Dépôt Institutionnel de l’Université libre de Bruxelles / Université libre de Bruxelles Institutional Repository

- - -

- - -

Dépôt Institutionnel de l’Université libre de Bruxelles / Université libre de Bruxelles Institutional Repository

Thèse de doctorat/ PhD Thesis Citation APA:

Renard, M. (1965). Les perturbations d'attitude et les lois de contrôle magnétique d'un satellite terrestre stabilisé par rotation (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.

Disponible à / Available at permalink : https://dipot.ulb.ac.be/dspace/bitstream/2013/215349/5/e96b4a20-6589-4dfa-ba54-b35c1b0ab7b5.txt

(English version below)

Cette thèse de doctorat a été numérisée par l’Université libre de Bruxelles. L’auteur qui s’opposerait à sa mise en ligne dans DI-fusion est invité à prendre contact avec l’Université (di-fusion@ulb.ac.be).

Dans le cas où une version électronique native de la thèse existe, l’Université ne peut garantir que la présente version numérisée soit identique à la version électronique native, ni qu’elle soit la version officielle définitive de la thèse.

DI-fusion, le Dépôt Institutionnel de l’Université libre de Bruxelles, recueille la production scientifique de l’Université, mise à disposition en libre accès autant que possible. Les œuvres accessibles dans DI-fusion sont protégées par la législation belge relative aux droits d'auteur et aux droits voisins. Toute personne peut, sans avoir à demander l’autorisation de l’auteur ou de l’ayant-droit, à des fins d’usage privé ou à des fins d’illustration de l’enseignement ou de recherche scientifique, dans la mesure justifiée par le but non lucratif poursuivi, lire, télécharger ou reproduire sur papier ou sur tout autre support, les articles ou des fragments d’autres œuvres, disponibles dans DI-fusion, pour autant que :

Le nom des auteurs, le titre et la référence bibliographique complète soient cités;

L’identifiant unique attribué aux métadonnées dans DI-fusion (permalink) soit indiqué;

Le contenu ne soit pas modifié.

L’œuvre ne peut être stockée dans une autre base de données dans le but d’y donner accès ; l’identifiant unique (permalink) indiqué ci-dessus doit toujours être utilisé pour donner accès à l’œuvre. Toute autre utilisation non mentionnée ci-dessus nécessite l’autorisation de l’auteur de l’œuvre ou de l’ayant droit.

--- English Version ---

This Ph.D. thesis has been digitized by Université libre de Bruxelles. The author who would disagree on its online availability in DI-fusion is invited to contact the University (di-fusion@ulb.ac.be).

If a native electronic version of the thesis exists, the University can guarantee neither that the present digitized version is identical to the native electronic version, nor that it is the definitive official version of the thesis.

DI-fusion is the Institutional Repository of Université libre de Bruxelles; it collects the research output of the University, available on open access as much as possible. The works included in DI-fusion are protected by the Belgian legislation relating to authors’ rights and neighbouring rights.

Any user may, without prior permission from the authors or copyright owners, for private usage or for educational or scientific research purposes, to the extent justified by the non-profit activity, read, download or reproduce on paper or on any other media, the articles or fragments of other works, available in DI-fusion, provided:

The authors, title and full bibliographic details are credited in any copy;

The unique identifier (permalink) for the original metadata page in DI-fusion is indicated;

The content is not changed in any way.

It is not permitted to store the work in another database in order to provide access to it; the unique identifier (permalink) indicated above must always be used to provide access to the work. Any other use not mentioned above requires the authors’ or copyright owners’ permission.

LES PERTURBATIONS D

ATTITUDE

BT LES LOIS DE CONTROLE MAGNETISUE D'UN SATELLITE TERRESTRE STABILISE PAR ROTATION

F i g u r e s

/'

Marc L. RENARD

- ^M

2oc.

E'.QUATO>=I

/ / /

i.q~!

o·

v/

C::....··

~'

S:l,G.2-1 t;:QUAT<DQIAL(oc) AND ORBITAL ~o1

Ch:OC~NTQIC 5YSl~M5

VliCTO'R

PE:i::tPENOICULAR TO ECLE:P"TIC PJ..A NE )

•

/

l=''G.2l.2 ,, EQUATOQIAL («) AND ECLIPT1!C {&)

G~OCENT~JC 5Y~T!;:MS

5PIN

A>< ^I fl

/ / /

/

/

I= LG.2'.3 ·

OQl.t:NTATION' OF THE: SPIN A:X15

IN OQSITAL SY5l'EM

SPIN A)(IS

I

I I I I I I

I

I

Soc I I

- '°'

/

l=lG2.4

OQl~NTATION OF'" Tl-IE: 5Plt'f AXl·S

IN l;:QUA1'0~1AL SYS'TEM

~AIELLITE' IN.JIOCTION POINT (PERIC.i;ic:)

---

:!!>EN5E 01'" ~E~1=:11;;:!)~10N OF NOOE~

..

JNJli.CTION

Io<:

/

1. \.•'

.l •·· - :.: .... !r I;

.)

'l r.:

'I· ' )' ' ~ .• : •.. ~ ... ~ t ••

i :

_•• '

. ·.- l

~ I '

'· '.

·'! _'!

·1

l " .. + I' I.

j '

. . ,

...

. ..

.

'• 'l

.. \:·I

.1: .. ·-,

. ..-.:

I .. .. ·t ... ""' ...

.

- T.

Is·

. •nj

'.·

L .

.

,

...

_

r : : :

- -

.._ __ f:.:

-:·-

j

l

1 '

- ·l

"1 j

,·

.•· .. J.-·

.

I ; .

~ ...

.

. ~- ,_

. o~ ~~ ~ 9o: :· .. ^1~0'" }d1-~0: ^{.icj~ -: ~~~~; .:} :~o ^{>' ;:~01 '~oo ·}

-·- .•. - . . _J; .. --;Jt1oc;;~---- ... -;...··- -

-~.~~-:~::-.:~ .. _:_. - - -:~:·_ .: ~-~f~. ', -:-

JN_J~---·~-.:..:~-'-:.;-:_ :;_-~ --:~·L-,-

- .... ~- .·- •. • -·~ - - --! .. __ -e- [" ,

~--~~:_-~v ~--: ·. ·1;_:_>~

-~-;,_ - '\ ,. 'r, "T'.I

... ' •. -1 -:::--;

~330

·;;

F l.G:._ _{. :2··i:n·.} -: ....

- -• ~.C.

. -

~ ...

:-.j t

.

~ ~

,._- • ,,._._,__._;. _.i..,.:. ~- __ :.:.-•..<·-'• __ :~.

#::- ~:v -

.- .. ,1. ; ·:~--. r1

• • <

.~l:.. ;_

.. j

J_: .·' ··;.

_,

•o•.a - •

• ·- - --· - .l

• ·! ·_

~ ... ~ -.+' - ·- .... - .,.

• »,"

-.

""" ^\

\

\

l="·I C. 2-10

501,...AR ANS~(;:

FlG.Q_H

CQNSTAMT SOLAR ~NG~t.

CU~V~fl FQ~ VARIOUS t

A~OUND ·1HE.i IDSRLi POINT

b

c

f.~0° A0':3" 6Ci,i

AIM." ~Ci,0° A0':-1° 4Ci:·2.

~Ga-'3°

'i Q.

.. ^~

\..I'

1 ^2. 3 "1

"= ^1.ts•

(£:225•)

1.go• ·

AG::'!

AC:.'2.

Ati:t•

AC':0°

(~: 270°)

(A.i.: -!' )

(~CS:.-2•)

. t.c: ::-1·)

t.J-t= o• ) ·

A.ti :-1° 11 3 '1 5' ~~·.a1•)

(At; :s 2

FlG. 2-12.

cusvcs I~ cl <CDNoiANT

VAL. ID F'OR l=IL.L. ~

SPIN~XIS

I

I

/

E..

\C.E.il'fTt,R Of C.~~n.i\

~L~ ME.JNl~~y G~AUIT.Y GR~Dl~NI ID~QUEi.

~I G. "3 __ 1

SPIN ~X\5

-- ^!

iOTAl. E.CDY· CUQ~EiNT TO~QIJL

LOCAL lt'lOUCilON

--- -- ^T

=fj_

P~E.CE.SS\DN --- ·--- -~--- --

)

-

F 1 G.3_2 ~DDY· C Ll~~E.NT ro·~ou~

-- ^{(1A B') /\B}

iOi~I.. _OE.S?IM -- i. _js - - -kW _- - ^kw' _s

_s B_L -- Is

P f·U'.:Cl::S~lDN -- T.L - - ^{kW s,}

^{B 11 BJ.}

I

SPJ/"I fiXIS.

I I

I

/

- - _T=cAlJ

/

F16.'3_3

flERODYtffl/1/C TORGUE EOR

.. C:.YLl/'IDRIC.Rl.. S/1TELL 1rE .

v

SPIN RXIS

-

-: -:

G

v

/

Fie,. 3_4

CoNSTArtT c ^FOR

- SPHERICAL .. S~TELLITE .·

•

•••

/ /

.. / /

/

I ..

f16. :L5

0RBITflL llXIS SYSTE11fP}

z

·;::::

u :::>

0

~ u

I-

w z

l!)

<(

::E:

0

w t::!

4

_,

<(

::E:

a::

0

:z:

1.0,---r---,---r---,---.

.8

I ^. ., ·' ^.,

ID '- ID

-.4

-.6

-.8

-1.0

ONE ORBIT

e·

20

40 60 80

35° INCLINATION

~ FIG.4-1 COMPONENT ALONG TRACKING LINE_, Bx .. AND ALONS TWO AXES PERPENDICULAR _!.0 IT .. By AND B .. AND MAGNITUDE

IBI OF INDCJCTION VECTOR B . z .

(From ref· 14)

LAWS OF CONTROL

m

RESIDUAL GENERAL

/:;. m

GENERATION BY

f

STEPS OF EQUAL WIDTH

15t. TYPE

x:W+V

ANGLE FROM ASCENDING NODE

0

-km

l;;.m

2nd

ANGLE FROM ASCENDING NO!)E

x:W+~

0

l;;.m

3rd TYPE

_~o •

ANGLE FROM ASCENDING NOl},E

/

, x: w+v

x +rr

0

2

ASCENDING N'ODE'

0

6. m

4th

6.

0

"

FIG. t.-2 VARIGlU5 LAWS OF MAGNETIC CONTROL

ANGLE FROM ASCENDING NODE

°"i;

-r:;

--

ALONG '(., 2 c(

~

FIG. 4-3 AVERAGE INDUCTION UNIT VECTOR 19

...

--- x•

, ALONG~

__...

FIG. 4-4 AVERAGE

PHASE." UN IT VECTOR x

v* _... ⁼ v: _...

X = X

(Am)= Am•

v•

" .\ *

V =

T

* ' *

X : X

(Am)=-Am•

v•

•

... 1

*

~ : Vo+ 1T

• •

X = X

+

(A~= Am*

' y *

.\• ·.I•

y : Vo

+ 2

X• = x•

.

(Am)=-Am*

" .

Am

Am

Am

~+71' l"C

.1I. 2 2

'JI'

T

ASCENDING N09E

· X=

w+~

+'JI' 1T

0

2

/

'JI' ₀

+

2 ANGLE FROM ASCENDING ·NOD.E 1T

T

Jto+ ₂

ANGLE FROM ASCENDING NO.@E'

FIG.L.-5 EQUIVALENT SECOND-TYPE SIGNALS FOR SMALL ...

e

AND AVERAGE-OVER-ONE DAY M

/.

--

^{... I}

---

ALONG~

__.

FIG. 4-6 AVERAGE

HALF_ PE~IOD PULSE

UNII VECTOR I h

21 DEC.

FIG. t.-7 CONTROL IN A PLANE

...

To

FIG.L.-8

o in plane of m

B.L s

E-S

II . 11

FIRST METHOD OF IN PLANE CONTROL

Ea 2 CT

IDEAL PLANE

+ a

ALLOWABLE REGION FOR

~ 1

3 tr SUN

FIG. 4-9 SOLAR ANGLE GEOCENTRIC SYSTEM (CT)

2

a;;

SUN

2~ .

--- 10-

1"

EQUATOR

Fl G. 4- 10 · TRANSFORM·ATION OF COORDINATES (.oc, er)

L--~-=-~~~--1~~~~_...,lCT

~ = o'

21 JUNE

~ =9.00

EARTH'S AXIS

21 SEPT.

~ = ^180°

30'"

3a-

SUN

~

FIG.L.-1.1 ·coMPONENT I ·. AND VALUES OF~

her, Zcr)

120-

21.0° 270° JQQO

1.0

0.9

1ao

I=0°

~ ^0.9

0.7

120° 90°

0.6 0.5 0.1.

...

b. POLAR DIAGRAM OF I

0.2

., -

0.1

- 0.5 -0.1. -03 -0.2 -0.1 0 0.1 0,.2 03

0.5 I

__...

OF (3·~(~) AND

r(1,cr,2a)

NUME.RICAL EXAMPLE POLAR DIAGRAM OF

(b (or ~ + 1ao

30°

E.

20°

100 0

<W ^-10°

-20°

-JQO

~ = ^.,!!_

2

a. REFERENCE ANGLE (?> OF

"SOLAR ANGLE MAGNETIC IDEAL"

... ORIENTATION

I '

FIG.4-13. CHARACTERISTIC TIMES tE AND f2E

o a

~>0 tEo

150 75

'100 50

10°

_.

a. Angle fJ between· I and ideal plane

{Ed /2 (DAYS) and tEo (DAYS) •

(LIMIT VALUE" t t ^{tE = for a 277}

= ^{DAYS 237}

and l: :303°

IF tfa/2.AND 'r • ARE COMPARED:

-. 0 -..

1) 1

ALONG 1( 1

2 ) IN IDEAL

PLANE. ~ ~

2) R.h. SCALE IS USED

b.

CHARACTERISTIC ·TIMES tEo AND t~

so

15

FIG. 4-14.

NO SOLUTION

FOR tea

INSIDE THE STRI

- -

9 180°· 270° 3 0°' ~

• le)

6, tEo -~ND tEa AS FUNCTIONS OF ~ (Numerical exernp-

••

"

\

FIG. 4-15

---.... __.,

PRECESSION OF 1 5 AROUND 1 18.

"INERTIAL"

·-

_DRIFT(d1s)in,-8 or

(d

a-)

,5'

t+di

a.

INERTIAL DRIFT FOR ... 1

^ALONG f>

MAGNETIC

INERTIAL DRIFT

--

(dlslin

.

!'

t

d t

- ^Is

_-- ^lii

--

_magn,,

- (dis )in

, 8'

Fl G. 4-16 INERTIAL AND MAGNETIC DRIFTS IN "'UJ

-..:...-- ^-·

__ -- ^~

~opt (deg)

- . -·1.

1.0

l:

(deg)

0.5

1.0

OPTlt-lAL SOLUTION: GIVES ZERO SOLAR ANGLE VARIATION MAGNETIC TORQUES ARE CONSIDERED TO BE ACTING ALONE- 0.5

.. ~ ..

F·1g 4-17 NUMERICAL·· EXAMPLE FOR ·tt opt

•

,

!

z

SPIN AXIS

COIL)

x

ct

(TORQUING

COIL)

•

FIG. 4-18 GRASSHOFF '5 METHOD FOR MAGNETIC RESPINN~NG

•

..

z

...

Z11

( RESPINNIN G TORQUE)

(INDUCED PRECESSION TOROU E) MAGNETOMETER rn

0

----v+---~IN VERSION

D.C

CURRE'~T m ^rototes

• lORQ_UING COIL

x

. FIG. 4-19 ALlC:RNATE RESPINNING METHOD

.,

•

~9· 5-1

Pf\fYSICAL REPRESENTATION OP\ SPIN AXIS. DRIFT UNDER

R~IDUAL MAGNETIC MOMENr 0 CONTROL OF FIRST TYPE

1 b '

- ⁽⁸

a. PRECESSION OF SPIN

-

UN IT VECTOR Is y

b. SYSTEM "b"

r

lot

- ^Is. Precesses around 118 at ^- rate w~ =-mo 18

Is Ws

--- ^118. Precesses around 12 --

ot

rate o: ⁼ d .Cle(

cc ar-

2b

•

a. PRECESSION OF SPIN

UNIT V~CTOR I;

b. SYSTEM .. x* ..

Fig.5-2

PHYSICAL REPRESENTATION O~

SPIN AXIS DRIFT UNDER CQ\JTROL OF SECOND TYPE.

-. ⁽⁸

- 1 5 Precesses about X

^~ at

rate c.J x* =-6m18*

. ls Ws

-: X Precesses about 2 « at ra~e .n~ ··

3°'

•

~ · Precesses about -i;« ^{at rate .n'o(,} = ~ f ^«

I; Precesses about~ at rate wh = kmo IBh

Is ^tu s 2

. 2o

Ascending node

3oe

Fig. 5~3 a

PRECESSION OF SPIN UNIT VECTOR 1 ^---+ 5

'I

I

•

•

(

.

3o (.IN ORBITAL PLANE)

3

' I

b - SYSTEM h

FIG: 5. 3 b PHYSl~AL REPRESENTATION OF SPIN AXIS

DRIFT UNDER CONTROL OF THIRD TYPE

•

•

---

\ pr e ce sses about 1 IK at r o t e

[

2 2 2 2 2 ~~

cos ~ (C t9A )sin 1o:+E cos 1~i Is W s

--

W !K =-M

- ^{1 lK precesses} -

n.' = d n. ex

ct d +

~ Pracassion of spin unit

vector\

about _{1 2} at rota

C1.

,,

3k in orbital

plcne ~ Systam k

Fig. 5-4 PHYSICAL REPRESENTATION

OF SPIN AXIS DRIFT UNDER A

GENERAL CONTROL TORQUE.

•

••

~---1.

Y. _{i = 180} I _.

j 6 '31 = 22,5 °/orbit

I~ SI= ^{7°/ orbit ·}

-- /I

6Mt.a::_

~Mt -+t"

.a.n "A1

~ql'J Ol'Jct ,.,, :::l:f s : ~

t,Qn 1-.J:.

v r

<

- ^.

Error on· BM · } 3,5 ° in direction t,a,n

A pproxiated by Er M ^{6 °lo} in magnitude (rvtg3~)

-- ^9::; _M -- ^B-- _M

t.cn ---- ---

3,5° ' --

View in orbital plane contclnlnq Mt-an

'

·-'

--- ^~~

Mt.a]l· M =Mt .on + J:.. 2

N.B. Some numerial figures are given in the case of ESROir nominal orbit.

Fig.6-1

PHYSICAL MEANING OF AVERAGE OVER ONE ORBIT

EARTH'S DIF()LE M

•

•

Fig.6_2

GENERALIZED ·MODEL RESIDUAL MAGNETIC MOMENT

DRIFT OR CONTROL OF FIRST TYPE.

- ls precesses about IM° at rate w,= ^{-m 0 18-r}

Is <.Js ( _M cos ~ sin ioc , 2 M cos ~· cos L« - ^, _{0 )} ... ·

(.... having directron of 118)

( ~ ) locus of iM"

y

Cone described

--

(M describes (C) when

=- M rotates at diurnal

rate about 2G(

•

••

- ^{1 5} PRECESSES ABOUT

-- 1M*OF ORBITAL PLANE AT RATE

* ... *

Wi;= - 6m !BC Is Ws

- ^M _3o,1o

VIEW IN ORBITAL PLANE OF VECTOR.S M ^AND TlM

FIG. 6-3

GENERALIZED MODEL: CONTROL OF

SECOND TYPE.

2ct.

M20 ALWAYS /o IF ict. < ~ - ~

M 20· 1 TIMES ZERO IF td. = ~ - ~ M 20 2 TIMES ZERO IF < ^ict < ~ ^{+ ~}

M 20 1 TIMES ZERO IF lex = ~ - ~ M 2 0 AL WA y s I ^{0 IF ict} > ~ ^{+ ~}

FOR. GIVEN lct I ^M2 I ^{MAX AT p OR/}

AND p' o

' . --

---coNE p DESCRIBED BY M

FIG. 6. 4

OPTIMAL USE OF CONTROL OF FIRST (THIRD) TYPE

FOR DEGENERATING CASE.

•

••

G)'

_0

M = I ^M I ^cos (TI ^{+ ~ - icx.)}

2o

= M cos ( ~ - ia. )

M ₂ ⁼ I MI ^cos (TI - ~ - icx)

0

= . M. cos ( ~ + id )

FIG. 6.5 OPTIMAL VALUE OF IM

20 I

2

20 la = ^{98, 35 dag.}

(ESRO II)

' '

Cone f..l _ de s cr lb ed by-M

eo

60

40

0 30 60 90 120 150 180 210 240 270 300 330 360

Ba_- ^{.nd (dag.)}

or t irne in the day

N.8. e

Angla Sis axaggaratad

Fig. 6-7 EFFICIENCY FACTOR OF CONTROL OF SECOND TYPE IN COURSE

OF·THE DAY FOR THE ORBIT OF ESRO II

180 i/

. ~- .,.;,,,::,j~J§ ,£-:.3

~~i. .

·F,fug·si ID~~l···

MAGNETIC MOMENT DRl·FT OVER 400

mo=+ 1,000 dyne

mo= - 1,0 0 0 dyne

270 DAY~

crnjqouss cm/gauss

•

.·

\

180 _I'

0

'360

.e

=12

180

0 360

ks=

....

270

. I

, .

UNDER

-e

•

UND~R

TORQUE ONLY

270

'

.

10

e· _'

350

@[SPIN

~s = {jso e--\:- ^{(,)so::: 40 r: pm}

m; = 1000 dyne cm/g ous S

\ = 100 days

'

. i:

r

.1.\

1i

..

.1 .. • ~ • !

....

,,

I

0

~: ³⁶⁰

r ii··

t'·

·· // ..

.... ii··

' '

IN DAYS

r ^ALL

100 DAYS m

'r

/

•

f c

.Q 4rf

+-'

0

• ^{u 'O 20} c ^OJ

^•

·o

~ •

> ^D

(/)

·~

c -20

(/)

a.

' 0

- D 500

- - - Experimental

--- NASACmo= -896; M = 6.77x10 25 (polar)) -·-·-Present t.heory

(m~ =- 78B, M:: 8,1 x

'K) 5, inclined a~ 1S

on polar axis.)

DAYS AFTER . ' LAUNCH

D --+---!-

---!---~

goo 130° 150°

Spin axis vector right ascension •

/

Fig. 7 _12

TIROS I SPIN AXIS ATTITUDE EXPLAINED BY MAGNETIC

MOMENT, GRAVITY GRADIENT, AND DESPIN TORQUES

· +i ₄ : ^)c _.. ~1L. ^l '>j

^.r.:

^':}-

^--

-+---~---L~ .. i::., ... > =:· :. , q---+-~...._.._.. __ _..._,. __ __.

... r: . ·- . - ^{--r -· - ·-}

l '· _: ~:i~; :. ::·:.. . :~j.t-:·

I· _~

• r

• •

•

. I4

A.(100)

/

(7.()) -

. E3

(78) :"'. 2

. (5.0)

/;

. E2 t,

E1 JI 1 (2,4) /

// - Parameter: time rn days

6

4

3

1 .2 3 4 5

D.

v-

Error on solar angle

- CONTROL PHASE - - - - FR E E DR I FT

!: INITIATION OF CON.TRQ:L ' E: END OF CONTROL

RA0<. 'de

_ ~ pe! threshold

/ /

Lower threshold

. T 1

-3 - - - -

/

I

I

I /

/ ^/

---+-"-- --

2

0 0 0

INITIAL CONDIT.IONS :~=0. ~oc..=0. RA.cx_=O · at t =O RESIDUAL MOMENT 1000 dyne cm/gauss

CORRECTING MOMENT; 7000 dyne cm/gauss

Fig. 7-30 CONTROL OF FIRST TYPE ON THE SOLAR ANGLE

/ I

+

3

/

I

/ _I

/

/

I

.

b «. ( deq)

50

--- - ---

f .

/

./I~

(33.3)... 1

(33.1)

• ../ f,.7( 1 7)

(31.9)~3· .,,,.

./ I16.(30.2) ( 3 0 4 ).::::::...--

/

./ I~ (2 B.7) (28.Q)..L ./

/,

./ I1}

(27.3)...,::::: (27.1)

/'

30

20

/' !13(

(25.7).L' 7 2 5.5)

,,..

E-~(23.9) (24.1)

E 11 " ,, I 1 1 (

22 3) (22_5)-"'-

/

Eio.,... l:1oc20.s>

(20.8)~

/

E9 _.,.,. ,,..Ig 68) (19.0)-'- ,,--< ^1.

/

· Ea ,., ... Is ·

(172)..G'.- 7(17.0)

. ....

/'.'.

E7 ...- I7 (15.4)..C 7(15.2)

....

10

/

EG _.,I

( 13.4

fl.(13.2) ....

E5 .... ,.I5 (114)~(11.2) . ,,..

/

E~(91)·

(9.3)

E3 -: .... 13( 69) ( 7.1 ,...,__ . ^, 7 '.

...

E 1 ,,. .... I 1 ( 2.J) (2.5)~

CONTROL PHASE T INITIAr''10N OF CONTROL

--- FREE DRIFT E= END OF CONTROL

INITIAL CONDITIONS: J\.Oi..=0° S e11.=d' R.A.cx.=0° at t.=0° Xt.= 270°

RESIDUAL MAGNETIC MOMENT: 1000 dyne cm/gauss CORRECTING_ MOMENT: 6 m : 7000 dyne cm/gauss

·Fig:7-31 CONTROL OF SECOND TYP~ ON THE SOLAFR ANGLE

.. ,

I

I

I

/

r: - I

0-+-~,'-'---=2..__+-7<'3_1~4..._--"5~~6~~~~~~~~~-

·0.5 _ _ _ __ _ _ · __

TJ me (do ys)

E1 Av deg

-3

.: '-0.

5

b<>-deg

. I2

~(5.1)

/

CONTROL PHASE -- -· FREE ORI FT

I= INITIATION O.F CONTROL E·. f:: ND OF CONTROL

4

/ /

3

/

..

. ,,. I1

·~/ ,,.(2.3)

/ /

E1 ,,, ,,, . (2.6) / /

.

/ /

,.,·

^.

RA

deg

2 3

5

E r r o r . on so I a r a n q I e·

I1. 1:2 .

- - - - /

Upper threshold

I / I

I

I

Lower t hr-ash old

+3 - - - ·- - - -

INITIAL CONDITION r,0<...=0°. boA..=0°: R.A.=0° at t.:O RES I DUA L MOM EN T: 1000 d y n e cm gauss

CORRECTING' MOMENT: 7.000 dyne cmgaus.s

Fig.7...:32 CONTROL. OF T.H I RD TY PE ON THE SO.LAR ANGLE