mvo 11 - relatorio_rapha
TRANSCRIPT
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m1 m2 R1 R2
m1 R1= +Gm1m2
r3 r
m2 R2= Gm1m2
r3 r
r= R2 R1 m1 m2 r= |r|
Ri=d2Ri/dt
2
G= 6.66950 1011N.m2/kg2
m1 R1+m2 R2= 0
Rc
Rc=m1R1+m2R2
m1+m2
Rc= 0
Rc(t) =Rc(0) =
Rc(t) = Rc(0) +Rc(0)t
Rc(0) Rc(0) t= 0
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m2 m1
r+r
r3 = 0
r = d2r/dt2
m2 m1 r = |r|
= G(m1+m2)
m2 m1
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= GM
G
G= 6.669501011N.m2/kg2
M
= 1DU3
T U2
= T U=
DU3
GM
=M.U.= 5.97219 1024
=D.U.= 3.8440 108
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=T.U.= 377625
42164 km
Rgeoestacionario = 0.109687 D.U.
Vgeoestacionario =
Rgeoestacionarioa= 3.01939
D.U.
T.U.
Tgeoestacionario = 0.2282 T.U. 1
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RLua= 1 D.U.
VLua= 1D.U.
T.U.
TLua= 1 T.U.
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160 km
2000 km
RISS= 6771km
RLEO = 0.0176145 D.U.
VLEO = 238.267D.U.
T.U.
TLEO = 0.000464501 T.U.
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i ++ 2
2
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L =
cos() sen() 0sen() cos() 0
0 0 1
L
=
1 0 00 cos() sen( )
0 sen() cos(
)
L++2
=
cos(++
2
) sen(++ 2
) 0sen(++
2) cos(++
2) 0
0 0 1
L
2=
1 0 00 cos(2 ) sen(2 )0 sen(
2) cos(
2)
LLHVInercial=L2
L++2
L
L
R= (x(t), y(t), z(t))
V = (u(t), v(t), w(t))
LHV = (0,n, 0)
a = (ax, ay, az)
ag =
|R|
3R
R
R
d Rdt
LHV
R=d R
dt
LHV
+LHV R = R=
x nz0
nx n2z
=
uvw
R
R= ag+ a
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R
R=dR
dt
LHV
+LHVR =
R=
uvw
+nz n2x0
nx n2z
= 3 x+ax 3 y+ay
3z+az
x= u+nz
u= ax+n2x+nz
3
x
y=v
v= ay
3y
z=w nx
w = az+n2z nx
3z
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r1
r2
r1
r2
r1
vc1=
/r1
r2
v1 =
(2/r1) (/a)
a=1
2(r1+r2)
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e= (r2 r1)/(r2+r1)
v1=v1 vc1 =
(2/r1) (/a)
/r1
v2=v2 vc2 =
/r2
(2/r2) (/a)
v= v2+ v1
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ax 2 ax 3
i
1ud
1.5ud
80%
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,e
LBLHV
LBLHV =LLL
L=
1 0 00 cos sen
0 sen cos
L =cos 0 sen0 1 0
sen 0 cos
L =
cos sen 0sen cos 0
0 0 1
B
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X
X
Y
Z
B = (p, q, r)
B =pq
r
= 00
+L 00
+LL 00
+LBLHV 0n0
(p, q, r)
= sec(rcos+qsen) +nsentan
= qcos rsen+ncos
= p+ (rcos+qsen)tan+nsensec
p q r
MCM=dL
dt
B
=dL
dt
LHV
+B L
L
IB I
I=Ixx 0 00 Iyy 0
0 0 Izz
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MCM=
d f= RcRc+3dm= 3n
2
Rc I Rc
Rc
R= (0, 0,1)
RB
=LBLHVRLHV
MG
MG=MxMy
Mz
= 3n2RB I RB
MG MxMy
Mz
=
3(Izz) Iyy)n
2cos2cossen3(Izz) Ixx)n
2coscossen3(Ixx) Iyy)n
2cos2sensen
p
q
r
p=Mx+ (Iyy Izz)qr
Ixx
q=My+ (Izz Ixx)pr
Iyy
r=Mz+ (Ixx Iyy)pq
Izz
q p r
=
0 0 0 0 0 0 0
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X =
q p r
p= r = 0
q= n
= = = 0
X
X=AX
A
A=
0 1 0 0 0 03n2 IzzIxx
Iyy0 0 0 0 0
0 0 0 1 n 0
0 0 3n2 IyyIzzIxx
0 0 n IzzIyyIxx
0 0 n 0 0 10 0 0 n IxxIyy
Izz0 0
p= r = 0
q= n
= = = 0
q
p
r
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det(A I) = 0
k1 k3
k1=Iyy Izz
Ixx
k3 =Iyy Ixx
Izz
k1 k3
(3(k+ 3 k1)n2
+ (k1k3 1)2
)(4k1k3n4
+ (1 +k1(3 +k3))n2
2
+4
) = 0
k1 k3
k1k3 > 0
1 + 3k1+k1k3>0
(1 + 3k1+k1k3)2 16k1k3>0
k3 k1
k1k3
>0
k1 k3
k1 k3
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n
D(s) =ansn +an1s
n1 + +a1s+a0
n + 1
bi ci
bi=an1an2i anan2i1
an1
ci=b1an2i1 an1bi+1
b1
an an1
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a4a21+ a
23a0
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ax 2 ax 3
i
1ud
1.5ud
75%
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y
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I
I=
I11 I12 I13I21 I22 I23I31 I32 I33
Iij
Iij =
(r2ij xixj)dV
ij
ij =
1,
i= j,
0, i =j.
I
det(I In) = 0
In n
i i = 1 2 3
(I11 i) I12 I13I21 (I22 i) I23I31 I32 (I33 i)
ai1ai2ai3
=0
00
a2i1+a2i2+a
2i3 = 1
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X=f(X, U)
X= [x u z w y v]T
U = [axayaz]
T
X
f
f
x= u+nz
u= ax+n2x+nz
3x
y=v
v= ay 3
y
z=w nx
w = az+n2z nx
3z
A=
fxx
e
fxv
e
fvx
e
fvv
e
B =
fxax
e
fxaz
e
fv
axe
fv
aze
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A
X= [0
0 0 0 ]T
A=
0 1 n 0 0 0n2 0 0 n 0 0n 0 0 1 0 0
0 n 2n2 0 0 00 0 0 0 0 10 0 0 0 n2 0
y
v
x
u
z
w
A
=
0 1n2 0
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A
=
0 1 n 0
n2 0 0 nn 0 0 1
0 n 2n2 0
det(A
I) = 0
det(A
I) = 0
2 +n2 = 0 = = ni
2(n2 +2) = 0 = = ni
= 0
n = 0
u
u= 1.05
x
u
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u
u
z
u
w
u
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y
u
v u
u
v
x
u
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u
u
z
u
w
u
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y
u
v
u
v
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http://mmae.iit.edu/~mpeet/class_frame.htmhttp://www.freemars.org/jeff/speed/http://www.ehartwell.com/afj/LVLH_(Local_Vertical/Local_Horizontal)http://www.ehartwell.com/afj/LVLH_(Local_Vertical/Local_Horizontal)http://hubblesite.org/the_telescope/nuts_.and._bolts/spacecraft_systems/pointing/graphics/point_ctrl_systm_lg.jpghttp://hubblesite.org/the_telescope/nuts_.and._bolts/spacecraft_systems/pointing/graphics/point_ctrl_systm_lg.jpghttp://hubblesite.org/the_telescope/nuts_.and._bolts/spacecraft_systems/pointing/graphics/point_ctrl_systm_lg.jpghttp://cdn.spacetelescope.org/archives/images/wallpaper5/hubble_in_orbit1.jpghttp://cdn.spacetelescope.org/archives/images/wallpaper5/hubble_in_orbit1.jpghttp://www.computerweekly.com/feature/Apollo-11-The-computers-that-put-man-on-the-moonhttp://www.computerweekly.com/feature/Apollo-11-The-computers-that-put-man-on-the-moon