Text
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