln.'Cs scoS^CoST: Sitv(lp-ja) + COsl SiHirs;.tv6coS((j>-p)+8irtlcOSd.S{.n'(7;
I
=-coslsin<f cosjjsWC + coslelnipeifipstnffcos'o + -t-svnAcosScost; + cos A- cosip cosp sitt£ cost +
+ cosAcostf slnpsvnT; =-cosAsiv'CaiiKC4'-j) + + cosAsiftefcos'ocosc<p-ja) + SiH cost cost; ZjecosA6in<f>sinpcos< + coslcs<f cosecos^~sin4,siw^ = =*cosA cos6 cosc<f-jo)-siw A- sin(3. OB, , X X Z :
cos A cost ia (4>-j8)+ cosAsin'Min6cOS(ip+jB)+- + sinA cos <5 sin's;
*.(y-*-Z) |
+ cOsXsin<CSvnCtf-J>); cosAcoegcos cif-j'J-iittAstne'-
ft
: |
-
Of eXU eCcos^sin^i-svn^ ', -cos^coscp,). cosA1costCsln(ip1+j3)-sinA1cos<9 svnt -
(2.68) |
05<--)^=^ |
- cos Of,+J) cos A-1 sin si n't; -(cos ^+-^; + + cosA-1eiH'usirt(tfl+j8)+cos(ocos'0sinA1; sin A, sIk(o - cos^ cos <S cos C^ + J).
2.5.3.
,
, , .
- X - * ■
1.^..., Aw _-) :
J - (; 1; ), X Z, 06 02, .
Ai (N_y- ) , j 90 (n-x-ZI
|
|
j(0; 1; ), *(__) m^V *V ^8 '* :
cos[90-X<(s.x.X)] =
"^ (ի) + (,)+ (Z,)*'" 1 : sUA^ ty_x^,)=siftAco*6co5,C +
+ cosAsin6costcosc<f-vp)-cosXsin'E Ctf-j). (2.69) t , OIL . _., , j (; 1; ), ^. (.X-Z5
'
,
s*HA1{(SI_X-i)=c0SCtp1+j3)C0sA,1sin(acos,G *
+ cosA1SvH'o svh((j>i+j3) + c0s6cos'C8vhA.1. (2.70)
(, ^ tx);^1) ■ ^f QC-Z) > ^11 X-Z) '") ' (2.69) (2.70) ,
(J8, ?, ) .
. , ,
^ w', = Ccos A, sin ,; - sin ,; - cos A, cos cpn).
X :
(2.71) |
X^cosA,- sin<f.,; a^-sinXtCOsS-cosA^cos^sinS; Zs-- cosA^os^cosS +sinA1sin6;
UX) |
C*1 M> ^1'i
svnA1l= siw^costf + cosi, coscf1 sine.
(2.71) (2.70) JJ *
<^ (__,. ( %i (--) <~> 'XOZ , Z .
XOZ* ty-%-z,) , Z, ..
, - X
Z, XOZ. (.
:
o"S/XOZ^c:(.x_X)=CKw;o;z111);
^x' = v z'"=v
*= (; ; 1) , (2.62), :
1^ ta_x_Z)= (0;siH6; cos<s).
^--) /<_/,)__^) :
cos6 [costf cos tp-i>l-tgAsi,n6],
^tS-X-Z.)^Y{*n.(if-j) cosx + slnt [cose tqA. + si-nScos Cif ^p>Jl-*+ (cosScosCtp-pJ-tgA st^]4
if., x_ ), f(<(u_x-z) XOZ (- ),
-KeXU |
Us-x-z) |
x-z) |
Z, .. /XOZ^ !)_
cosgfcosficosd^tpi-tq Justus]
(2.73|
X . jeX^Z = (; 1; ) (X Z)^() : 7()1()= (0;cos<3' -itntf).
j XVZ.,., iL () > Z : J eXVZnx) = (0;cos6; 5<). , f: 9cos<5 + Zsine "- 0 6 > , , DB j. , :
coslsinif; sitvA; eosAcasif
0; cos6; si-; ,
X Z
X (cos6cosip-tQAsin6)+ysvnGsittT-ZsiH<pcos(3 =0.
:
X(cos6cos<f-taAsin6)+ysiH6sin(p-ZsiHificos6 = 0, cos<5 t Z St< =0-
a,X +,+ c,Z=0, , +Cj,Z = 0.
. (j>* /. %t () > fyty-X* ' fitfZ> '^tfX-) ,* , (2.72) (2.73) <t, 6, .
(2.72) (2.73) . X Z : , , , .
Vwy} fiffxi '
+ c.
( .) :
^= fsvtup;-(cos6cos(f-tgisvH6)sin^■, (cosecosip-toA sinejeostf].
IB, Z .:
(cosiftos6-tg3,5in<5)cos6
tflitp =-==" 3 - (2.74)
ux) ysiK'ip + Ccostfcosif -taAsineO1
|
|
(2.74) (2.72) J>= = .
\<- _
, 01 j:
cose; |
j,= (0:, cosff ■, si-),
0!D = (cos^siHi^-sitvA.^ > -cbs^cosip.,)
C0SV'H<?,i -siV> -cosA, cosq,
0, |
0; X |
SiK<3
Z
X(C08fj-ta,te)-'St'^VvKiftt Zsin^sO. : XCco's(f-tol,to<S)- ytjgsui^+Zstitcp^O, 5<5 + Zsin6*0. = [1^/; Ccos4.1-tgA1t^6)sin0;-(costp1-tgA.1tg6_b:ose]-jJronif.M -Z
^ - ʫ
cos. |
(2.75) |
(; ; -1): (cos if, - 1 tt|6) CosV
vft(z) <^() XYZ Z fe X V Z< (z) - (; 1; ), ,
}",* XVZ = (-Sih^cost; 0). , , j, 2) :
" Xcost coscp + slut cosif-Z (sin < cost: + sint tol) = 0;
Xcosip t ytQ*cosif, + Z(Hft^-to<ttoV=0. , JA-XSitVC * ycOSX = 0),
Ml,?-- [cost(.Svuu>cos<t + taXsi-Wb)-, sinl (svnifcost +toAsvti/B)-,cos(pj-
= [cos-c csuift- toe toj 4-,); + 9ini;csiu^-t^<ci^0;-MS4l,/oos't^
Z ,, Z :
"St ■ (2.76)
COS
^tosJip + (slntpcosfc + tflXivwt)4
COS ? |
COS(fl (2.77)
1^(z) ^ COS2^ +(*<* If, cost -sittt t^i,1)4
. ., -
: ' '
[co s6co8C^-p)-tj[Xivttg ] (2 78)
*W"*' ^sih.sL(?-ja)+[cos(3iC05Ctf-i>)-t^sins']2 '
cosfl [costf cos CtyjO- tg^stng 3, ■.
COS 1..C- j v i- fl i g
2.6. »
2.6.1.
, Z.k., -
■ > WWW
, , XVYZV . XwywZw , .
XWYWZ , . X \Z.V . W Xv^vZ.y.
(.2.17).
W V V<:
,------ 4, _ 'wr="V + v's,
1^(*Y|?(4]VS|, JV(- 51 , /, f.^J:*-S',H /. -
. 2.17.
V . . .
siHu) = ih/H, £ \\ - , (+) - , (-) - ; - V .
. W V
- ^ - 5* - S,
s , /; - , ; . , /.
, . . X1 Xw*vv^W X1 \
Z' X' .
2.6.2. .
, ^ " w^w ^ w .
1. __ X Zy.
2. Xy^/vZv .
3. X ywZw .
4. () .
, ( -, JL,., , (fj), . , ( J,dp, . 'ip)' . , _ . :
1J ;
2) , W, .
at. !* , :
1) ;
2) . .
:
1) ;
2) , W, .
, .
: 1. , , W Xv 5L Z.y.
2. , W. X Xv Z v.
3. (, , , W).
4. ,
5. , W.
6 . :
1. , , W Iv.
2. , W .
3. .
4. . .
2.7.
2.7.1. ,
, , | (X; ; 1) = , _ = ip(t); V (t); % Ct). * .
, 0(, 0, Z0) (. 2.18) t, Q(X-t-; + ;2+£)-
t + t. , 0 Q :
X ~ X 0 _ - _ X - X _
" Z
t :
" __ Jj " ְ - Z ~ Zo /-t " /At ~ AZ/At
At *- , 0100):
_ |
Z-Zi
dX/dtL' oLy/at|Mo~ dZ/dtJ^
. 2.18, ,
3", , :
(2.80) |
' dt |
0' dt |/'
it dt |
(-0)+^- |
U-Zo)=0. (2.81) |
, 0(0) , :
̄
, ^ j(X,if) =0 9=ip(X), S, , :
-, dX |
(2.82) |
.=ii;y-yo=cty/dx|MU-K0).
cdif/dX 1 /dLX =J)
|(,) ■ ".( :
S-(cBSdjcoipjcos-c);
-■-ifjfjV'-w l2'e3)
*,0) :
ا!1 (X-XJ. (2.84)
e 3f / |.
^(.,,} . Mp^X^S.jZ,), pfx i ' 8Z 01 , - MpQ (. . 2.18).
M,N, 5LL_ J it-L. grL (,0) ^(X,y,Z)* . :
C05J3 |
,,,; cosoi = -7= .... 1; -
2.7.2.
, (. 2.19). : (0; R; 0); B(R5vnycosy; Rsiti^jO). :
-4 _ -< _ 2- Z,X - 0 _____________ -
(2.89) |
Xcosr+ ӫ* - ftsv =0.
*. |
(2.85) |
, (2.86) |
1^ *\, *%