MVO 11 - Relatorio_Rapha

7/21/2019 MVO 11 - Relatorio_Rapha

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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


5/41

m2 m1

r+r

r3 = 0

r = d2r/dt2

m2 m1 r = |r|

= G(m1+m2)

m2 m1


6/41

= 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


7/41

=T.U.= 377625

42164 km

Rgeoestacionario = 0.109687 D.U.

Vgeoestacionario =

Rgeoestacionarioa= 3.01939

D.U.

T.U.

Tgeoestacionario = 0.2282 T.U. 1


8/41

RLua= 1 D.U.

VLua= 1D.U.

T.U.

TLua= 1 T.U.


9/41

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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11/41

i ++ 2

2


12/41

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


13/41

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


14/41

r1

r2

r1

r2

r1

vc1=

/r1

r2

v1 =

(2/r1) (/a)

a=1

2(r1+r2)


15/41

e= (r2 r1)/(r2+r1)

v1=v1 vc1 =

(2/r1) (/a)

/r1

v2=v2 vc2 =

/r2

(2/r2) (/a)

v= v2+ v1


16/41

ax 2 ax 3

i

1ud

1.5ud

80%


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18/41

,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


19/41

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


20/41

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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22/41

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


23/41

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


24/41

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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26/41

a4a21+ a

23a0


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ax 2 ax 3

i

1ud

1.5ud

75%


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32/41

y


33/41

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


34/41

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


35/41

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


36/41

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


37/41

u

u

z

u

w

u


38/41

y

u

v u

u

v

x

u


39/41

u

u

z

u

w

u


40/41

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

Documents

MVO 11 - Relatorio_Rapha