M
M

CyαM
Cx0
MAM
CxCyM
k
k

Cy
R
R
YQ
ZS
q        CR CyCx
Cz 2
q=1   2
Y
Cy
Cy
Cy
Cy
M
Cy
αCy
Cα
y
M

Cy  α
α
Cyα
Cy
Cα
yα0
Cα
y
dCy(α)/dαα  Cy
α  Cy
Cα
y
Cy=Cα
y(α-α0)(
1
.1)∗
α0
α0=0
Cy=Cα
yα.
(1.2)
Cα
y
Cα
y=2π
1+2(1+τ)
λ
.
(1.3)
λCα
y
Cα
y
Cα
y
2π=6,28

Cα
y
Cα
y
Cα
y
Cα
yλ
α0
α  CyCα
y
τ
Cα
y
M
Cα
y=4
√M2-1.
(1.4)
Cα
y
Cα
yM
Cα
y
Cα
y
Cα
y

Cα
y       M α
Cα
y
M
Cα
y
λ
Cα
y
Cα
y
α
Cy
M
α
Cy
αCy
α0
Cy
Cyα
Cy
α  Cy

α  Cy
α0
Cy
MCy
M
Mα  Cy
CyM
Cyα
Cyα
Cy
Cy
Cy

M
Cyφφ
Cy
Cy=CyCy=Cyφ
Cy
Cx0
QCx
Q0
Q0

1/3
Cx0
Cx0

M
Cx0
Cx0
Cx0
c λ
χ
Cx0

M
Cx0(M)
M
Q0M>1
c =d :l
λ =l :d
c
c=

Cx0
Cx0
A
M
Cx
Cx =AC2
y,
(1.5)
A
A
A
A=1
πλ   ,
(1.6)
λ
Cy
λ=l2
S=l
b
,
(1.7)
lSb
λ        λ
λ   λ
λ
λ
λ=5,36λ   =4
,52λ   λ
λ=2,22λ   =1,3
Aλ

A
Cα
yA
Cα
yA
A=1
Cα
y=√M2-1
4
(1.8)
A
M
M
A
AM
Cx=Cx0+AC2
y.
(1.9)
Cx(Cy)
Cy(α)
Cy
Cx(Cy)
Cx0 CyCx
Cy     k    =Cy  :Cx     k=Cy:Cx
Cy(α)
α

M
Cx0AM
MCy
Cx0(M)A(M)
M
Cx(Cy,M)
k=Cy
Cx0+AC2
y.

M
 dk/dCy=0
Cy  = Cx0
A;
Cx=2Cx0;
k    =1
2 1
ACx0.
k
Cx0Ak
∼0,25
k
AM<M
Cx0
k    16-22  k    50-54

k
Cx0M>1A
k    M
M
Cx(Cy)
CxCy
CR
CyCx
Cx(Cy)
Cy
Cx=AC2
y
ACyCx=A(Cy)C2
y
ACyCx=ACn
y
n>2
Cx(Cy)
Cy=+0,5 A=0,1        Cx=
0,1·0,52=0,025
Cy=-0,15Cy
Cy=+0,5Cy=+0,65
Cx=0,1·0,652=+0,04225

ΔCx=0,04225-0,025=+0,01725
M

M
M
M
M
Cα
yCyCy
CyCy
ny
A
ny
k
χ=70-80◦
c

M
Cx0
k
χ=70-80◦

ΔCx0 ΔCx0(M)
ΔCx0(M)
M
M=M  M=1
M
MM
M
k    =4-6   k    =7-8

M=2
,5
M=2,05
ny=7
ny=5

xy
z
z
xy

x1,y1,z1
Ix1,Iy1,Iz1
R
Q1,Y1,Z1      PPx1,Py1,Pz1 MMx1,My1,Mz1
R
RP
R
R
 Z=0
 R=R
R

RR
YQ
Y
Z
R
RZR
R
R YQ
Mz
ΔR
ΔR
 MyMx
ΔZ
Mz==Mz0
Mz0

Mz
Oz1
Ox1
Cx,Cy,Cz
mx,my,mzMz
mzS
qbA
mz=Mz
SqbA;
Mz=mzSqbA.
(2.1)
Mz
mz
Cyδ ωz
˙
α=dα/dt
δ φ
mz
mz=mz0+mCy
zCy+mδ
zδ +mωz
zωz+m˙
α
z˙
α
(2.2)
mz0Mz0
Y=0
-1000
+1000

Mz0
mCy
zCyMz
YΔx
Mz=-YΔx
mz=-CyΔx
(2.3)
mzCy
mCy
z=-Δx .
(2.4)
Δx =x
bA
bA
 Δx >0
 Δx <0
mδ
zδ
mδ
z<0
         δ >0
   mz<0
mωz
zωz
Oz1mωz
z<0
mωz
z
ωz=ωzbA
V.
(2.5)
mωz
zmωz
zωz
  m˙
α
z˙
α
˙
α=dα/dtα=
V
m˙
α
z<0
Vm˙
α
z
mωz
z
ωz=0 ˙
α=0
mz=mz0-Δx Cy+mδ
zδ .
(2.6)
mz(Cy)ωz=0 ˙
α=0 δ =0

 Δx >0
Cy
 Δx =0
Cy
 Δx <0
Cy
Δx
mz0
mz0
δ Mzmz
mz=0 mCy
z=-Δx
ωz
δ =-1
mδ
z(mz0-Δx Cy+mωz
zωz+m˙
α
z˙
α)(
2
.7)
mz =0
ωz=0 ˙
α=0
δ =-1
mδ
z(mz0-Δx Cy).
(2.8)
CyV
M
Cy=Gny
S0,7pM2.

δ =-mz0
mδ
z+Δx Gny
mδ
zS0,7pM2
(2.9)
ny=1
Gnyp
mz0
-mδ
z
Mmz0
-mδ
z
Δx
Δx
Δx
-mδ
z
δ (M)
M
R

M  -Y r ,
(2.10)
r
P
P dx +M δ =0
   P =-M δx
=0.
δx
=dδ
dx
δx
=3,5
ΔY    ΔMz
ΔY    =k ΔY
(2.13)
k
k =1,85  M>1
k =1

ΔMz=-ΔY    L    =-k ΔY L
ΔY
ΔMz=-k ΔM
r L
ΔM
ΔMz=-ΔP  k L
r δx
  .
(2.14)
l
l  = k L
r δx
  .
(2.15)
ΔMz=-ΔP l  .
(2.16)
l  =70
   ·
   ·
l

l
ωz=0
Mz=Mz0-Δx Y=Mz0-Δx bAGny.
P l
Mz0-Δx bAGny=P l  ,
P =Mz0-Δx bAGny
l
.
(2.17)
Mz0=mz0S·0,7pM2bA
Mωz=0
P =bA
l  (mz0S·0,7pM2bA-Δx Gny).
(2.18)
l  mz0p Δx ny
P (M)
M
              ny=1
Δx
M
+mz0p

Δx
l
r
M=1
M

nyCyα
mny
z<0 mCy
z<0,mα
z<0
ΔnyΔCyΔα
Δx >0   mCy
z mCy
z=
-Δx <0  Cy
Cy
ΔY
Mz
Mz
ΔYΔx=Mz /ΔY
σn=Δx +-mωz
zωz
 ,
(2.19)
σn
Δx
mωz
zωz
 =2m
SρbA
-mωz
zωz
σn
Δx (M)

Δp          Δα
Δp
Δp Δα
Δp
Δx (M)

Δp
ΔCy  Δα
M>1
M<1
M>1

M
M>1
M<1M>1
M>190◦

mz(Cy)
Cy
Cy
Cyα
Cy
α

dY
dV>0(
2
.20∗)
YV
CyY
dY
dV<0(
2
.21)
Cy
M=1
P=Q Y=GMz=0
Y
YΔx
-ΔMz=YΔx
ΔY
+ΔMz=-YΔx
Θ
Y-ΔY=GcosΘ          VP+GsinΘ =Q

ny=cosΘ
VM
 δM
>0
PM
>0
 δM
<0   PM
 <
0
 M0,9-1,2
M
ΔP
Δx Δδ
Δδ
ΔαΔCy
ΔnyΔV
Mz=0
ΔP /Δα Δα/ΔP
Pny
=ΔP
Δny

xny
=Δx
Δny
PV
=ΔP
ΔV
xV
=Δx
ΔV
Δx σn
P =bA
l  (mz0S·q-σnGny).
(2.22)
ny
Pny
=-bAσnG
l
.
(2.23)
Δny=+2
Pny
Pny
 =
-20÷-60 -2÷-6
Pny
Δx
r
ΔP nyPny
V

Pny
r
l
Pny
Δx σnδ =δx
 x
x =-mz0
mδ
zδx
+σnGny
mδ
zδx
 Sq
(2.24)
ny
xny
 =σnG
mδ
zδx
 Sq
(2.25)
xny
Δx nyxny
V
Pny
xny

q=0,5ρ0V2
V ny=
PV
=bAmz0Sρ0V
l
.
(2.26)
P V PV
V
ny
q=0,5ρ0V2
V ny=
xV
=-4σnGny
mδ
zδx
Sρ0V3
.
(2.27)
x V xV
V
σn
l
r k
-mδ
z

M
l
l

P =k    x ,
(2.28)
k
x =P
k    ;xny
=Pny
k    ;xV
=PV
k
.
(2.29)

k
δx
 ◦
P =0
ny=+2
P =-50 -5
ny=+2 ny=+1

P =+50  +5
q
 +δ
+ΔP
 -δ   -ΔP
P =0
PV

PV
 PV
=0
δ  =-5◦
PV
P (V )
PV

mzCy
M
M
Pny
mdV
dt=P-Q-GsinΘ
(2.30/1)
mVdΘ
dt=Y-GcosΘ
(2.30/2)

Izdωz
dt=Mz
(2.30/3)
θ=Θ+α
(2.30/4)
ωz=dθ
dt,dωz
dt=d2θ
dt2
(2.30/5)
P(V,ρ)
Q(V,ρ,α) sinΘ Y(V,ρ,α) cosΘ Mz(V,ρ,α,ωz,δ )
Vρ α Θ
θV0ρ0α0Θ0θ0
ΔVΔρ Δα ΔΘΔθ
     V=V0+ΔV ρ=ρ0+Δρ
y=y(x)Δx
y=y0+y Δx+...
y=sinx P=
P(V)Cy=Cy(α)
x0
y =cosx
x0,y0  y=sinx0+cosx0Δx
V0
PV
V0,P0  P=P0+PVΔV
Cy(α)
Cy=Cα
yα
1)mdV
dt=P-Q-GsinΘ.
dV
dt=d(V0+ΔV)
dt
=dΔV
dt;
P=P0+PVΔV+PρΔρ;
Q=Q0+QVΔV+QρΔρ+QαΔα.
sinΘ=sinΘ0+cosΘ0ΔΘ.

ΔΘ=Δθ-Δα
sinΘ=sinΘ0+cosΘ0Δθ-cosΘ0Δα.
mdΔV
dt=P0+PVΔV+PρΔρ-
-Q0-QVΔV-QρΔρ-QαΔα-
-GsinΘ0-GcosΘ0Δθ+GcosΘ0Δα.
P0-Q0-GsinΘ0=0 m
dΔV
dt+ QV-PV
m ΔV+ Qα-GcosΘ0
m Δα+
+( cosΘ0)Δθ+ Qρ-Pρ
m Δρ=0.
n11 n12n13 n14
d
dt=p
dΔV
dt=pΔV
1)(p+n11)ΔV+n12Δα+n13Δθ+n14Δρ=0.
1)(p+n11)ΔV+n12Δα+n13Δθ+n14Δρ=0
2)n21ΔV-(p-n22)Δα+(p+n23)Δθ+n24Δρ=0
3)n31ΔV+n32Δα+(p2+n35p)Δθ+n34Δρ=n36Δδ .
(2.31)

n11=QV-PV
m
n21=-YV
mV0
n31=-MV
z
Iz
n12=Qα-GcosΘ0
m
n22=Yα-GsinΘ0
mV0
n32=-Mα
z
Iz
n13= cosΘ0
n23=- sinΘ0
V0
n14=Qρ-Pρ
m
n24=-Yρ
mV0
n34=-Mρ
z
Iz
n35=-Mωz
z
Iz
n36=-Mδ
z
Iz
Vθ ρ ΔVΔθ Δρ
V=V0=
ΔV=0
ρ=ρ0=Δρ=0
Θ0=0 sinΘ0=0 cosΘ0=1 n23=0
n12 n13n22
δ =0
1)
2)-(p-n22)Δα+pΔθ=0;
3)n32Δα+(p2+n35p)Δθ=0.(2.32)
Δα(t)Δθ(t)
pΔθ=(p-n22)Δα;
pΔθ
n32Δα+(p+n35)(p-n22)Δα=0;

n32Δα+p2Δα-n22pΔα+n35pΔα-n22n35Δα=0;
p2Δα+(n35-n22)pΔα+(n32-n22n35)Δα=0;
(n35-n22)=2ξΩ0,(n32-n22n35)=Ω20;
p2Δα+2ξΩ0pΔα+Ω20Δα=0.
(2.33)
p2Δα=d2Δα
dt2 pΔα=dΔα
dt
ξ
Ω0
x2+2ξΩ0x+Ω20=0
x1-2=-ξΩ0± ξ2Ω20-Ω20;(
2
.34)
Δα=C1ex1t+C2ex2t
(2.35)
n
nCiexit    i=1,2,3,...
xi=x1,x2,x3,...xnn  Ci=C1,C2,C3,...
ξΩ0Ω20
2ξΩ0=n35-n22=-Mωz
z
Iz+Yα
mV0;(
2
.36)
Ω20=n32-n22n35=-Mα
z
Iz
-YαMωz
z
mV0Iz
.
(2.37)
Mα
z Mωz
z
Δx
Ω20=YαbAσn
Iz
,
(2.38)

σn
Yα>0YMωz
z<0
Mα
zMα
z<0
   Mα
z>0
 x1<0   x2>0  Δα(t)
Δα0
Oz1
Ω20<0
σn
 x1<
0,x2<0  Δα(t)
Ω20>0ξΩ0>Ω0
ξ>1 -Mωz
z
Ω20>0ξΩ0<Ω0ξ<1
x1-2=-ξΩ0±i Ω20-ξ2Ω20;
   i=√-1

Δα=C1ex1t+C2ex2t
extx
cosx=eix+e-ix
2
Δα=C1e-ξΩ0tsin  Ω0 1-ξ2 t+C2
C1C2
C1t=0 C1=Δα0 C1e-ξΩt

C2t=0
       C2=π
2 Ω0 1-ξ2=
ω
ξ=0 ω
Ω0
T=2π
ω
(2.40)
ξΩ0
t
C1e-ξΩ0t   =1
20C1,
t   =ln20
ξΩ0 3
ξΩ0.
n
n   =t
T 0,5 1ξ2-1.
q
V           VMmIz
Δx σn
Mα
zΩ0
q
Mα
z Yα
Mωz
zΩ0
mIz
Ω0

t
q         Mωz
z
 Yα
ξΩ0
Vq
-mωz
z=-mωz
αbA
V
-mωz
z
Cα
y
mIz
ξ
 n   5
H0=0 V0=100q=
6130   2     2       Δx =0,1m=3000

Yα
=Cα
ySq=4,1·19,8·6130=500000     ;
mα
z=mCy
zCα
y=-Δx Cα
y=-0,1·4,1=-0,41;
Mα
z=mα
zSqbA=-0,41·19,8·6130·2,04=-102000      ;
mωz
z=mωz
zbA
V0=-2,5·(2,04:100)=-0,051;
Mωz
z=mωz
zSqbA=-0,051·19,8·6130·2,04=-12600        ;
n22=-Yα
mV0=-500000:(3000·100)=-1,67;
n32=-Mα
z
Iz
=102000:12000=8,5;
n35=-Mωz
z
Iz
=12600:12000=1,05;
2ξΩ0=n35-n22=1,05+1,67=2,72;ξΩ0=1,36;
Ω20=n32-n22n35=8,5+1,67·1,05=10,25;Ω0=3,2     ;
ξ=0,425;
ω=Ω0 1-ξ2=3,2 1-0,4252-2,9       ;
T=2π
ω=6,28:2,9=2,2 ;
n   =0,5 1ξ2-1=0,5 1:0,4252-1=1,06
ωΩ0Ω20n32=-Mα
z
Iz
T 2π
Ω0 2π -Iz
Mα
z
.
(2.41)∗
Mα
z=-Cα
yΔx SqbA
MCα
y
Δx
 ΔV0
 ΔΘ0
VΘ
H
ΔV0
ΔΘ0
T

 Mz=0
Mz
α==α0Δα=0
ρ=Δρ=0
Θ0=0 sinΘ0=1
cosΘ0=1        n23=0 n13=
1)(p+n11)ΔV+n13Δθ=0;
2)n21ΔV+pΔθ=0;
3)(        ),
(2.42)
2ξΩ0=n11=QV-PV
m,Ω20=-n13n21= YV
mV0.
YV<0
ΔV=C1ex1t+C2ex2t,
(2.43)
x1<0x2>0
ΔV
YV>0
ΔV=C1e-ξΩ0tsin  Ω0 1-ξ2 t+C2 ,
C1
C2
Ω0 1-ξ2=ω
V
ω=Ω0 1-ξ2YV
mV0,
Ω0=√2
V0,T
 2π
Ω0 0,45V0;
T( )18V0      .
(2.45)∗

V0=80
T=10  V0=1000T=120
M
 Cα
y
ξΩ0=QV-PV
2m,
Q(V)P(V)
Q(V)=CxS0,5ρV2Cx=
Q (V)ny=1 Cx=
QV>PV
QV<PV
Δδ =Δα(t)     Δδ  =0
1)(        );
2)-(p-n22)Δα+pΔθ=0;
3)n32Δα+(p2+n35p)Δθ=n36Δδ
(2.46)
p2Δα+2ξΩ0pΔα+Ω20Δα=n36Δδ .
(2.47)

(Δα1)
(Δα2)
Δα2=n36Δδ
Ω20
.
pΔα2=0 p2Δα2=0    Δα2
Δδ
Δα=Δα1+Δα2=C1e-ξΩ0tsin[(Ω0 1-ξ2)t+C2]+n36Δδ
Ω20.(2.48)
Δδ <0
C1
C2t=0
C2=32π(sinC2=-1),
C1=n36Δδ
Ω20
.
αΔ(t)
T
C1e-ξΩ0t
t
n

Δα
Δα
Δα
t1
Δα
Δα
t→∞e-ξΩ0t→0
Δα   =n36Δδ
Ω20
=Mδ
z
Iz
·Iz
YαbAσnΔδ ,
Δα   =mδ
z
Cα
yσnΔδ ,
(2.49)∗
(Δδ )mδ
z
Cα
y
 σn
Δny   =Cα
yΔα   Sq
G.
Δx
σnωT
Δα

σn
σn=Δx +-mωz
z
 ·
-mωz
z
Δx  Δx Ω20  -mωz
z
Ω20  ξ
1)Δx =0,05;-mωz
z =0,02;σn=0,07.
2)Δx =0,12;-mωz
z =0,02;σn=0,14.
3)Δx =0,05;-mωz
z =0,09;σn=0,14.
Δx     -mωz
z
Δα
Δx
t1

-mωz
z
t1
Δα=Δα
t1 1
4T.
t0,5T
Δα     Δα   e-ξΩ00,5T.
(2.50)
Δδ =kαΔα+kωpΔα
(2.51)
kαkω
Tt   Δα
p2Δα+2ξΩ0pΔα+Ω20Δα=n36(kαΔα+kωpΔα).
p2Δα+(2ξΩ0-kωn36)pΔα+(Ω20-kαn36)Δα=0.
pΔαΔα
2ξAΩ0A=2ξΩ0-kωn36;(
2
.52)
Ω20A=Ω20-kαn36,
(2.53)
ξA

Ω0A
Ω0A
kαξAΩ0Akω
Tt
Δδ =kαΔα(   Δδ =kθΔθ,Δδ =knΔny),
Δδ =kωpΔα(   Δδ =kωpΔθ,Δδ =kωpΔny),
Δδ =kωpΔθ=kωωz.
Δδ =kθΔθ+kωωz,
Δδ =kθΔθ+kωωz+k˙
ω˙
ωz-kpΔp,
p˙
ωz
 kθ,kω,kp

Z=CzSq,
Cz
My=mySql,
my        l
bA
Mx=mxSql,
mx
Cz
βδ
Cz=Cz0+Cβzβ+Cδ
zδ ,
(2.54)
   Cz0
Cz0=0
my
β     δ
δ
ωy
ωx
my=my0+mβyβ+mδ
yδ +mδ
yδ +mωy
yωy+mωx
yωx.
(2.55)
my0
my0=0
mx
β     δ
δ
ωx
ωyωy
mx=mx0+mβxβ+mδ
xδ +mδ
xδ +mωx
xωx+mωy
xωy.
(2.56)
mx0
mx0=0 mγ
xγ
mx

mωx
y
+ωx+my
mωx
y0
mωx
x
mδ
x
mδ
x
 mx0,my0
mx=mβxβ+mδ
xδ +mδ
xδ =0.
(2.57/1)
my=mβyβ+mδ
yδ +mδ
yδ =0.
(2.57/2)
Z
ZGsinγ
Z
Z+Gsinγ=0
Cβzβ+Cδ
zδ +Gsinγ
Sq=0
(2.57/3)
δ δ γ
δ (β)
δ (β)
γ(β) Oz1

mδ
x=0,m
δ
y=0,Cδ
z=0.
1)δ =-mβx
mδ
xβ;
2)δ =-mβy
mδ
yβ;
3)sinγ=-CβzSq
Gβ.
(2.58)
Cz0mx0my0
My0=(P    +Q   )z  ,
z
my0=My0
Sql,
l
M

-mβy-mδ
x-mβx
M
M-mβy
-mβx
-mδ
x -mδ
y
M
δ =δx
x ,
δx
P =k    x =k
δx
δ .
δ (β)
P (β)

r
δ =δz
z ,
δz
P =k    z =k
δz
δ ,
P (β)δ (β)
r
My=Mβ
yβ
my=mβyβ
β Mβ
y
mβym(β)
β

M
M
M
M
M
90◦
Mx=Mβ
xβ
mx=mβxβ

Mβ
xmβx
mx(β)
(+γ)
(+β) -Mx
Mx
Z
y=Mx:Z
Cy>0

(χ-β)
(χ+β)
Mx
α
0,9-1,2
Cα
y

M
χ=40◦β=+10◦
30◦50◦
M
+Mx
mβx>0
Δβ
ΔnzΔδ Δx
ΔPn
βδ ,nδ
z
δβ ,δnz
xβ Pβ

M
xβ
my mβyβ+mδ
yδ =0,
δβ =-mβy
mδ
y;
  δ =δx
x ,
xβ =-mβy
mδ
yδx
.
(2.59)
mβymδ
y
xβ
 -mδ
y-xβ
 -mβy
-xβ xβ =0
P
-Pβ
q
-Pβ
 -mδ
y
-Pβ
-Pβ
mβy=0

mδ
x
Mx
 Mδ
x>0
 Mβ
x<0
δβ zβ
Pβ
β
mx mβxβ+mδ
xδ =0,
δβ  -mβx
mβ
x;
  δ =δz
z
zβ  -mβx
mδ
xδz
.
(2.60)
δβ z β    mβxmδ
x
 -mβx
 -mβ
x-δβ -zβ
 -mβ
x
M>1-δβ
-z β
-Pβ
-zβ q

-Pβ
-zβ
ωx
-Pωx
P z
-Pωx
-zωx
M<1

β         ZMy
Mx

β
Iy
T 2π
Ω0 2π -Iy
Mβ
y
(2.61)∗
Mβ
y=mβySql
T
-mβy
2ξΩ0=-Mωy
y
Iy-Zβ
mV0
Mωy
y=mωy
ySql.
-mωy
y
+β0
1/4
1/2

-β  1/2
+β
T
π
290◦  Ix=0
Ix
β=0          +β-β
90◦     ◦Ix
90◦
ββ0=
Δu
Vγ
-mβx
 -mβx
χ=ωx    /ωy
χmβxIy
Ixmβx
χ1-2,5
IxIyIy/Ix=10-15
 -mβx
 -mβy
-mβx -
mβyχ
β=0

 χ=1-2,5
 -mβy -mβx
 -γ
Gsinγ -β
 +ωy
 mx=mωy
xωy
         γ ωxβ ωy
          -δ
ωx=0,95ωx
Ixdωx
dt=Mδ
xδ +Mωx
xωx,
(2.62)
Ix-Mωx
x
-Mδ
x
ωx     ωx
dωx/dt=0
ωx   =-mδ
x
mωx
xδ .
(2.63)

-δ
Mx=Mδ
xδ +Mβ
xβ,
δ =β=β(t)

 Cα
y

χ
Cα
y
      ◦

   2     2
+ΔY
ΔY =k1qδ ,
k1

ΔY
-Δα=1
k2ΔY =k1
k21δ ,
k2
ΔY  =k3Δαq=-k1k3
k2q2δ ,
k3
+ΔY
-ΔY                   V4
ΔY ΔY
ΔY +ΔY  =0   k11δ -k1k3
k2q2δ =0,
q   =k2
k3V   = 2k2
k3ρ.
V    = 2k2
k3ρ0.

 k2
 k3  M>1
V =1000
 V=1000M=0,81
V =900 V=1550M=1,43
M>1

M<1
M
Δx (M)
M

M
M
+Y
Y

mβx
α
mβy
α
IyIzIx
αβ
F
Mz
My
αβ
ω

ω
ω  α= -Mα
z
Iy-Ix
,
(2.64)
ω  β= -Mβ
z
Iz-Ix
,
(2.65)
Iy-Ix0Iz-Ix0
IxIy-IxIy
Iz-IxIzω
90◦
     ◦
Mα
z Mβ
y
ω
-Mα
z
         ω  α-Mβ
y
ω  β
ω  αω  βM
M
ω
MM<1
M>1

M
M<1
M
M=2,05                    M=1,60

M
M
Z
M    M>1

M>1
ε
ε=Cy
πλ   .
(2.66)
mz(Cy)

ΔαΔY  =m VΔα    m
ΔY
ΔY
ΔY
ΔY  m
P
M<1

ny=+8
-5
+10
      -5
-5

γ
˙γ
-γ
+˙
γ ˙γ=0  γ=0
δ =-k1γ-k2˙γ.
x yz
γ
φ
θ
˙
x=Vx ˙y=˙
H=Vy ˙
z=Vz ˙γ ˙
φ ˙θ

Vx
˙Vx
x
˙
x=Vx

H
Vy=˙
H
˙
Vy=
H
˙γ
γ=˙γdt
m
J=  m,
J
mm        m=log2m

2J=m.
(560-400):5=32
m=32
32=5
64=6
8=3
γ       θ         VHφ
T   =6
T   =6

±20◦5◦
±10◦5◦
±15
±80±5◦
2◦
3+2+2,6+4+2,3=13,9
13,9:5=2,78
0,03-5=0,15
2,78+0,15=2,93
2,93:6=0,49
k
k   =0,49
T   =6
T
k
 k   >1
k   >1
k
 k   =1

M

 x     Δx
x
x
 x   =200
±50
Δx   =50

x   Δx
x   =450
450±20
Δx   =20

200±50
200±40
Δx   =
40
±50±40
ny=7
Δny=±0,5
ny=6
1/15+1/55+1/330+...=1/11
ny=5
ny=7-7,5
Δny=±0,25

ny=6
ny=7-7,25
560±10
600±50
60◦
60◦

  P=Q+GsinΘ             V=
     ∗
Y=GcosΘΘ=
γ=0             φ=
P=Q
  Y=G   γ=0
P
p M
αβ
N
P=N
Vη,
   P
NV
     η

 216,5◦p
ρ
Q=CxSq.
(4.2)∗
q=1
2ρV2q=0,7pM2.
Q=Yk=Gny
k.
(4.3)∗
G→Cy=G
Sq   →k=Cy
Cx
→Q =G
k.
Cx=Cx0+AC2
y
Q =Cx0Sq+AG2
Sq.
(4.4)∗
G
              Gny
Q (V)Q (M)

Cx0=
A=Q0
q  Q q
Q V
k=k    ,Q
0=Q ,Q
=2Q0.
(4.5)
Q (V)
V2:V1=√ρ1:ρ2
α       Cα
y=
Q=G:k q=1
2ρV2
V  Q
H2>H1
V
V
q=1
2ρ0V2
=
G1G2

                   Q 2:Q 1=G2:G1       Q =G:k  k=
V2:V1= G2:G1G=CyS0,5ρV2
ρ=Cy=
ny1=1  ny2ny=cosΘ
G2>G1
Cx0A(M) Q (V)
Q (V)
Q
k

H(V)H(M)
MCy(M)M
CyCyCyφ
G=CyS0,7pM2

Mp H
M
V=aM
VH
Cy
G/S
V
V  V
P (V)
Q (V)
V
V
MM
M
M
   q

H
HV
H=H     -V2
2 .
(4.6)
G=CyS0,7pM2
p
G
p
p2
p1=G2
G1,
(4.7)∗
p2p1M
P =Q =G
k G=CyS0,7pM2.
MHG
Cy
Q  P <Q
G
pCy
kQ =G
k
P
P =Q
p2
p1=G2
G1,
(4.6)∗

p2p1
M
M
q
P =Q
M
q
Cy=Cy
V
Q
Q

M<1
   2     2
a=20√T
M        V=aM
ρ
q
P
H-M
n    =
          H-M
n    =n 288
T(1+0,2M2),
nn    =
Tn
n=
n    =
Θ
sinΘ=P-Q
G.
(4.9)∗

P>Q        Θ>0
P=QΘ=0               P<Q
Θ<0
Vy
Vy=VsinΘ,
Vy=P-Q
GV.
(4.10)∗
P
cosΘ1 Y∼GQQ
Θ    Vy
Θ
(P -Q)
V  Θ
Vy
[(P -Q)V]
V
V      Vy<Vy
V
V

V
V
V
V       Vy
H
M
Vy

G
(P -Q )Q )
(P -Q )
G
Q )Q0
P
Θ
1)sinΘ=
-Q
G;
2)GcosΘ=Y.
Y/Q=k
tgΘ  =1k.
(4.11)∗
L
H
L  =H
tgΘ
=Hk.
(4.12)∗
V  k=k
Vy  =VsinΘ   VtgΘ  =Vk.
(4.13)
V  V  4√31,3
VΘ
Vy
QQ   =
Q-Pkk   =Y:Q
YGP=P:G
k   =k
1-kP.

tgΘ  1k-P.
(4.14)
P=1k
H
Vφ
H
˙
H=Vy
ΔHVy
H=1000
H=1100 ΔH=+100
ΔH
H=1050 ΔH=+50   Vy=-10
±ΔH
V
±ΔV˙V
˙V=(nx-sinΘ)
θ=Θ+α
˙V
φ
˙
φ
˙
φ        γ
˙
φ
tgγ

ABBC
B C C D
            k   >1

M
H1
H2

H2
αα

M
M
θΘVy

V       Vy=VyV
H V
    dH /dt=V
y=V
y
V(H)
t

V
L(H1-H2)k
V   =
H1=18  V1=2000 V 1=630
V   =300
V1=2000k
M<1
q

Δu/ΔH
ut
u
±Δu
u

Δu(t)
Δu
Δu
dΔu/dt
dΔu/dt=∞
L
Δu
t1
ΔuV
W
β1Δu/V
W
t2
t2
β γ

Δu      L
β γ
V
Δu
ωz
Δα=Δu
V
ΔCy=Cα
yΔα
ΔY=ΔCySq
Δny=ΔY
G=Cα
yΔu   SρV2
V2G
ny=1
Δny=n y-1

V
V        =2G(n y-1)
Cα
ySρΔu   .
(4.15)
Cα
y
Cα
y
α =2G
Cα
ySρV2
Δα=Δu
V
Δα=α   -α
Δαα
V
V       =Δu
2α   +  Δu
2α    2+2G
Cα
yα   Sρ
V        V
Δu   =15

G/S=3000   2     2  n y=3 Cα
y=4
α   =0,3 17◦
n yα
V=335-575
    V =335-575               V=495-1710
 V =290-1000
Δu
t1
 t2 ΔαΔnyθ
t2

αny

du/dH
Vy=
100du/dH=0,05
0,05·
100=5
ΘVy

Θ=
P-Q-GsinΘ
-Q-GsinΘ
P=Q P=Q+GsinΘ
Y=G
Y=GcosΘ
P(V)Q(V)
ny=
ny=1
V
 ny
P(V)
Q(V)
M=1,1-1,2   M=1,8-2,2
Q(V)P(V)-
GsinΘ-GsinΘP

Q(V ,ny,α)
 Cx0 A
Cyα0=0
 α=
 Cy=Cx=
Q=CxS0,5ρ0V2
 ,
Q(V )
α=0◦3◦7◦14◦28◦
nyα=
 ny=
α
α Q(V )
Q=Cx0Sρ0V2
2+2AG2n2y
Sρ0V2
.
Q(V )
ny=0,1,2,4,6,8
α
V2
α=0 ny=0
α0=0
V2
P=Q

 16◦  Y=G
+ΔV
12◦
V1
Q P
2◦V1
V2
V2
   22◦
V2

V2
 α=16◦
V2
α==16◦QY
Y>G Q>P
V2
Y<G Q<P
V2

α=
θ=
α=θ-Θ        θ=
YQ
Θα
YQV2
V2α=
Θ    θ=
α          YQ
α=
θ=Q(V)
ny=Q(V)α=
Q(V)θ=
ΔV
V2
V
8◦
α CyCxYQ
Θ
Q Y
α CyCx YQ
Θ

P Q+GsinΘ
V<V  V>V
P=Q+GsinΘ
P
G
θΘ
α=10◦
α=14◦P =Q
Θ      P =Q+GsinΘ

15◦
30◦45◦
M
1,2-1,8

ny

→
V1→
V2      →
V2=→
V1+Δ→
VΔ→
V

Δ→
V →
V2
P Δ→
V
Δ→
V
Δ→
V
Cy
Δ→
V
Δ→
V
ΔV
ΔV

Δ→
V
Δ→
V=→
+9,8(→
nx+→
ny+→
nz).
(5.1)
→
Δ→
V   2 →
nz
→
nx →
ny
 →
nxny
r
tφΔφ
ω
r
tΘΔΘ
ω
jx
Vy
V
y
ny
ny=Y+Py
G.
ny1=nycosα-nxsinα,
nx1=nxcosα+nysinα.
Py
ny=YG=CySq
G.
ny
Cy
ny =Cy Sq
G.

Cy
Cy=Cy
Cy=Cyφ  CyM
ny
ny
n y
ny
Cy (M)
nyM
M-H
ny=1
ny=7
n y=7
ny 2:ny 1=p2:p1
nyM=1 H=14  A
B
   2     2
 A     ny =14750:5760=2,56
G1
G2
ny 2:ny 1=G1:G2.
ny=1
G1
G2
ny 2
ny 1
=p2
p1
G1
G2
.
(5.3)
ny
r r ω ω
ny
Q
P nx=0
MP

M
nyP =Q=CxSq       Cx
MCxCy
Y=CySq
ny=Y/G
P =Q
Cx0(M)
A(M)
P
P =CPSq    CP
P =CPSq=Q=Cx0Sq+AG2n2y
Sq
ny  =Sq
G CP-Cx0
A.

Q =
Q1 n2yQ ny=1
P =Q0+Q
ny  = P -Q0
Q1
.
M
ny=1
P 2:P 1=p2:p1CP=
M
ny  2
ny  1
=p2
p1
G1
G2
.
p1ny1=1
CP
ny
r ω tφ
r ωtP =Q
nx
Px=p
nx=P-Q
G.
P
nx =P -Q
G.
(5.7)∗
ny
P
ny
ny→Y→Cy→Cx→Q
nx
Q=Q0+Q1 n2y
nx =1
G[P -(Q0+Q1 n2y)].

ny=ny
P =Q0+Q1 n2y  .
Q1
nx =AG
Sq(n2y-n2y).
(5.8)
ny=1
n1x =AG
Sq(n2y  -1).
(5.8)
n1xMH
n1x (M,H)
ny  (M,H) n1x=0
ny=1
n1x
jx
VyV
y
 nynynxn1x
H1MnyCyn y
nynx=0  n1xny=1  nx
ny
ny (M,H) ny  (M,H)
n1x (M,H)
nyny
MH
ny
nx
G
Q
ny

ny
Cx0 CP-Cx0
nxCx0
Cx0nx
ny
p
ρ
VCy
nyV
Mny
nyM
P
CP
nx
ny
nxP Q
ny√2n1x
ny=1
P -Q
ny
n1x
Cyny
Py∼
=0
ny
nyn ynyn1x
ny (   )=6
ny (   )=4
n (       )=6:4=1,5 Δny (   -
   )=6-4=+2
n (       )=4:6=0,67Δny (   -   )=4-6=-2
ny
ny =Cy S
Gq,
(5.10)

n =Cy S
G(   ):Cy S
G(   ).
(5.11)
nyn y
pp1
ny1=1
ny =p
p1
.
(5.12)
n =p1(   )
p1(   ).
(5.13)∗
M=1,1
p1=6670   2
 p1=5350   2  M=1,1
               n =
5350:6670=0,8
n =n y    (   )
n y    (   ).
n
n =1,2
 n2y-1nyny-cosΘny
Δny=ny (   )-ny (   ).
ny

ny
ny
n =Δny=
M>1,3
n =1    Δny=0
n >1
Δny>0 n <1Δny<0
n =1,01Δny=+0,01
n 0,9÷1,1Δny 0,2÷+0,2
n >1,1Δny>+0,2
n <0,9Δny<-0,2
ny
n  =ny  (   )
ny  (   );Δ
ny=ny  (   )-ny  (   ).
ny  (   )ny  (   )

ny  =p
p1
,
(5.14)
pp1
M
ny=1
n  =p1(   )
p1(   ).
(5.15)∗
n  =1
 n2y-1ny
ny=5  ny=4,5n  =1,1
ny=5
n
Δny
30◦1/12
n  =1
,2
             150◦150·1,2=
180◦
30◦  Δny=+0,9
Δω=
 V
Δny=9,8·200
0,9=+0,044Δt=30:2,5=12

n  =Δny=
n  =
n  =1 Δny=
Δny=0
ny
n  =1    Δny=0
n  0,9÷1,1Δny -0,2÷+0,2
n1xny=1
nx 1=n1x (   )
n1x (   );Δ
n1x=n1x (   )-n1x (   ).
nx=Δn1x=
n1xny
A·G/S
Vy=
nxVjx=nx
V
y=nxV
nx 1=1,5
Δn1x=+0,3
0,3V
9,8·0,3=3   2
V=720Δn1x=+0,3
t=500
200·0,3=8,3
t= 2·2000
0,3·9,8

Δn1x
nx 1
ny=1    Δny=0  ny=1    Δny=0 nx1=1
Δn1x=0
 +                -
nyny
n1x
++
+
-+
+
+-
+
-
-
+
+-
-
-
-
-
nyn1x
ny

nyn1x
n1x
nyn1x
M
nyny
ΔH
Δt=ΔH /(ΔnxV  )

ny
n∗y
ny
nxn1x
dH
dt=d
dt H+V2
2  =nxV.
ny=n∗y
nx =AG
Sq(n2y-n2y)
nx
nynx (ny)
nxny=1  n1x
nyP =Qnx=0
ny
nx (ny)nx=+0,2ny=3
70◦
   2
11,5◦71◦
30◦73◦
-3   2
-11,5◦71◦
+4   2
90◦
-8   2 -29

ny=3
nx=+0,2
A
G/S nx (ny)
A·G/S
nx (ny)
ny
n1x
nx (ny)ny
n∗y
n∗yny>n∗y
nx
nyn∗y
n∗y
ny=n∗y
ny<n
∗y
n∗y
ny>n
∗y
n∗y
M-Hn∗y=
n∗y
Δny=0    ny
ny=n∗y
nx=0
ny=n∗y
Δny=0 nx<0
ny=n∗ynx>0

n∗yn∗y
A·G/S
ny
ny
A·G/S
ny
ny
Cyny
Cy
nyny

H1
ny

ny
n1x

M

O
Ox
Oy
Oz
Z
  Ox P-Q-GsinΘ
  Oy Ycosγ-GcosΘ
  Oz Ysinγ
PyPsinα
YY+Py
jx=dV
dt;

jy=V2
r
=VdΘ
dt=Vω
 =r ω2
(6.1)
jz=(VcosΘ)2
r
=VcosΘdφ
dt=VcosΘω =r ω2
 .
(6.2)
x,y,z
1)mdV
dt=P-Q-GsinΘ;
2)mVdΘ
dt=Ycosγ-GcosΘ;
3)mVcosΘdφ
dt=Ysinγ.
(6.3)∗
G
   G= m ny=YG nx=P-Q
G
1)dV
dt= (nx-sinΘ);
2)VdΘ
dt= (nycosγ-cosΘ);
3)VcosΘdφ
dt= nysinγ.
(6.4)∗

Θ0÷+90◦
0÷-90◦Θ
0÷+90◦÷0÷-90◦÷0 γ
180◦
nxny
nx
4)nx=nx(V,H,ny,δ   ).
5)dH
dt=VsinΘ;
6)dL
dt=VcosΘ.
V,H,ny,nx,δ   ,L,Θ,γ,φ,
7)ny=ny(t);
8)γ=γ(t);
9)δ   =δ   (t).
t Θ
7)Θ=Θ(t);
8)φ=φ(t);
9)V=V(t).

t  =t
dt dVdΘ dφ dHdL
Δt ΔVΔΘ Δφ ΔHΔL
1)ΔV= (nx-sinΘ)Δt;
2)ΔΘ=
V(nycosγ-cosΘ)Δt;
3)Δφ=
VcosΘnysinγΔt;
4)nx=nx(V,H,ny,δ   );
5)ΔH=VsinΘΔt;
6)ΔL=VcosΘΔt;
7)ny=ny(t);
8)γ=γ(t);
9)δ   =δ   (t);
(6.5)
ΔtΔt=1
V1 Θ1 ny1γ1 H1
ΔV1 ΔΘ1 Δφ1ΔH1 ΔL1
V2=V1+ΔV1 Θ2=Θ1+ΔΘ1 ny2 γ2 H2=H1+ΔH1
ΔV2 ΔΘ2 Δφ2ΔH2 ΔL2
V3=V2+ΔV2
V=V1+ΣΔV;
Θ=Θ1+ΣΔΘ;
φ=φ1+ΣΔφ;
H=H1+ΣΔH;
L=L1+ΣΔL.

Δt
dΘ/dt=0 dφ/dt=0   Θ=0
dV/dt=0
1)nx=0(                   );
2)ny=1(           );
3)γ=0(         ).
nx=0 ny=-1 γ=180◦
 dΘ/dt=0 dφ/dt=0  dV/dt=0
1)nx=sinΘ;
2)ny=cosΘ;
3)γ=0.
nx=sinΘ ny=-cosΘ γ=180◦
 Θ=0
 dΘ/dt=0 dφ/dt=0
1)dV
dt= nx;
2)ny=1;
3)γ=0.
 Θ=0 dΘ/dt=0  dV/dt=0
1)nx=0;
2)ny=1
cosγ;
3)Vdφ
dt= nysinγ.
dφ
dtV
r
r =V2
 tgγ=V2
  n2y-1
(6.6)∗

 dφ/dt=
0
1)dV
dt= (nx-sinΘ);
2)VdΘ
dt= (ny-cosΘ);
3)γ=0.
Θ
   ◦ Θ  90◦ 180◦    ◦
   ◦
dΘ
dtV
r
r =V2
 (ny-cosΘ).
(6.7)∗
r
 ψ=
         Gcosψ=YsinΔγ
sinΔγ=cosψ
ny,
Δγ
ψ=90◦Δγ=0 ψ=0
sinΔγ=1
ny
GGsinψ           YYcosΔγ
1)dV
dt= (nx-sinΘ);
2)Vdφ
dt= (nycosΔγ-sinψcosφ  );
3)sinΔγ=cosψ
ny.
(6.8)
dφ
dtV
r
r  =
V2
 (nycosΔγ-sinψcosφ  ),
(6.9)
φ           r
φ  =Θ r  =r φ  =φ
r  =r

Θφ
sinΘ=sinψsinφ
(6.10)
Δt
Δε Δφ
ΔΘ
 Δε ΔS
R Δt
V =R
mΔt;(
6
.11)
Δε =ΔV
V;(
6
.12)
ΔS =ΔV
2Δt=R
2mΔt2.
(6.13)
ny=4 Δt=
3

R =nyG+G=4G+G=5G
ΔS= 5G
2G32 220
 E
E=E +E =GH+mV2
2.
(6.14)
1095·108
H =H+H =H+V2
2
(6.15)∗
   H =E
G
H=E
G

H =E
G=V2
2
H =4500H =9500
H =H+H
H =H+V2
2 =V=0
H=H  H=0       V= 2 H
H     =40
Θ=+90◦P=Q nx=0
dEPQ
dS
dE=(P-Q)dS   dH =nxdS;
dS=Vdt
dH
dt=nxV.
(6.16)∗
V
y=dH
dt
(6.17)∗
nx P=Q
H =P>Q   H P<Q   H

H =
H=ΔH
ΔH =V2
2-V2
1
2 V=
     ΔH =ΔH V
y=Vy
V1=1800V2=1440
P=Q nx=0
nx=0   H 2=H 1
H2+V2
2/2 =H1+V2
1/2 ,
H2-H1=ΔH=5002-4002
2·9,8=4600
V1=560V2=200
P=Q nx=0
ΔH=1552-552
2·9,8=1050

 ±1050 ±360
 ±360 ±4600
L
      dH =nxdS=nxdL
cosΘdS
P=0
nx=-Q
G=-QcosΘ
Y=-cosΘ
k;
dH =-cosΘ
k·dL
cosΘ=-dL
kdL=-kdH ,
L=-
H   H
kdH =
H   H
kdH .
k
L=k  (H  -H  ),
(6.18)∗
H
H
V1=1800H1=10   V2=288
H2=0 k  =6
L=6 10000+5002-802
2·9,8 =134600  135
dH
dt=nxV;dt=dH
nxV;t=
H   H
dH
nxV.

H  H
1
nxV
H =
nxV=nxV
nx1
V
H =
nxV=nxV
V=V(H)
t  =
nxny
nyn ynynxnx 1

mdV
dt=P -Q ,
P =50000m=10000G=
98000S=25 2 Cx0=0,02 A=0,1 V   =100
V   =200ρ=1    3
Q =Cx0SρV2
2+2AG2
SρV2=...=V2
4+77·106
V2;
dV=P -Q
mdt=...;
ΔV= 5-V2
40000-7700
V2 Δt.
 1002=10000
 1002:40000=0,25
 770:1002=0,77
[2]-[6]-[7] 5-0,25-0,77=3,98
ΔV
   ΔV1=3,98   2
[1]+[8] 100+3,98=103,98
    V2=103,98
 103,982=
10811,84
V    =200

+100+27,1
+6+11+66
+10-10
f
u
f(u)
f(u)=u3
+2+8
+3+27
-72+52
-20
+5
+5tt
dVy
dt=- .

Vy= - dt;Δ
H= Vydt.
-9,8
-9,8t
Vy
 -9,8t
-9,8t2
2
dV
dt=P -Q
m.
V=V   +P -Q
mdt.
V=100+  5-V2
40000-7700
V2 dt.
+200
+100V
+3,98jx
t=0
ΔV

V
V
V(t)
V

360◦
45◦45◦
1)mdV
dt=P-Q   dV
dt= nx.
(7.1/1)∗
2)Ycosγ=G   ny=1
cosγ
(7.1/2)∗
YY+Py
mVdφ
dt=Ysinγ   Vdφ
dt= nysinγ
(7.1/3)∗

dφ
dt=Vr
r=V2
 tgγ=V2
  n2y-1;(
7
.2)∗
ω=Vr= tgγ
V=  n2y-1
V;(
7
.3)∗
Δt=Δφ
ω.
(7.4)∗
rω Δt
Δt=2π
r(V)
ny=
γ=
r
ny1 ny2 ny3,...n y
r Vny
n y
Cy=
ny
Cy1 Cy2 Cy3,...Cy
r VCyCy
Cy
V→V       r→∞         V→∞

r→r     =V2
V       =220
r     =602:9,8=360
Cy
Cy (M)
V1 V2 V3...,V    ny
P =Qr
P =Q
r=∞
r(V)ω
Δt  r=Vω
ω= ω1 ω2 ω3,...
r
V
Cy
V
M
r Vny γ Cy α Δt nx ω

ω
|Δ→
V|=Vω=  n2y-1
Cy=Cyφ
Cy=Cy
       Cy=Cy

Cy
Cy
n y
n y
ny

ny
          θ =α
ny=1
cosγ α=α
cosγ.
    θ=αcosγ
θ=αcosγ=α
cosγcosγ=α =θ .
θ
ω
ω
x1 y1 z1
z1
ωz ωsinγ= tgγ
Vsinγ

γωz
y1
ωy ωcosγ= tgγ
Vcosγ= sinγ
V,
γωy
ωz
x1
ωx
ωx ωsinθ= tgγ
Vsinθ,
ωx
x1
ωzωyωx
ωx
ωzωyγ

y1Mx
tωxx1
Mωx
xωx
˙
ωx
Ix˙
ωx
Mωy
xωy
Mδ
xδ
tωy
Mωy
yωy
˙
ω
Iy˙
ωy
Mωx
yωx
Mδ
yδ
δ (ωy)

tωz
Mωz
zωz
˙
ωz
Iz˙
ωz
Mα
zΔα

ωz

Ycosγ=G
ny=1
cosγ
γny
     ∼1,4 ∼3∼6
dVy
dt= (nycosγ-1).
ΔY    Y1sinγΔγ.
ΔY
ΔY    =cosγΔY.
γ=80◦ny=5,75
6◦74◦

  ◦
ΔZsinγ
ΔZ
Y
   ◦
YY1Y2

VV   ny
VV  =450
ny=1
ny=3 γ=70◦
V450·√3=780
 α
α

ny=8
180◦
 H1
ny>n y

n y=ny
n y
ny
n y
Cy=Cy=Cy
180◦
 H2
Cy=Cy
Cy=Cy
 H3
6
Cy=Cy

ω=
ω=
α=
x1
x1
 +β
 -α
 +Mx

H=12  M=1,5      1/2
ny=2,3
1/2
ny=4,4
→→
M
M=0,85-1,2

ny
YZ
PyPzGcosΘ
YZ
         Z 0,1Y
N = Y2
+Z2
=1,005Y .
Y0,7Y

N=0,71Y
ny
Y1Y2
Y2
Y2N2
MM=1
 M=
0,9

      90◦
90◦

360◦

x1
ωx
ωx
z1Y
G
ωz
Y=G
 Vω
z,
ωz= ny
V
(7.5)

ωy=0    β=0
ω= ω2
x+ω2
z
φ
tgφ=ωz
ωx
= ny
Vω
x
.
(7.6)
φ
V
G
φ
Vcosφ
Vsinφ
r
Y=G
 r ω2,
r = ny
ω2= ny
ω2
x+ω2
y= ny
ω2
x+  ny
V 2.
(7.7)
ωxωzωωx

r   ny
ω2
x
.
(7.8)
ω=2π
t t
ny=2 ωx=1     r =19,6
L5-7  V=
L5-7=L1-5sinφ=(Vcosφt )sinφ.
sinφcosφtgφ
L5-7= nyV2ωxt
( ny)2+(Vω
x)2.
(7.9)
V=200ny=2 ωx=1      t =6,28
L5-7=125
ωx→0 ωx→∞        L5-7→0
ωx
L5-7
ωx= ny
Vφ=45◦
nyωx
L5-7 2πr  2π ny
ω2
x
.
(7.10)
G
ωx=ny=
t
ΔVy=- t ;(
7
.11)
ΔΘ ΔVy
V=- t
V;(
7
.12)
ΔH=VsinΘ1t - t2
2.
(7.13)
Θ1 sinΘ1= t
2V,

Θ5=Θ1+ΔΘ= t
2V- t
V=-Θ1.
        H5=H1 ΔH=0              Θ5=-Θ1 Vy5=-Vy1
Θ5=0 Vy5=0
Θ1=-ΔΘ= t
V,
Θ
ΔH=V  t
V t - t2
2V= t2
V.
ΔH=0
Θ5=0 Vy5=0
     ◦
     ◦

      ◦
t =10-12
90◦
270◦

1/4
28◦
7◦
Ysinγ+Zcosγ=0
nysinγ+nzcosγ=0;
Ycosγ-Zsinγ=G
nycosγ-nzsinγ=1.
      Cβz Cα
y
Z
nz βα
Z=G
ωx30-35◦
180◦

90◦
ny=0
ny=+1
180◦ny=-1
270◦
ny=0
nz=-1
360◦nz=0
r
φ
nyωx
           ny=5-6  ωx=0
   30◦
180◦

t
ΔtΔLV1V2

D
P=Q
P =Q
P<Q      P>Q
P =Q
n1x
V ==1200
V=1640

V =1200
 V=1550
D=50-100
MV=2170M=2,05
M

V1V2
V2
H2=H1
ΔPV
 V
y

Θ
   30◦
H2
V2
H2V2
V1V2
V2
 H2=H1
V1=1000V2=450
k1=3,1k2=8
              -11,4-4,4
 k1=3,1

H1
n2y
Δ
180◦
 H=2-3
ny
ny
nx

1)mdV
dt=P-Q-GsinΘ   dV
dt= (nx-sinΘ);
2)mVdΘ
dt=Y-GcosΘ   dΘ
dt=
V(ny-cosΘ).
Θ
360◦sinΘ0÷-1÷0
cosΘ-1÷0÷+1
VΘnxny
ny
ny(t)ny(Θ)
nx
 P V H ny
r  =V2
 ny
.
(7.14)

-ΔH=2r  =2V2
 ny
.
(7.15)
t=πr
V
=π
V
ny
.
(7.16)
V2
V
V2
nx0
ΔH =0
V2= V2
1-2 ΔH.
(7.17)
P =Qnx =0
ΔH =nxπr  ,
(7.18)
V2= V2
1+2 (ΔH -ΔH).
(7.19)
V2
r
H1
-ΔHH2
-ΔH
V1
ny  =Cy  Sρ  V2
2G.
-ΔH=4G
 Cy  Sρ
.
(7.20)
G/S=3500   2 m/S350    2  Cy=
0,9    α 20◦  ρ  =1,0    3    H  =1400
                  -ΔH=1600        H1=2200   H2=600

ny-ΔH
ny==n y
V2
-ΔH=2V2
n y    .
M1>1
H1(V1)
V1       H1nyH1
nyH1
q
M1=1,6
H1=8
n y
V2
P-GsinΘ
Q
Qnyα
-G(sinΘ)  =G2
π=0,64G
Q0,64G
ny=3-5

 V2=V1
 V2<V1  H1(V1)
Q
P    +0,64G
ny=5-7
V1<550
V1>850

H1(V1)
M=      V=        V =
Q
P +0,64G
ny=7
V1<650
ny=7
V1>650
V1H1
G2>G1
G1G2
 α1=α2  Y1=Y2
ny=YG
α1=α2
G1G2
 ny1=ny2
G1G2
dV/dt=(nx-sinΘ)
nx
- sinΘ
nx=1
G(P-Q)=P-Q0
G-An2yG
Sq.
P>Q0 Gnx
nx+0,20+0,15-0,05-0,10
Q0>P(Q0-P)<Q G
nx-0,15-0,25

Q0>P(Q0-P)>Q  G
nx-0,30-0,25
P=0 Q0<Q
G
P=0 Q0>Q
G
nyωx ny
ωx
2φ tgφ=-ny
Vω
x
V=540
ωx=0
,8ny=2
tgφ=0,163 φ=9,25◦2φ=18,5◦
180◦
2φ

ny=0,5-0,7
 2φ=3-5◦
-ΔΘ=t
V
α
-Δθ=
-ΔΘ+2α t=4  V=540α=6◦
-Δθ=0,46=26◦
180◦
     ◦
90◦
Θ=-40÷45◦

ny

ny=2
,53/4
ny=1,5
ny=4,5-5,0
M1<1
M1>1
M1<1
M1>1

ny=7-8
ωx0,3ωy

-90◦
ωz
20-25◦ωx
ωz10◦
ωx 3-5◦ωz

180◦
1)mdV
dt=P-Q-GsinΘ   dV
dt= (nx-sinΘ);
2)mVdΘ
dt=Y-GcosΘ   dΘ
dt=
V(ny-cosΘ).
Θ               +180◦
sinΘ0÷+1÷0
cosΘ+1÷0÷-1

VΘnxny
nytΘ
nx
ny
nytΘ
ny
ny
ny
nyΘ
V
Θ=30-45◦
ny=6
160-180◦

ny=1,0-1,5
45-50◦
ny=5   ny=3,5
ny=7   25-30◦
ny=6,535-40◦50-60◦
ny(Θ)Θ=
120-130◦Θ=
120-180◦
ny=1,5-2ny=2-3
V
V
Θ=60-140◦
Δ
Θ=15◦
ny=5 ny=4-8
ny>4
Θ=120◦
ny=2,2

45◦90◦
135◦
Δ

Δ
Δ
α12-15◦
5-6◦
Δ
ny(Θ)α(Θ)

Vny
ny=5-6
Θ=30-50◦
θ=40-60◦
ny=5-6θ=70-80◦
θ=100-110◦

θ
ny=1,5-2,0
ny=2,0-3,5
θ=80-100◦
110◦

PR
y1-o1-z1
Y1YZ1Z
β
tgβ =nz
ny=Cβzβ
Cα
yα.
β
nz αny
β
β =α
ny
βnz
ny=1
ny=6
1/3
αny

ny=1,5-2,5
160◦
180◦
160◦

-ΔΘ
ny=1,5-3,5
ny=0,5-0,7
5-7◦

20-30◦
2φ

180◦
+90◦
90◦

ny(θ)
 ωx

 ωx10-15◦
1-2-3
1 -2 -3
4
1-2-
3-4
 γ=180◦
4
 ωx
 ωx
ωx

Cy
M
1-2-3
4-5
(1-2-3-4-5)
 1-2-3
3-4

M
 ωx
30◦30◦

r =
V2
 (nycosγ-cosΘ).
(7.21)∗
γ=0 cosγ=+1
ny>cosΘ
nycosγ<cosΘ
    r  <0
γ=0
nyγ=180◦ny
γ=0-90◦
nyγ=90-180◦ny
Θ
Θ
V

V   = V2
+2 (ΔH -ΔH),
(7.22)∗
ΔH
nxr  Θ
r
V       V   V      V   ΔH ΔH
r
V   r  V
ΔH=r (cosΘ   -cosΘ   ).
(7.23)∗
Θ   =0 Θ   =Θ
ΔH1=r  (1-cosΘ ).
(7.23/1)∗
ΔH1r
γ=0 ny
Θ   =Θ Θ   =0
ΔH3=r  (cosΘ -1),
(7.23/2)∗
r
ΔH3
r
ny90◦ny
90◦
Θ =50◦ny=4 γ=135◦
V  =200ΔH3
        cosγ=cos135◦=-0,7 cosΘ =cos50◦=0
,64 cosΘ  =
cos25◦=0
,9 r  =2002/9,8(-2·0,7-0,9)=-1775
ΔH3=-1775(0,64-1)=+643
ny=cosΘ
ΔH2=V  sinΘ t.
(7.24)
ny=2-3
Θ
Θ >50-60◦
Θ =40-45◦

Θ ΔH3
 γ=180◦
r  ny<cosΘ
r
20-30◦
r
ΔH3
Θ =40-50◦
ny
50◦
Θ
30◦
Θ

θ               Θα                 θ=45◦
α=10◦35◦
θΘ
α
Θ
ny=cosΘ
Θ =45◦ny=+0,7
90◦
10-20◦
 V   H
90◦
ny=+0,3-0,5
30◦
30◦
90◦

r  nycosγ<cosΘ
r
nycosγ>cosΘγ=0 cosγ=+1
V
V   V
V  V
Θ   =0 Θ   =Θ
ΔH1=r  (1-cosΘ ).
Θ   =Θ Θ   =0
ΔH3=r  (cosΘ -1);
ny=
cosΘ
ΔH2=V  sinΘ t.
(7.25)∗
 γ=180◦

dΘ
cosΘdφ=nycosγ-cosΘ
nysinγ,
ny=γ=Θ  =1
2Θ
ΔΘ
Δφ=nycosγ-cosΘ  cosΘ
nysinγ
,
(7.26)
ΔΘ/Δφ
cosΘ  =0,9
90◦
-45◦-ΔΘ/Δφ=0,5
ny=1 γ=63◦ 84◦ 94◦ 105◦
119◦γny

ΔΘ/Δφ

θ=0    ΘΘ=-α
15-20◦
Θ   =-αΘ   =0
cosΘ   -1
cosΘ
nyα
Θ=-α  α
nyjy

 ωx
 ωx
45◦45◦
    ωVynynx
n∗yny
AG/S
ny
nx
ny<n
∗ynx
ny
r
h
P=Q+GsinΘ   nx=sinΘ;
(7.27)∗
nx>0   nx<0
nx=0
nx>sinΘ    nx<sinΘ
Ycosγ=GcosΘ   ny=cosΘ
cosγ;(
7
.28)∗

Ysinγ=G
·(VcosΘ)2
r
r =(VcosΘ)2
 nysinγ,
r =V2cosΘ
 tgγr =(VcosΘ)2
  n2y-cos2Θ.
(7.29)∗
t =2πr
VcosΘ.
(7.30)
h =VsinΘt    h =2πr tgΘ.
(7.31)
tgΘ=nx
nycosγ,
(7.32)
tgΘ=-1
kcosγ.
(7.33)∗

VP
P=0      γ
Θ
nyω r
VHPnyγ Θ r
VHny
Q
PQG        nx
nx   Θ
nyΘ   γ
     VΘnyr t h
Δφ
h
γk    =8   V =450
 P=0 V =600
60◦
60-75◦
65◦  90◦
h (γ)
γ
tgγ   = 1+ V
V   ,
(7.34)∗
 cosΘ1
P=0
     ◦

     ◦
     ◦
     ◦
ω
ω x1,y1,z1
ωxωyωz
z1
 +ωz
y1
 +ωy   -ωy

x1
 +ωx
 -ωx   -ωx
 +ωx
50◦
20◦
 ωzωy    ωx
 ωx

 45◦
90◦
180◦

90◦180◦
nx
nx
ψ ψ=0
 ψ=90◦
90◦
Δγ

Gcosψ=YsinΔγ
sinΔγ=cosψ/ny
φ
sinΘ=sinψsinφ
ψ
Δγψ
Δγ
ψ=90◦
Δγ
Δγ
ψ=45◦
ny=6      Δγ=7◦
γ=38◦
ny=2       Δγ=21◦ γ=
114◦
ψ
γΔγ
γ=90◦-ψ-Δγ
γ=90◦+ψ-Δγ
γ
Δγ=0 γ0
ψ
φ
tgγ0=tg(90◦-ψ)
cosφ
.
(7.35)
γ0=
90◦-ψ    90◦γ0=90◦
180◦γ0=90◦+ψ 270◦
γ0=90◦γ0=90◦-ψ
γ0Δγ
ny
γ0(φ  )
γ(φ  )
nyφ
nyψV
ΔHΔHsinψ

V H
ψ=90◦
ψ
ψ
Δγ
γγ0
ψ30◦
ψ=0 15◦
ψ=45◦
γ=37◦ny=5  90◦
γ=80◦ny=4  γ=120◦
ny=2,7  120◦60◦
37◦

37◦
ψ=45◦ ny=5-6
φ  =20◦39◦
φ  40-50◦
120◦
60◦
φ  =160◦φ  =200◦
±3◦

45◦
37◦
γ>120◦
 γ=120◦

Δγ
γ0(φ  )              ψ
Δzψ
4
Δγ
180◦
+0,2÷+0,3

45◦
120◦ 60◦
1-2-3 ψΔγ
          3-4 -5 -1
90◦
180◦
γ=90◦+ψ-Δγ
ψ
ψ
 ψ=40-50◦
 ψ=90◦ ΔH
ΔHsinψ

ψ
H V
sinψ     ψ=90◦
ψ=0
ψ=30◦         ψ==30◦
ψ
180◦
180◦

 1-2-
3-4-5
     3 3-4 -5 -1

     ◦90◦
180◦

ny=c
o
sΘ/cosγ Θ=30◦γ=60◦
ny=0,87:0,5=1,74
 Θ=35-40◦
90◦
180◦
Θ
ny
           180◦
Δγ
Θ

φ
180◦
180◦
180◦
γ>90◦γ=60-70◦

δP
δP
δD
2δD

3δD
δV
2δV
  3δV
δP
 δP=0,08P

δPδCy
ny
γ=60-70◦ny=2-3
δD
δ˙
D

-Z
-Z
+Z
-Z
-Ysinγ
+Ysinγ+Z

δPδα        δnyδV

δP
CyδCy
n yδny
V   δV
ω=dfracVr
r

ny
r
r =ny
ω2
t =8  ω=0,785
r >20
r =(9,8ny):0,7852>20ny>1,26
N=Y+Z
Y

2φ ny=2,5 V=200
ωx=1     2φ=0,25 14,3◦

V(t)ny(t)

G NY
P
PxPy  Q
F=fNf
1)mjx=Px-(Q+F);
2)G=Y+Py+N,
(8.1)
jx=dV/dt
jx= Px-(Q+fN)
G
.
(8.2)
f
f=0,020
      2
      2
f

PxPcosαP
Q
Q=G/k k
N=G-Y-PyN=G
      α 0 Py Psinα 0
(Q+fN)
(Q+fN)  =1
2 G
k+fG =G
2 1k+f .
jx  =  P-1
2 1k+f  ,
(8.3)
P=P/G
P
1/k>f
Q=G/k
F=fG       jx
1/k<f
QF
jx
jx

P=P/G
G      p
TT
+3◦P
k
k
jx
- sinΘ
Θ   =1◦ Δjx=9,8·35
2000=+0,17   2
P
 G k fp TΘ
N=0 Y=
G-Py
V   = 2(G-Py)
CySρ.
(8.4)∗
GV   V
Py=0
CyV   V
Py=
ρp
TV
ρPy  pT
Py=0
G/S
m1=100
 p1=760
T1=288◦
p2=740
T2=300◦  +27◦
        ρ2
ρ1
=p2
p1
·T1
T2
=740
760·288
300=0,935 V   =V
m2
m1=ρ2
ρ1m2=100·0,935=93,5

L =V2
2jx  ;
L =
G2(1-Py)
Cy   Sρ  P-0,5G 1k+f  ,
(8.6)
Py=Py/G
GL
    P0,5G 1k+f    G
L
0,5G 1k+f
PGL
CyL
pT
ρ
+3◦
f
 u
V   u
L =(V    u)2
2jx
.
V
V
V   =80    jx=5   2u=15
L =640L =422
L =902

L
u          G             p
T
L =1000
L L
V1=V    H1=0 H 1=V2
   /2V1=V   H2=25
 H 2=25+V2
   /2ΔH =H 2-H 1
nx
L cosΘ=1      ΔH =nxL
L =1
nx   25+V2
-V2
2  .
(8.8)
P=P/G
Cy
Cy

Cy
Cy
             Py0,5
Py
G Py=0,5
Py>1
Py

Px-(Q+F)
V   =60   L=30
jx=V2
2L=602
2·30=60   2nx=+6,1
+ΔY
+ΔY
+ΔY
+ΔY

F

Iy

1◦1◦
 u
β 90◦
    ◦tgβ=u
V
Z
Mx
Z
F
NNF
Mx
N
Mx(β)
My
Z
Z

Z
My

Px-(Q+F) (Q+F)
F
 f=0,035-0,020
Q
V
F f=0,07-0,20
F
f
(Q+F)f
α
α=

ε=Cy
πλ   .
λ
Cy
ε

Mx
Mx=k1z -k2γ-k3ωx,
          Mxz

γωx
k1k2k3
Y+Py=G
Py=0
V   = 2G
CySρ.
(8.9)∗

GV   V
CyV   V
ρpT
V
V
G/S
jx= (Q+fN)-Px
G
,
(8.10)
Px
f
f=0,4-0,5
           f  =0,15-0,25
FQ
(Q+F)
Q  0,5G
k
 F   0,5f  G

Px0
jx   0,5  1
k  +f   .
(8.11)
G
 Q  F
 -Px
 f
k
Δjx=sinΘ
L  =V2
2jx
(8.12)∗
L  =
2G
Cy   Sρ  1
k  +f   .
GL
CyL
Cy
ρp
T+3◦
      L
V
V   ±u u
f
Θ

Cy
f
Y
N=G-YF=fN
Q
L  =1750
V=V   L  =1000 ΔL  =-750
V=0,8V   L  1375 ΔL  =-375
V=0,4V
      L  1700
-Px
Δjx=Px
G

 Py>1
L  =ΔH
tgΘ;(
8
.14)
tgΘ -1k+P-1
 dV
dt
cosΘ=1
k=5 P=0,1G dV/dt=-0,5   2
ΔH=-15
L
tgΘ=-1/5+0,1+0,5/9,8=-0,049 Θ=-2◦48  L  =
-15/-0,049=300
tgΘ=-1k L  =-ΔHk.
jy=(ny-1)
t  = -2ΔH/jyt  =-Vy1jy Vy1
L  =V  t
ny=1,1 ΔH=-7V  =80
L

   jy=9,8(1,1-1)=0,98 1   2 t  = 2·7/1=3,7
L  =80·3,7 300
L  =V2
  -V2
2 k  ,
V
k
L  +L  = H1+V2
1-V2
2 k  ,
H1
V1
k
L  +L
G
√G
√G
G
ρ
√ρ ρ
u
[(V1-u)2-(V   -u)2]
ΔL=ut t

ΔL
1
4u
G/S

   ◦
   ◦
˙V=-(0,5-0,7)   2
˙V

V
V˙V
V
V˙V
˙
ωz
ωz
θ
H˙
H=Vy
H=˙Vy
H
H
˙
H=Vy
H˙
H=Vy
H=˙Vy

=u
V
N
Z
Q

Q
Q

C
C
 ·
Ce
Ce
   ·
P=1000·Nη
V,
(9.1)
N
η
V
P
Ce
C
C  =CeV
1000·η
.
(9.2)
P  ·
C  =3600
P
.
(9.3)
C
M
C  =C  C
M=2,0-2,5
√T
 H=0
,M=0
    ·
C  =8-15      ·

C
C =C  P
  .
P=Q
C   =C  Q =C  G
k.
(9.4)∗
M
C
Q C  =
C   Q
V
k    Q
C

C
C
C
√T
MkQ
C   =CeN =CeQ V
3,6·1000η
,
(9.5)
V
N
η
Ce=
N     =(Q V)
V  4√3=1,3V
V
Q
V  V
Ce
C   =C  P .
C   (M,H)
P (M.H)   C
C
C
C
C   C

C
C =C
V=C  Q
V=C  G
kV
   ,
(9.6)∗
V
C   /V
C   (V)
     C   /V

C (M,H)
C m
C =C  G
kV
√TC  a
V
τ =m
C
=km
C  m
.
(9.7)
m
m

C
C
kC
L =m
C
=kVm
C  m
(9.8)
kV
C
C
k
V
m
dL =dm
C
=-dm
C
=-kV
C
·dm
m;
kV
C
=
m   =m
m1
L =kV
 C  ln1
1-m
.
(9.9)

m   =0,3m   =0,6
k=18 V=950C  =0,08    ·
m   =0,6L =20000
k=7 V=3000
C  =0,25    ·  m   =0,6L =7850
m
m
m Δm  i
Δt=ΔH
Vy    Δt=ΔΘ
ω
,   Δt=Δφ
ω
,
   Δt=ΔV
jx
:ΔL =VcosΘΔt;
Δm =C  P
3600Δt.
Δt(ΔH) ΔL (ΔH)
Δm (ΔH)
 M=0,9

 M=0,8
H=0 M=0,9
2,5·400=1000
19000·2
60=633
3000-545-1000-633=822
822:400=2,06
C 2
C =2,5
C =1,5
 M=0,9
 M=0,8
1·500·2=1000
3000-545-1000=1455
1455
14000·60=6
m =m
m
m
m
m 0,3-0,35 m 0,2-0,25
m
n y
m
m   0,12-0,17          m   0,05-0,08
m
m

m =
0,25-0,35m =0,5-0,6
m
n y
ΔQ
(kV)
k
  ◦  V
kV
(kV)
     ◦
     ◦
(kV)
(kV)
k
C
kVVV
(kV)
kV
C

kV
C
Vτ
L=Vτ uL=(V+u)τ
L=(V-u)τ
VW=V±u
kW
C
C   (V)±u

m   =m
m
=
m
m-0,5m
m1=8000m  =2000m     =2000:7000=0,286
m2=9000
m =2000:8000=0,250
Cx
Lτ
TM
p
√T
p
p1=742
p2=700
M=
C
1/31/3

1/31/3
C
1/31/3
1/9
8/95/9
4/94/9
 5/9+4/9=1
V
Vy=Vy
MVH
n G1
kV
C
=kaM
C
     C =C
n
M
Vα
CxCyk         C
kV
C

Cy=M=G
p:p1=G:G1G1
Gp1
p
kV
C
=
C
G
M
MVn
HkV
C
C
α CyCx
kC   M
kCy
M
VM
MV

M
C
C

  1  1  1  1
  1
  1
 1  2
 1  2
 3

Θ
ny=4

Gsinγ
Mβ
xβ

ny V2
V
V
V    Cy
ny=6

+0,2÷+0,4
α1
α2
ω
ω
ω

α=40-50◦90◦
Cy(α)ω (α)

VyV

G
Q
V= 2G
CxSρ.
Y
r
Y=mr  ω2
 ;
r  = CySρV2
2Gω2
= Cy
ω2
 Cx
.
YQR
α
F
ω
ω
ω
ωx
ωy
ωz
ωz
ωz
IyIz
Ix
x1y1ωx
ωy
Ixx1 ωx

Mx
My
αβ

ω
ω
F
α
ω =0
ω

α     =
27◦25◦15◦
α=5
0
◦
α  =50◦+15◦=65◦
α  =50◦-25◦=25◦α  =25◦
α  =65◦

-ny

ω
αβ
360◦
V2
ω2
±1,2
±0,2
M=0,6-0,9M>1,7
ny
+8-6
nz+2-2

90◦
90◦
90◦

 +ωz
 +ωx
+ωz
+ωx
Iz
Ix
α,β
Mx

AA1,BB1,CC1
AB
C
CC1      C
L1V1
D
A
A2  C
B
L>L1
V>V
1
L<L
1 V<V
1
L<L2V<V
2
L>L2V>V
2

Θ1k k
A
A
ABCDR   1
AE
E A
B
FC
CG
GVy
A

1.m
βyβ+mδ
yδ +mδ
yδ =my(P);
2.m
βxβ+mδ
xδ +mδ
xδ =0;
3.C
βzβ+Cδ
zδ +G
Sqsinγ=0.
β γ δ δ

+My
-Z +Zβ
+Mx
+ΔY
x1,y1,z1
z1
+My
-Z
-Z
+Gsinγ -Z
-Mx

-Z
+My
-Zβ
-Z
-Zβ-Z
-Zβ
-Z +Gsinγ

5◦30◦
35◦
25◦

˙
ωyMy(P)
Iy
ωyt β
t2
β˙
ωx
Mx=Mβ
xβIx
βt2  ωx
t3  γt4
˙
ωx
Mβ
x
My(P)

            1◦
16◦81◦
V
u=ωrW
     ◦

WV
-P
Q

Mx
90◦
30◦

2◦

ny=8
+28-60

M
M

M
M=1
ωy= sinγ
V.
ωy
90◦
ω ω
 ωy=0

Cy
Cy

      ◦

Cy
Cx0
A