已知:
Mf11 5,Mf12 0,Mf13 0
Mf 21 0,Mf 22 60,Mf 23 0 Mf31 0,Mf32 0,Mf33 70 J11 4,J12 0,J13 0
J21 0,J22 12,J23 0
J31 0,J32 0,J33 11
ms 40,mh 37,mm 5,mr 5,mb 3,mo 0,Bh 490,B0,g9.81
r0.1,rr1 0.3,rm2 0,rm3 0
ro1 0,ro2 0,ro3 0,rb1 0.7,rb2 0,rb3 0
r 0,r 0,r 0 hb1 hb2 hb3
KD0 2,KD 45,KL0 0,KL 132.5
KM1 60,KM2 50,KM3 100
K 20
Kq1 20,Kq2 60,Kq3 20 变量:
r t 00000000 ,,,,,,,m1均为时间的函数,且 , , , ,
0 0, 0 0, 0 0,rm1 0 0.04 函数关系:
ud 2 2 2 dt Vuvw
1 coscos sin 0
d w v arctan cossin cos 0 dt u 2
d v w d t a r c t a n V
sin 01 3
coscos cossin sin R sin cos 0
wb sincos sinsin cos
cos cos
coscos sinsinsin
cossin sinsincos ba
cos sin
sin sincos
S
DK K2V2
coscos
sinsin cossincos D0 D
sincos cossinsin
SF K V 2
LK KV2 L0 L
M K V2KV2 w1M1 q11
M K K V2K V2 w2M0M2 q22
M K V2KV2 w3M3 q33
X D YS R SF
ba wb Z L
M1 Mw1
M S R M 2 ba wb w2
M M 3 w3
rr2 rsin rr3 rcos
0 XT
r T T
F0Y
h1 rrr
1 BmgZ
1 h h2 r
h h 0 0
T
h3 r T
F 0 S ucos
r1 rrSr
2 ba r
m g u sin
2 r bar2 r
rr 0 T
r3 rT
FS ucos
r1 rSr
3 ba r usin
3 ba r2 r
r
r3
rT m m1
0 uT F F 0 S 0
r r r S r j4 mbam2
rT m1
j4ba m g 0
r m3
m uT
m
FS0 rSr
5 ba 0
5 ba m2 r
m3
rT
0 T
o1 rrS r
F 0 6
6o ba o2 r
mg o
o3 r T
0 T F 0
b1 7 rrSr
mgB
7bbab2
q6 T6 M1sinM2 sincosM3 coscos q7 T7 0
qr T0 8m8
q2
T 0 T2 0 T3 0
q3
b b
r b3
q
1 1
q
q4 T4 1
j q i
5 52 3
Qi
7 j1
rj
Fjq Ti i18
j
T M
T M cosM sin
T a h
0 0
cos
1 0 sin
T
0 sin sinsincoscos 0 cos sincos
h
0 sin
sincos cossin
T
0 sin
cos cos
h 1 T
1
s i n
h h2
0
0 cos sincos
0 sin coscos
h3 rrrT
r1 r1 r1 aaS r 2S r S r
r h b a r 2 b a r 2 b a r 2 r r r
r3 r3 r3
0 0T r h Sba 0Sba 0
r1 T 0T S 0
ba
r r2 h r3
rrrT m1 m1 m1
aaS r 2S r S r
m h
bam2 bam2 bam2
I0 1 0
m3 m3 M f 11
m3
M f 12 M f 13
rrr
1 0
f f21 f22 f23
0 0 D 0 00
0
001 MMM
M M
f31 f32 f33
M M 0 r r rT
0 00
h3 h2 s1 rr0rrrSr rr0r
h h3 h1 s s2 bahb2 s s3 s1
r r 0 r r r r 0 h2 h1 s3hb3 s2 s1
0h3h2 0
0 r3 r2 0
h h3 h1 0
r r3 r1 0
r2 r1 J06 0 J06 0 JJJ
h2 h1
200 200
sfsf
0 0 5.5 0 0 5.5
0
f
r T hb1
0rr s3 s2
65 g 7 7
ba r ba r m m I
g g g 0
G q
g 0 44
0 a a/q i18 rr i
r2r2rrrr r2r2 rr rr m2m3m1m2m1m3 r2 r3 r1r2 r1r3
Jmrrr2r2rr Jmrrr2r2rr
m mm1m2 m1 m3 m2m3 rr rr r2r2
r
r r1r2 r r
r1 r3 r r
r2r3 r2 r2
m1m3 m2m3 m1 m2 g 1 1 m s I M f
r1r3
r2r3
r1 r2
g mrDT 12 sh f
g m I M r 13 s fhs
g mrD 21 sh f
g S JST S J ST S J ST 22 ba s ba ba m ba ba f ba
g TS J J ST TS J ST 23 hbasfbarbamba
g S J J S T S J T S T
g31mIM r
g44 mrI
g S JST 55 ba r ba
g TS JST 56 r ba r ba
g S JTST
sf
T
11 12
g g g 0
0 0 0
0 0 0 0
0aTa/q hhi
21
22 32
23 0
0 0 0 0
0 /q hh i
g g
0
31
0 0
i 00
32 ba s f bah bambar
sh
13
0/q hh i
0 0
0 g 0 65
0 /q rr i
0 0
0 0 0 g a a / q 77 m m i
恒等式:
Qi G i18 q
0gg 55 56
0 /q rr i
i
求:利用 Matlab 编程,采用 Runge-Kutta 方法,数值求解在t 3000s 时间范围内, , , ,,,随时间t的变化规律,并绘出图像。
要求提供所有代码,每条代码都要加注释。工期 7 天,结果正确才交付(有论文结果作比对)。