sprr
i
rAe
z".au) : zs.6(7.p^o (l), Qop 0, x);
zr.a!) : zn.6(Q".u (t), z".on@, T)
'tr'nfl 
"o, ro
Q".uU): Qrec (l) + Q*.cop (/) : 
e (Q"r (t)*Qx.cop (0) : Gn (l) *Q" (/);
Q"(i): ry:v"p^o(t),
T. e. B o6rqeM Br{Ae
y'/rec: /Vrec (Zrp"o, i"p^a, zo, *, Qon, X, f , t),
rAe X w Y - BeKTopbr AonoJrH?rreJlbHbtx nepeMeHHblx, or Koropblx 3a-
BHcflT ypoBHH 6leQon rrpH HeycraHoBnBuleMcfl ABHIKeHHH BoAbI.
Bo.nrurzHcrBo cesseft B (9.15), H? Koropble HaKJIaAbIBaiorcfl yc-
JroBHff qeflor{r4cJrenHocrr.r pa6ornr arperaToB (onruuaJIbHoe rrucfio go
u coctan so), ue.nuueftHrre, HegBHoro BVAa. Pearrasallut groro BbIpa-
lI(eHHfi B o6qeru BHAe BecbMa 3arpyAHeHa. I4crnroqeur.reM flBflflForctl
aHaJroroeHe 3BM, Koropbre c yqeroM HeBbrcoKoft roqnocrH r.rcxoAHoft
uuQopuaqr.ru Moryr HcnoJrb3oBarbcr n yue6HoM npoqecce AJIfl peaJII4-
saw4vr (9.15) B caMoM o6u{eu BHAe.
BnHqHrae pa3JrHtrHbrx napaMerpoB r{a pe}KHMbr fOC paccMorpHM
Ha Hau6onee pacnpocrpaueunoi.t BoAHo3HeprernqecKoll 3aAal{e.
, 3 a[aqa pacqera napaMerpoB pelKHMa cpa6orrcn
B OAOX p aHH JI H IIIa //rJTII T eJIF, IJ O r O peryJtHpoBaHHf,
Br,ipa)Keiifie (9.2i) - HenirHei.inoe airSSepeiiiiiidirbHoe ypaBHeHHe
l-ro nopflAKa rro orHorxeHHlo K Vcpaa.Beaaqplsa Tcpao HeflBHo cBr3a'
Ha c Nrec, H e o6U{eM BtlAe Hallirlt rlcKoMyro SaBHcl'IMocTb l/spa6 (l) :
: 7cpa6 (N rec(/) ) HeBo3Mox(Ho. ff oaHoe r\{oAeJrrrpoBaHrre ypanueuuir
(9.16)-(9.20) MolKHo noryllHrb ronbKo Ha aHarloroBol? 3BM.
nepenr4rxeM (9. 16) - (9.21 ) B crreAyroureM BHAe:
A/f3c (l)
Q'ac(/): zoQ^(t): zoQa (9;t
Irec (l) : q, (Q, (t), H ^(f));l
Hrec(f) : 2".6(Vqpao (l)) - z".a(Q".a(t));
Q".o (l) : Q'p (4 + Q" (l) : Qrsc (l),
ifrec - ly'rac (V"p^a, V"p^6, t).
,\ifOC (l)
(e.r l)
(e.12)
(e.13)
/n | ,{\(u. r ?,
(e.15)
(e.17)
(e.l 8)
(e.r e)
(e.20)
(e.21)
Qnp (r) (9.22)
.reeofi H npanofi
9,81q.r. (t) Hrec(t)
[,rJrH nocJre pa3AeJreHHfl nepeMeHHbrx u HHTerpvpoBaHHff
q.ACTH COOTBCTCTBCHHO NOTVIIACM
Q"e (o)-'t or"o^u. (9.23)
V.p^a(t) 3a nepHo.A T:t,,-to (oAHH 14Jrv 6onee Mecfl-
qeB HItH 4eraa) npH Lr3BecrHoM HaqaJIbHOM co-
CTofl,HHH ero 2n.60:zrr.o(V,tprr6(/o) ) I'I saAaHHot? OrAArIe
f 3C no aKrraeHoIl MorqHocrn,M rac (/) . tr4ssecrHbl: Harlop-
HbIe H oHeprerur{ecKne xapaKTepHcrHKH craHuI4I,I: peN(HM fOC-yc-
TaHoBHBtuaftcR, r. e. zs.6:zr.a(Vt) Lr zn.6:2n.6(Q".0). PaccnnarpgBae-
Mafl fAC - pycJroBafl c oAHHaKoBbIMI4 arperaraMn, rAe AHcvc :
KoTopbtx 3HaqeHnf lV rec H Qnp Moxtuo ctIHTaTb npaKTHqecKH nocTo-
tHHbrMH. KoseqHo, rrocJleAHee 3aMeqaHHe cnpaBeAJII'IBo H D,rn 4rec.
( C yqeroM npuHsrbtx Aorlyueuatt MolKHo 3anllcarb
9,81r1.r" (t) HrccU)
C yqeroM cA€JIauHbrx npe!,noJloltenrti;i
(9.23) IlorllrqvM Arln t-to:Lt.i vr Vcpa6c,:
no Nrec II Qrec BMecTO
V cpaatu
Nreci dvcpaar, (9.24)
9,81t1a"". Hrsc(7.p"0, V"p^e , t)
rAe Vspa6;H Lr 7.p"6r,.-cpa6orKa BoAoxpaHHJItIUIa B Haqa.Te tt KOHUe
r4HrepB ana L^tt.
Aaxe npn nolo6Hofi 3anncu ypaBHeHHfl ero peueHne B oOIIleM
BHAe HeBo3MolKHo I43-3a cnoxHofi cBf3il H rac C Vcpa6, H6o H rsc:
:H rec (V"pua, V"pu6, /). BeeaeM B cBff3H c srHM eule oAHo Aonyue-
HHe, Koropoe no3BoJrrer yrrpocrrirb (9.25) Lr Haiiru HcKoMyro Be,THtIH.
HY Z"p"orn AJIfl [IHTepBaJI a L,tt.
flpavreu cpa6orxy BoAoxpaHLrJrHn\a paBHoMepHoft B TeqeHHe L'tt
Qst
Vcpadin-Vcpa6tx
: COflSt. (e.25)
(e.26)
H lrecl =!
BbrP ax(eHHH
Ltt
3ro ogsaqaer,H nocrorrHcreo_fl".6,
Qreci : Qn.6i: Qnpl * Q"i: coflst'
I4e ycnonwn (9.26) cJleAyer, qro npu lV reci :coflst
:coflst Aoax{eH 6strl nocrorHHbrM rr cpeg,urrir lra[op B
t
t-t^-(dt:-r)
to
234
rVrec (l) : 9,8lqps6 (l) Qrec (t) Hrec(t), (e.16)
235