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ANALYSES RELATED TO THE HUGHES GYROSTAT SYSTEM 

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Approved for Release: 2019/01/11 C05105855 

• 

ANALYSES RELATED TO THE HUGHES GYROSTAT SYSTEM 

A. J. IORlllG 

Assistant Manager 

Advanced Design 

Satellite Systems Laboratories 

• 

F----------------, I I 

iHUGHESi L ________________ ~ 

HUGHES AIRCRAFT COMPANY 

SPACE SYSTEMS DIVISION 

DECEMBER 1967 

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, 
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• PREFACE 

This document is a compilation of four papers written 

during the course of Gyrostat development. The first 

two comprise analyses which led to formulation of the 

general nutational stability criterion for dual- spin 

satellite s. The third paper summarize s the subsequent practical application of the theoretical results. 

The last paper discusses operational and performance 

aspects of Gyrostat systems. 

ii 

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r 

tL 

~' - t'" 

-/ 

:'-

;. I /. 
• 

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CONTENTS 

lINutation Damping" 

Hughes Aircraft Company IDC' 2230. 14/69 

October 1964 

"Nutation Damping Dynamics of Rotor Stabilized Satellites" 

Presented at ASME Annual Winter Meeting 

Chicago, Illinois 

November 1965 

"Development of Hughes Gyrostat System" 

Hughes Aircraft Company SSD 700 12R 

January 1967 

IIPr ecision A spects of Hughes Gyrostat System" 

Presented at Dual-Spin Satellite Symposium 

Aerospace Corporation, Los Angeles, California 

August 1967 

iii 

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. Page 

1-1 

2-1 

3-1 

4-1 
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NUT A TION DAMPING 

ABSTRACT 

A nutational stability criterion is derived for dual-body satellites, 

such as OSO. The derivation comprises Routh-Hurwitz analysis of 

iinearized system equations and subsequent physical interpretation of 

the result. 

1. INTRODUCTION 

The object of the following analysis is a 

stability criterion which ensures that autations 

experienced by a dual-body satellite, such as 

OSO, 'will decay when damping is introduced. The 

criterion sought is analogous to that for a simple 

spinning body. like Syncom. which states that the 

body must be spun about its axis of maximum 

inertia. 

The approach taken is somewhat different 

from that used to establish the single - body criterion. For the single body, kinetic energy considerations' in conjunction with momentum 

conservation, serve to establish the criterion. 

Since dual-body satellite momentum and kinetic 

energy are defined by three quantities (vehicle 

rate, wheel rate, and nutation angle), the two 

equations do not suffice to solve for the nutation 

angle change unless assu~ptions ara made regarding the wheel and vehicle rates. Certainly, sensible assumptions can be made and the criterion 

may be derived using momentum and energy con-

. siderations. However, as in the single -body 

case, no insight into the mechanics of nutation 

damping is derivable from an energy dissipation 

analysis. Thus, the approach taken here is 

mechanistic. That is, the equations of motion 

for a dual-body system with a damper are written. 

Then small oscillations about a steady spin condition are assumed, resulting in a linearized 

dynamical system. This linear system is examined to determine the stability conditions. 

As a result of this approach, a physical 

description is derived of the reaction torque on 

the vehicle due to damper action causing nutation 

damping. The concept of a "roving" dynamic 

unbalance which causes a resonant damping torque 

is presented. 

The damper considered in the analysis is 

the mechanical analog of the Syncom mercury-ina-curved -tube damper at small nutation angles. . . 

II. DISCUSSION 

Dual-Body Vehicle 

The dual-body configuration considered is 

shown in Figure 1. Both the wheel and the main 

satellite are bodies of revolution. The wheel 

spin axis is coincident with the satellite spin axis. 

The wheel spin inertia is Iw , the satellite spin 

inertia is C, and the combined vehicle transverse 

inertia is A. In an equilibrium steady spin, the 

vehicle angular momentum is 

J-J 

"z • SATELLITE RATE 

Q • WHEEL RATE WHEEL 

MAIN SATELLITE 

Figur e 1. Dual-Body Vehicle 

ClIJ+I \l z w 

Nutation Dampe r 

The nutation damper configuration assumed 

is shown in Figure 2. The damper consists of a 

small mass, m, constrained to travel in a tube 

located on the vehicle x axis. The displacement 

of the mass is along the body z axis and is denoted 

by z. The mass is coupled with the body through 

a spring and linear damper with constants k and 

c, respectively. The mass of the vehicle- is M, 

and 

M »>m 

The spacecraft transver se inertia is A when the 

damper is at z = O. 

z 

x~-----+"I---------41~ 

y 

Figure 2. Nutation Damper 

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III. EQUATIONS OF MOTION 

The x, y. 21 system shown in Figure 1 has 

its origin at the system mass center and is fixed 

in the main satellite. The rotation of the x, y. 21 

system is 

1ll==1ll i+1ll j+1ll k x Y 21 

- i. j, k:: unit vectors along xyz 

T.h.e torque -free equations of motion for the vehide-damper system are: 

+ mx 21 III III - 2m xx III o X Y X 

2 . 2 (A+mz)1ll -(C-A-mz)1ll III -lwOIll~=mxoz y... x 21 ~ 

C III :: m x 21 III - m x Z W III + 2 m x 21 Wx + T 21 0 X 0 y.z 0 f 

1w 0 = - T f 

... mz+cz+'kz= mx III -mxlllill o y 0 x Z 

where 

T f = frictional bearing torque between 

whee I and satellite . 

~ «< 1 

In a steady spin condition, 

1ll::1ll =21=0 X Y 

CW +1 0=0 21 w 

(1 ) 

Now consider a very slight deviation from the 

steady spin condition, a small nutation angle. 

Then quantities Wx, illy. and z and their rates of 

change are accordingly very small. 

Neglecting products of small quantities, the 

torque-free equations of motion given above 

become: 

A ,j, + (C-A) III III + I Ow :: mx 21 III X zy w y 0 21 

A W - (C -A) W W I 0 W :: mx 21 + mx w

2 . z y zx w X 0 0 Z 

1-2 

r n:: - T w f 

(2) 

Equation 2 describes the system motion for small 

wobbles. Now assume that the friction torque, 

Tf, is small such that the change in vehicle and 

wheel rates are very small during the wo bble 

period. This is a sensible assumption since the 

wheel used should be essentially frictionless. 

Then. 

A w +! (C -A) W + r 0 1 w = 0 x Z w! y 

A w I (C -A) w + I 0 I w == mx . z + mx w 2 . x Y .21 W) X 0 0 21 

z+..!:...z+~z=x til -x w w m m oy oz x 

Defining 

A :: _( C_-_A_l _w..,:z,--+_I....;w.:..-O_ 

A 

j3 ::: ..£. 

m 

WI :: ~ :: damper natural frequency 

Then, 

III + AW :: 0 X Y 

til _ AW ::: (mxo)z + (mxo) 

y x A . A 

•• r.t' 2 . z+l-'z+w 1 z=x III -x W ,w '0 y 0 Z x 

W 2 Z 

z 

(3) 

(4) 

where the quantity A is the system nutation frequency. It is noted that the relations in Equation 

3 are identical to those describing a single spinning body characterized by a nutation frequency A. 

The presence of a wheel merely changes the 

nutation frequency. Therefore. what follows is 

valid for the single-body case. 

Equation 3 forms a linear system and may 

be analyzed by standard methods. The system 

characteristic equation is 

A Routh-Hurwitz analysis indicates that stability 

requires 

2 

A. A Illz - Illz 1) + W ~ > 0 mAx,o (\2 2) 

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Z) 

3) 

when 

Z mx 

__ 0 .... 0 

A 

The meaningful condition (3 above) is 

Condition 3 may be rewritten as 

Then the condition is 

By defining the initial spin momentum as a 

positive quantity. the stability condition becomes 

As expected, this condition is the same as the 

result for a single spinning body. Although this 

forIll is Illuch simpler I condition 3 has physical 

significance, as shown later in this paper. 

IV. PHYSICAL INTERPRETATION OF RESULT 

Consider the equation of motion for the 

damper mass: 

(5) 

The transverse rates lIlx and lIIv are forcing 

functions for damper motion. Consider a freely 

nutating body before damping is effective. Then. 

W :: W cos A.. t x 0 

W :: W sin At 

y 0 

Substituting into Equation 5 yields 

·z +·8 z + wZ

l z :: X W (A - w ) co SAt o 0 z 

This is the familiar equation of a damped harmonic oscillator, sinusoidally forced. The fo rced 

response is 

1-3 

The effect of the damper mas s motion on the satellite is given by 

W +AW =0 x y 

The term 

is recognized as a "dynamic unbalance" term. 

The term 

mx o .. -;;:- z 

(6) 

represents the torque due to the reaction force of 

the restraining spring and damper. Substituting 

z(t) into Equation 6 results in 

W +AW = 0 x y 

A t 

(7) 

Equation 7 is seen to be of the form 

W+AW=O 

x y 

W CAW =Aw +Bw 

y x y x 

The term A Wy is a "damping" term. The sign of 

the damping constant A is governed by 

the same criterion obtained earlier. The term 

B LI.Ix represents a torque normal to the rotating 

tran sver se angular ve 10 city vector tending to 

"turn" the vector rather than affecting its magnitude. The se concepts are explained later. 

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Now, to solve Equation 7, it may be rewritten 

as 

W + AW :; 0 x y 

2 mx Lil ->..w = ___ 0 

y x A 

where 

" = 

-1 

tan 

(8) 

SA 

Equation 8 may be solved in quadrature. Letting 

M 

Y 

2 mx o ---w A 0 

. W i 1jr e -1 i)..t ~. -i>..t cos(At-~)=-2-'e + 2 e 

w=w+ W, x Y 

the solution is 

The nutation angle history is given by 

sin At 

(9) 

Equation 9 reveals several interesting results. 

The effect of damper motion at nutation frequency, causing a resonant torque which acts in 

a constant fashion on the initial rate wo' and the 

effect of "tuning" the damper are observable. 

For a tuned damper, 

• = n/2 

The decay term becomes 

. Aw j 

9(t):; CW: f 

Thus. tuning the damper places the damping 

moment along the initial angular velocity vector 

thereby maximizing its effectiveness . 

. .... 1-4 

Using these results, a physical picture of 

the damping process may be constructed. The 

rotation of the angular velocity vector relative to 

the body gives rise to inertial forces driving the 

damper mass up and down. The mass then 

becomes a roving dynamic unbalance with frequency A. However, 'due to damping, S, the 

mass lags the transverse velocity vector. Since 

the reaction moment due to mass motion is along 

an axis normal to the damper plane, the lag 

places a component of the reaction moment along 

the transverse angular velocity. Further, since 

the reaction moment frequency is resonant with 

the transverse rate, the reaction moment acts 

constantly to either increase or decrease the 

angular rate. If the phase lag is 90 degrees. the 

total reaction moment acts along the trarisve r se 

angular velocity. 

From the representation of the damper 

reaction moment as a vector rotating in body 

coordinates, it was seen that the moment is the 

sum of two coun terrotating vector s 

This is the result of having a single damper. If 

there were two dampers spaced 90 degrees 

apart, the reaction moment could be, represented 

by a single vector rotating at nutation frequency 

To fix ideas, consider Figure 3, The'damping 

mass has displaced from its equilibriuITl location 

in its attempt to ,j:et as far from the total angular 

velocity vector w as possible. The reaction 

forces on the body cause the moment &I along 

the y axis. When the vector W rotates through 

180 degrees, the mass tends to move as 

irldicated. 

The re sultant reaction moment now acts 

along the negative y axis. Due to damping, 6, 

the mass motion lags W. For simplicity of 

illustration, consider the two -damper case. 

Here, the moment M can be considered a 

rotating vector. Then the concept of the lag 

can be thought of as shown in Figure 4a. The 

vectors wand :1M rotate at the same frequency, 

allowing the damping component to act continuously along the vector Ill. For the case of 

A < 0, the unstable condition, the same moment 

Iii{ would be located relative to w as shown in 

Figure 4b. Here, the component of M along 

W acts to increase wand thus increases the 

nutation angle. The validity of these repre sentations may be checked by considering the detailed 

motion of the mass and the resultant moment 

for the two cases).. > 0 and A < O. The principal 

difference between the two cases is the rotational 

sense of the transverse angular velocity vector 

relative to the spin sense. The lag. in the stable 

case, tips the moment M away from the vector 

w. For the unstable case, the vector :1M is tipped 

into the vector w. 

Although a specific damper was selected 

for the analysis, the same concepts may be 

extended. The induced relative motion at 

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F2_---+---'-_ 

x 

Figure 3. Damper Mass Dynamics 

DAMPING 

COWl'ONfNT 

\urAnoN SENSE ... >0 

., TRANSVERSE 

X~--------~~~~r----------+ 

MTorAl 

a) Stable Case 

• 

Figure 4. 

nutation frequency, the resultant roving dynamic 

unbalance, the lag caused by damping, and the 

relative orientation of the moment and the transverse angular velocity vector may be extended 

to the quasi -rigid body where the body itself 

experiences a cyclic distortion of its inertial 

symmetry giving rise to dynamic unbalance. 

Further detailed study of the mass motion 

unveils the second-order reaction torque acting 

along the spin axis. This torque causes a change 

in spin rate required to conserve momentum. 

This reaction torque is due to a coriolis reaction 

between the mass and the body. The direction of 

this torque is also dependent on the nutation 

sense. 

.. 

DE-DAMPING 

COMPONENT 

NUTATION SENSE. A> 0 

\ X .-----------~~E_--------

;;;; TRANSVERSE 

b) Unstable Case 

Lag Concept 

V. CONCLUDING REMARKS 

The dual body (as the single body) must 

satisfy the condition 

relati ve to the body carrying the nutation damper 

to ensure stability. 

Thus, when a despun section is added to 

Syncom. the configuration must be designed 

such that 

.c.. > 1 

A 

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NUTATION DAMPING DYNAMICS OFAXISY MMETRIC 

ROTOR STABILIZED SAd'ELLITES 

ABSTRACT 

The equations of motion of a dual-body configuration with nutation 

dampers in each body are linearized about a.n initial nutation angle. 

The linear equations are then solved, yielding the relation between 

system parameters and nutation angle change. The solutions are 

compared to those obtained by applying energy principles and are 

found to be identical. Further, from the dynamic analys is, insight 

is derived into the operation of pendulous nutation dampers. It is 

shown that nutational stability of dual-spin systems can be achievedfor nearly any system inertial distribution. 

NOMENCLATURE 

C moment of inertia about configuration 

figure axis of body I (with damper 

mass at rest) 

I moment of inertia about configuration 

figure axis of body II (with damper 

mass at rest) 

A :: transverse moment of inertia of entire 

config~ration (with damper mas ses at 

rest) 

~ :: spin rate of body I 

~ spin rate of body I! 

Wo :: initial transverse angular rate of 

entire configuration 

A :: 

o 

~ ::: AO - "'I 

AI! :: AO - ~ 

1'r :: energy dissipation rate in body I 

1'I! :: energy dissipation rate in body I! 

J ::: motor to rque 

Wx :: configuration angular rate about OX 

w ::: configuration angular rate about OY 

y 

w' ::: perturbation angular rate about OX x 

w~ :: perturbation angular rate about OY 

~. mIl :::: damper masses in bodies I and II 

c!' cIT oscillator damping constants 

Itr' 1trr = oscillator spring constants 

<I 

2-1 

2 ~ 2 

WI ::: W m I 0 

~I 2 

2 

~~ w 

0 

wI! = - - mn 2 

Xo ::: distance from OZ of oscillator in 

body I 

h ::: distance from OXY of oscillator in 0 body il 

z(t) ::: displacement of damper mass, m I 

Pit) ::: displacement of damper mass, mIl 

'PI J ~ dt 

'PI! :: J ~ dt 

I. INTRODUCTION 

This paper discusses passive damping of 

the transient motion, nutation, of dual- body 

satellite configurations typified by the 050 I 

satellite which is composed of two bodies free to 

rotate relative to each other. 

Recent works (References 1 and 2) derive 

nutational stability criteria for dual-body configurations by applying energy and momentum 

principles similar to the approach taken by . 

Thomson and Reiter (Reference 3) in deriving the 

criterion for spin-stabilized satellites. However, 

each of these works considers only the special 

case of configurations where one of the bodies is 

rigid. They find that a vehicle stabilized by a 

rigid rotor is essentially free of inertia constraints and that a rigid platform stabilized by a 

nonrigid rotor is subject to the classical inertia 

constraints, i. e .• the rotor spin inertia must be 

larger than vehicle transverse inertias. 

Here, the general case of dual-body vehicles with dissipation in both bodies is considered. 

An energy analysis is performed, and generaL 

criteria are derived. To illustrate the tacit 

asswnptions made in the analysis and to corroborate the results, the equations of motion of a 

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dual-body configuration with energy dissipators 

in each body are solved. The angular velocity 

changes predicted by the two analyses are compared and shown to be identical. The general 

criteria indicate that all dual-body configurations 

can be made stable by adjusting the energy dissipation rates on each body. (The practical implication is that platforms stabilized by nonrigid 

rotors which violate the earlier criterion can be 

made stable simply by plaCing an efficient nutation damper on the platform.) 

U. ENERGY-MOMENTUM 

CONSIDERATIONS 

A dual-body configuration is illustrated in 

Figure L Except for rotation about the axis of 

symmetry, bodies I and U are rigidly joined. For 

convenience, and without loss of generality, W 

and Ao are defined as always positive. Thus the 

nutation angle, a, is understood to be measured 

from the direction of the positive angular 

momentum vector, as shown in Figure 1. Consider the case when the bodies are uncoupled in 

spin and free of exterior torques. The system 

angular momentum, ho' and kinetic energy, T, 

are 

( l) 

(2) 

To investigate the change in angular rates when· 

energy is dissipated in the system, the derivatives of Equations 1 and Z. are combined, resulting in 

where T is the rate at which "work" is done by 

nonconservative forces within the system. In 

this sense, it is the rate at which energy is dissipated. Since it is assumed that both bodies 

contain dissipative mechanisms, the total rate· is 

written as ~e sum of. the dissipation rates in 

each body, TI and Tn. As such, both quantities 

are always negative. 

Since the bodies are assumed uncoupled, it 

is possible to identify the reaction torques acting 

On the bodies tending to chang e the rates: 

C~ 1'1 Tn = ~ , I~=-x;- (4) 

AWw = A (1'1 + o ~ 

Tu) 

AU (5) 

The energy diSSipation implicit in the analySiS is a consequence of the motion of nonrigid' 

elem.ents within the system. It is assumed that 

. "' .. ' ... ~. .' 

2-2 

Figure 1. Dual-Body Config~ration 

the energy and m.om.entumassociated withinternal 

motion. and deviations of systeITl inertias froITl 

steady-state values, are negligible. Since no 

dissipation is allocated to daITlping of transient 

relative ITlotion of internal eleITlents. the analysis 

does not presume to apply to situations wherein 

transients are important. During nutation, sustained relative motion is possible by virtue of 

cyclic body forces acting throughout the bodies. 

The fundamental frequencies of thes e cyclic 

inertial forces are A.1 and A.n. the nutation frequencies with respect to the bodies. Should A.10r 

All be zero, the inertial forces in that body are 

static, and internal motion (thus. energy dissipation) cannot persist in the presence of damping. 

Proceeding with the analysiS, the system is 

stable, W < 0, when 

1 ~ > 0, An < 0 a.nd ,TIl /I. I >1 ~I1 .1: 1 

~ < 0, Au> 0 and I "1: 

~I1 I < I ~I1I I 

As indicated by Equation 4, the secular transverse rate change ITlust be accoITlpanied by 

secular spin rate changes. If the conditions in 

Equation 6 are satisfied, the nutation angle, 

e, win decrease since 

(6) 

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tan e w 

=r-o 

However, as w decreases, the body spin rates, 

and hence nutation frequencies, change. If the 

nutation frequency in one of the bodies, say I, 

diminishes to zero before e ::: 0 is reached, the 

energy dissipation. 'II. ceases and .th.at body acts 

like a rigid body. If body II were ngld, the systern would be content to remain at this terminal 

nutation angle. This result is easily visualized 

by considering the space-viewed motion of body I 

when 

In this state, each element in I rotates steadily 

about the space-fixed angular momentum vector 

at the rate Ao' The body forces in I are then 

static. The forces in II are clearly cycilc, but 

since that body is assumed rigid, no energy is 

dissipated in the system. Thus, the configuration 

should be designed to ensure that, as nutatlons 

are dalUped, the nutation frequency with respect 

to the body containing the primary energy dissipation lUechanism does not vanish. (This is the 

essence of the discussion of stability regions 

presented in Reference 1.) 

To consider the effect of a motor torque, J, 

coupling the bodies, Equation 3 is written 

' ... 

The stability criteria may be derived for this 

case by assuming one of the bodies is rigid. The 

result of this assumption, assuming body II to be 

rigid, is 

A~ > 0 

as found in Equation 1. Alternately, it may be 

assumed that the torque is applied to keep one of 

the bodies at a constant rate, say body I, such 

that 

1'\1 + 

and 

Aww 

duplicating Equation 5. Thus,. for two practical 

cas es of interest, the stability criteria may be 

inferred from the conditions given in Equation 6. 

Although the criteria are not affected by the 

torque, the motor can change the lUomentum distribution between the bodies and thereby change 

the nutation frequencies seen by them. ' 

From the preceding results, it is seen that, a 

dual-spin systelU of nearly any inertial configuratlE>n 

2-3 

can be rendered nutationally stable by proper 

adjustment of energy dissipation rates. 

m. DYNAMIC ANALYSIS 

To corroborate the foregoing arguments and 

to demonstrate, by example, the underlying 

assumptions of the energy analysis, the motion of 

a dual-body satellite with nutation dampers in 

each body is studied. The nutation dampers are 

assumed to be simple damped harmonic 

oscillators. However, they are analogous in 

principle to pendulum dalUpers currently used in 

Syncom and 050 I. and help develop insight into 

the mechanic s of "real" dampers. 

System Equations of Motion 

The dual-body configuration to be analyzed 

is illustrated in Figure 2. Each body contains an 

energy dissipation mechanism, idealized as a 

single-degree-of-freedom damped harmomc 

oscillator. The oscillator in body I is oriented 

parallel to the OZ axis and located a distance Xo 

from the axis. When the oscillator is at rest, the 

mass. mI' lies in the transverse plane con,taining 

the configUration cente r of mas s. The osclllato r 

in body II is oriented norlUal to the OZ aX1S at 

z ::: h. When the mass, mIl, is at rest, it lies 

on th~ OZ axis. It is as sumed that the oscillator 

masses are small relative to the system mass, 

so 'that the center of mass is essentially stationary 

Figure 2. 

z 

Reference Frame and Nutation 

Damper Geometry 

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in body coordinates. 'The system equations of 

motion relative to the OXYZ frame, with origin 

at the center of mass and nons pinning , are then 

( Z, .) +m1x z -w sm<ill-w W cos <ill ' 0 y x y 

AU, - (en + 1CL_} W +mlzZw +Zm1zz W 

y -"1 -'11 x Y • Y 

+m1x z[w 2 coS<ilr + W W sin<ilrJ o x x y 

+mrrh p [wZcos<ilrr+ W W sin!Prr J o x x y 

(8) 

2-4 

The complementary equations of motion for the 

oscillator masses are 

.. c1 · ~ z + - z + - z + x (iii sin <ill - iii cos (pr) m l m l 0 x ,y 

-z(W; + w:)+ 2xoOI(Wxcos<ilr+Wysin!Pl) = 0 

.. cn · ~ . . p + -- P + -- p- h (w sin<ilrr-w cos CPrl) mn m ll 0 x y 

(9) 

Equations 8 and 9 are the complete system equations of motion, recalling the assumption that mI 

and mIl are very small relative to the total 

system mass. 

Linearization About Initial Nuta tion 

If the dampers were caged, Equation 8 

reduces to. the ordinary Euler equations written 

with respect to a nonrotating body-fixed frame. 

The nutational motion of the configuration in this 

state is described by 

W (t) = W sin i.. t Y 0 0 

To examine the effect of oscillator motion, the 

following assumptions are made. The oscillator 

springs are stiff enough to prevent "bottoming" of 

the masses or 

and the damping forces are large enough to 

ensure that P and z are small quantities. 

Further, the time constants associated with secwar changes of the vehicle rates are large compared to oscillator damping time constants, 

permitting neglect of oscillator transients. 

Moreover, the torque J is applied to keep one of 

the bodies at a constant rate and not to radically 

change the spin momentum distribution between 

the bodies. Introducing: 

::: W cos i.. t + w' o 0 x 

( 10) 

W (t) = W sin i.. t + w' Y 0 0 Y 

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. Approved for Release: 2019/01/11 C05105855 . 

where w~. w~,.., perturbation rates. substituting 

into Equations Sand 9, and neglecting the products of small quantities. yields 

~xo) 2 - --- zw cos()" -n)tsinA t A 0 0 -"] 0 

~xo)... (mIto) 2 +. ~ z sm"r t - -A--. P Wo cos (1.0 

(

mI:fO) . - ~ 2 P "rl cos "rr t = 0 

~o).. n 

--;:- z cos 1 t 

+ cos~ t 

• m ro eL+ -- zW A sin(A - "I) t -"] Coo 0 

(11) 

'. mUh J ILl + __ 0 P W A sin( A - n ) t - - :: 0 -"] I 0 0 0 -"] I 

2-5 

z =x W ()" -2 (l)cos(A _eL) t o 0 0 -"] 0 -"] 

• 

It is observed that the spin rate changes no 

longer appear in the transverse equations and 

that. consistent with the assumption of small 

perturba tions, 

The equations describing the perturbation spin 

rate changes are retained since they are of 

interest. From these equations, it is seen that 

the torque J serves to transfer the oscillato r 

torques from one body to the other. Thus, to 

investigate the effect of oscillator motion on the 

spin rates. the motor torque need not be considered. The effect of perturbation quantities on 

oscillator motion is also neglected, 

Neglecting transients, oscillator motions 

are given by 

PIt) :: 

-h W A o 0 0 

2 2 ] + (Wn - An) cos '-II t 

( 12) 

To facilitate solving for the perturbation 

transverse rates, let 

Wi Wi + i Wi 

X Y 

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• 

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and add the first two relations of Equation 11 

in quadrature: 

d (' -iA.ot) dt w e 

Solution of Linearized Equations 

(13) 

Substituting Equation 12 into 13, integrating 

and retaining only secular terms gives 

],(i) 

( _h2) 2 ).,CL)., ~r-o Wo 0 --II II [\3 )., 

- -A- [ 2_,--2 J

2 '" 2,2 II II wII '"II + i-'1l"II 

( 14) 

2-6 

It is seen that 'total transver~e rate is a vector 

rotating with frequency ).,0- which is the 

sum of the initial rate. WOo a.nd the perturbation 

rate, Wi. The perturbation rate comprises two 

components, The a)" component lies along woo 

while the (W 2 - ).,2) component is normal to WOo 

The effect of the l:l A component is to increas e or 

decrease woo while the (w 2 - ).,2) component tends 

to merely "turn" woo The essential change in the 

initial rate is expressed by 

('iI

) t J 

( 15) 

Note that the initial rate is diminishing if 

If either ).,1 or AIl were negative, the sign of the 

change of Wo would depend on the relative magnitude of the two time-varying terms. 

Examining the oscillator-induced perturbation torques on body spin rates. from Equation 

11 it is recalled that 

2m-xo Ai, . . m-x 10 \ " .. :---W ZCOS"'rt---w I'. ZSlnll.1t reo COO 

Substituting Equation 12 yields 

- 2 Arcos 2).,r t)+ (WI

2

- Ar2)(\ + 2Ar)sin¥cos Alt} 

( 16) 

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Observe that the secular torque acting on the 

spin rate is due to the phase lag, ~ A term. If 

the dampers were "tuned" to the rates, Ar, All 

such that 

the effect of the oscillators would be entirely 

secular, contrary to the notions stated in 

Reference 4. Taking average values over nutation cycles gives 

o = I 

i.lJ2 

o 

2 

·w o 

(17) 

Here, too, the signs of the spin rate changes are 

governed by AI and An' 

Solution About Small Nutation Angles 

If the initial nutation angle is small such 

that 

the nutation frequencies do not change appreciably during the nutation decay. In this case, it 

is appropriate to write 

This result has been verified by digital computer 

simulation of the exact equations. Exc elient 

agreement was found when the previously stated 

assumptions were satisfied. 

IV. COMPARISON WITH ENERGY 

ANALYSIS 

To compare these results with the previous 

energy analysis, form 

From Equation 12. z2 and p2 are obtained: 

.2 

z = [ 

2 2 2 ~I AI cos ~ t 

Taking average values over a nutation cycle, 

. CiI) 

Recalling from Equation 6 that 

and substituting Equation 18 results in 

2-7 

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( 18) 
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duplicating Equation 17. Writing Equation 7. 

W =~ Aw o 

and substituting Equation 18 results in 

(:1 ) 

duplicating Equation 15. 

V. CONCLUDING REMARKS 

The dynamic analysis indeed corroborates 

the vehicle rate changes predicted by the earlier 

energy analysis and illustrates its underlying 

assumptions. Also demonstrated are the inertial 

forces whlch sustain relative motion and the role 

of nutation frequencies, AI and All. With the 

2-8 

analysis as background, it is not surprising that 

the effect of a nutation damper depends on the body 

in which it is located; for its motion, and thus 

its reaction torque. is governed by the local nutation frequency which may be quite different in 

each body. . . 

REFERENCES 

1. V. D. Landon and B. Stewart, "Nutational 

Stability of an Axisymmetric Body Containing 

a Rotor, " Journal of Spacecraft and Rockets, 

Volume 1, No.6, 1964, pp. 682-684. 

2. A. J. Iorillo. "Nutation Damping," Internal 

IDC, Hughes Aircraft Co., October 1964. 

3. W. T. Thomson and G. S. Reiter, "Attitud.e 

Drift of Space Vehicles, " Journal of 

Astronautical Sciences, Vol. 7, 1960, 

pp. 29-34. 

4. .W. F. Cartwright, R. D. Trueblood, and 

E. C. Massingill, "Circular Constraint 

Nutation Damper Analysis, " GM Defense 

Research Laboratories Report TM 62-205, 

December 1961, General Motors Corporation. 

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DEVELOPMENT OF HUGHES GYROSTAT SYSTEM 

ABSTRACT 

This note describes results of theoretical and experimental research 

performed in the last several years which has led to the development of 

Hughes Gyrostat stabilization concept. 

1. INTRODUCTION 

The Hughes Gyrostat system is, generically, a spin-stabilized spacecraft with a despun platform. The unique feature of Gyrostat 

is that the platform is virtually unlimited in size. 

The system is not constrained to have the pancake shape demanded by the familiar inertia ratio 

criterion used to design current spinning satellites with or without despun platforms. Due to the 

"pancake" criterion, requiring spin about an 

axis of maximum inertia, pre sent craft are 

limited in both overall length and despun platform size by launch vehicle shroud diameters. 

Also, since shrouds are longer than wide, the 

pancake constraint results in nonoptimum use of 

shroud volume. 

Alternately, Gyrostat may be described as 

a rotor -stabilized spacecraft differing from 

present designs of thi.s type in a fundamental 

way. Gyrostat is not constrained to have a perfectly rigid rotor, i. e., a metallic flywheel; 

dictated by the nutational stability cr iter ion used 

to design satellites of this class. In essence, 

Gyrostat is the broadest application of spin stabilization. It bridge s the gap between pre sent 

nonrigid spinners with despun platforms and 

perfectly rigid rotor stabilized spacecraft. Free 

from the rigid rotor constraint, the rotor in 

Gyrostat is used to perform many functions in 

addition to effecting gyroscopic stability. ExampIes of some of these additional uses are: 

• An apogee kick motor may be housed 

within the rotor and passively stabilized 

by its spin. 

e The attitude and velocity control 

system may be spun, thereby requiring mere~y three jets for all 

axis control.' The jet system spin 

also makes the spacecraft essentially 

insensitive to the torques induced 

by leaks' since they are averaged out 

every spin cycle. 

• Relatively simple attitude sensors may 

be rigidly mounted to the rotor and scan 

targets by virtue of spin. Pointing 

accuracy of 10 arcseconds may be 

achieved by using ~ rigidly mounted 

star scanner (a visible-light sensitive 

phototube located at the focal plane of 

a 2-inch telescope, weighing 8 pounds). 

For less demanding missions, the 

sensor would be an IR earth scanner. 

• Solar cells may be fixed to the rotor. 

e The rotor may also carry payload 

-requiring spin. such as the ATS spinscan meteorological camera. 

3-1 

• The rotor may act as a sun shield for 

electronics. permitting passive thermal control for most missions. 

Further, since the rotor comprises a significant 

portion of the spacecraft, it has a high spin 

moment of inertia, and large gyroscopic stiffnesses may be achieved at very low spin rates 

(10 to 100 rpm). 

In summary, Gyrostat provides a fully 

stabilized platform while maintaining features of 

well-proven spinner technology. In fact, all 

hardware aspects of Gyrostat have developmental 

roots in the 5yncom and 050 programs. This 

hardware has been combined into a new configuration long recognized as attractively suited for 

man y mis sions but heretofore con sidered 

dynamically unstable. 

The Gyrostat concept evolved simply from 

the discovery that it is possible and practical to 

passively stabilize the spin of a nonrigid body 

about an axis of least inertia if the body contains 

a counterrotating element on which a nonrigid 

ener gy dis sipation me cha nisIn, a nutation 

damper, may be placed. In present Gyrostat 

de signs (F igure 1) the counterrocacing element 

carries payload as well, thus it is large. However, it need not be. For example, a quite small 

counterrotating box containing a nutation damper 

can be used to stabilize a large, slender spinning 

liquid rocket or could have been used to stabilize 

Explorer I had the principle been known at that 

time. 

II. REVIEW OF THE DEVELOPMENT OF TWOBODY THEORY 

A study of the dynamics of two-body configurations was initiated at Hughes in early 1964. 

This study was motivated by the desire to add 

despun elements to Syncom satellites after the 

050 program demonstrated that rotating elements could be operated in space for years. 

The object of the study was to determine whether 

stability of two -body configur ations was gove rned 

by the well-known criterion for spinning monobodies. That is, a mono-body must be spun about 

its axis of greate st inertia. By simple extension 

of analysis used for mono-bodies, it was learned 

1) that two-body stability does not necessarily 

require spin about a major axis and 2) that the 

distribution of energy dissipation between the 

two-bodies plays a role (Reference 1). This 

same conclusion was reached by Landon and 

Stewart at RCA in a paper which appeared at 

nearly the same time (Reference 2). Both of 

these works had an important shortcoming, however. To perform the simple extension of monobody theory, both analyses were limited to the 

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Figure 1. Typical Hughes Gyrostat System Design 

special case of a two-body configuration wherein 

only one of the bodie s is nonrigid. With this 

assumption, detailed quantitative conside ration 

of poorly understood nonrigid effects (i. e .• 

energy dissipation) could be avoided. The 

important results of these analyses are twofold: 

1) if the spinning member is nonrigid, its spin 

moment of inertia must be greater than the combined configuration transverse moment of inertia, 

essentially the same as the inertia ratio criterion for mono-bodies; and 2) if the spinning 

member is perfectly rigid, a flywheel, the twobody configuration is practically free of inertia 

constraints. To attack the problem of a general 

two -body configuration wherein both bodies are 

nonrigid, it was clear that detailed understanding of the role of nonrigid effect s was required. 

By analyzing equations of motioi:t of twobody systems with specific nonrigid elements, 

nutation dampers, physical understanding of the 

3-2 , 

manner in which motion of dampers affected 

gross system motion was developed (Reference 1). 

The relationship between the amount of energy 

which a damper dissipated into a dash pot, for 

example, and gross sytem motion was learned. 

With this understanding of specific case s, the 

classical energy-sink method was reconstructed 

to deal with the general two -body nonrigid system (Reference 3). This energy-sink analysis 

is reproduced below. 

III. GENERAL TWO -BODY ANALYSIS 

The symmetric two-body system analyzed 

is illustrated in Figure 2. Except for rotation 

about the axis of symmetry, bodies I and II are 

rigidly joined. Only the nutational, or torquefree. motion is to be considered. The rates 

III and Orr are the ~pin rates of bodies I and II, 

respectively. The rate Wo is the transverse or 

~obble rate of the combined system. The vector 

H is the system angular momentum vector and 

is thus the vector sum 

( 1 ) 

where 

C, I - spin moments of inertia of bodie s 

r and II, respectively 

A- combined system transverse 

moment of inertia 

For convenience without loss of generality. 

W 2: 0 o 

This definition is tantamount to establishing a 

reference total momentum direction. Also, the 

spin and transverse moments are orthogonal. 

CO I + III n 

A" . TAN 8 

A .. z __ ·_~-2. 

cll r + IOn k. 

Figure 2. Nutational Geometry Axisymmetric 

Two -Body Configuration 

Since the nutation angle, e, is directly 

related to the'angular rates, 

(2) 

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nutational motion can be stud~ed by considering 

angular rates alone. The question to be answered now is what is the change in these rates 

when energy is dissipated within the system. 

This does not mean frictional losses in the 

shaft cOupling the two bodies but rather losses 

due to flexing structure and the like within the 

bodies during nutation. (In real systems, a 

servo loop-controlled motor acts to exactly 

counterbalance shaft friction. It is assumed 

here that the shaft is frictionless. ) 

If the system were lossless, perfectly 

rigid, the kinetic energy integral of the equations of motion would exist as 

2 2 2 2T :: A 1.1.10 + C 01 + I 0lI :: constant (3) 

Introducing internal dissipation, T is not a constant but a function of time. Equation 1 is then 

written as 

(4) 

where T represents the total rate at which 

energy is dissipated and, by definition, is a 

negative quantity. Since the total dissipation is 

the sum of the dissipation in bodies I and II. let 

• 

Considering now only the system motion 

due to dissipation and not due to exterior 

torques 

H :: 0 (6) 

This is the statement of conservation of momentum. Equation 6 demands 

o (7) 

or 

With Equation 5, there are now two equations 

which the change in rates must satisfy. Rewriting them. 

(9) 

Earlier analyses made simplifying assumptions 

for an obvious reason. There are three quantities of interest and only two equations. The 

simplification to a system wherein one body is 

perfectly rigid permits reduction to two quantities. For example, assuming body I to be 

rigid permits. after valid physical argument. 

letting O. t :: O. 

I I 

3-3 

The present analysis, however, combines 

Equations 9 and 10 to form 

_ (C 01 +A I °u TI+TU= 

( 11 ) 

With the background of earlier noted analyses of 

equations of motion of specific systems and a 

development of physical insight into the role of 

dissipation, Equation 11 was recognized as the 

sum of two equations: 

where 

Equations 12 relate the dissipation rates in each 

body to the change in spin rate of that bod y. As 

such. they are equations of motion. The quantities AI and An are characteristic frequencies 

of motion of nonrigid elements within bodies I 

and II, respectively, when these elements are 

dissipating energy. Substituting Equation 12 

into 9 re suIts in 

A w W :: A. (.::1.+ T ) o 0 0 AI ( 13) 

where 

which is, by definition, a positive quantity. The 

quantity Ao is recognized as the total system 

nutation frequency. Equation 13 is a fundamental 

relation between the change in system wobble, 

wo ' the energy dissipation rates within each body 

and system parameters. The question of system 

stability is equivalent to asking under what conditions an initial wobble rate, 1.1.10 ' subsides. 

For subsidence, Wo < 0, the conditions are 

those which satisfy 

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• 

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( 14) 

recognlzmg that AI and All can be of either sign, 

depending on system parameters. 

IV. INTERPRETATION OF RESULT 

For a spinner with a despun platform, the 

relations stated in Equation 14 may be written 

( 15) 

where subscripts sand p refer to spinner and 

platform, respectively. 

I 

A = s s 

A = p 

I 

s 

n + I n s p p _ n 

A s 

n + I n s p p _ n 

A p 

Assuming the spinner momentum is much larger 

than the platform spin momentum due to its 

nominal once per orbit rate, ~:=. orbital rate, 

I n 

A n :=. (~- 1 ) n s:-!.-!.. _ ( 16) s A s A s 

I n 

Ap :=.-L...!. 

A 

Substituting Equation 16 into Equation 15, the 

'stability conditi~n becomes 

<0 

For a satellite like 080, whose rotor spin 

moment of inertia is larger than the system 

transverse inertia, 1. e. , 

I > A s 

H 7) 

the condition cited in Equation 17 is satisfied 

independent of dissipation distribution. What 

this implies is that a damper may be placed on 

either the platform or spinner to dampen 

nutation. 

For a satellite with a rigid flywheel', T s = 

0, stability is a.ssured practically independent 

of the ratio Is I A. 

For a Gyrostat design, 

I 

...§.. < 1 

A 

3-4 

and thus the quantity 

while 

T s -Is

--

X- 1 

>0 

T 

2<0 

I 

....lL .. 

Stability of a Gyrostat design then requires 

For tYPlcal deSiil' n'S-:---------

and thus 

I 

-ll. < 1-

A 3 

. ' 

T 

.,!. > 2 

T s 

or the dissipation rate on the platform must be 

at least two times the dissipation rate within the 

spinner. (As the inertia ratio decreases, the 

minimum dissipation rate required on the platform also decreases.) 

V. PRACTICAL DESIGN CONSIDERATIONS 

The relation of Equation 18 specifies the 

ratio of energy dissipation required for Gyrostat 

stability: The design requires quantitative 

measure of dissipation rates to ensure that this 

ratio is achieved. In typical Gyrostat systems, 

the principal source of destabilizing dis sipation 

is liquid propellant slosh. An analytical model 

of fuel slosh dissipation was developed by 

D. D. Williams in mid-l965 for the Applications 

Technology Satellite program (Reference 4). 

Using his model, sloshing effects for typical 

propellant loads (100 to 200 pounds) were found 

to be small relative to the dissipation rate 

achievable with a small well-designed nutation 

damper (1 to 5 pounds). Thus, for Gyrostat 

..designs, 

. . T > > T P s 

The primary design constraint for a damper 

becomes the need to dampen spacecraft wobbles 

due to booster separation, for example, within a 

reasonable time. Satisfying the relation in 

Equation 18 is then a natural fallout. The following computation will clarify this point. 

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~ 

VI. EXAMPLE COMPUTATION 

A configuration designed to be launched 

into synchronous orbit by a Titan IIlC, about 

1600 pounds. will be analyzed. The satellite 

consists of a nominal 10-foot diameter spinner 

weighing SOO pounds and carrying an SOO-pound 

platform. Typical parameters for this configuration are 

I:: 400 slug-ft2. 

2 A:: 1000 slug-ft 

o :: 100 rpm == 10 rad/ sec s 

The principal energy dissipa.tion mechanism in 

the spinner is the sloshing of 100 pounds of 

H2.02. reaction control fuel distributed in five 

spherical 12-inch diameter tanks. It is interesting to compute the destabilizing effect of this 

propellant loading if no nutation damper were 

present. 

Williams shows that the energy dissipation 

rate of a sloshing, half-filled tank of fluid is 

given conservatively by 

• 1 ( M.t. _)2. 

T.:: 21£ As 

Ba2. z 

where, for the present case, 

M :: mass of fluid = 2.0 pounds 

a:: radius of tank:: 0.5 foot 

If;;: 2./5 M a2. :: 0.066 slug-ft2. 

.t. ;:: 3/S a ;:: O. 187 foot 

15 x 0 j Z 

wn:: Ib' ~ = 19.4 rad/sec 

(propellant natural frequency) 

Xo :: radial location of tank:: 2. feet 

(19) 

A :: (I/A - 1) Os :: As:: 0.6 Os:: 6 rad/sec 

s (nutational forcing frequency) 

a = Xo (II A - 2.) Os . w = 32. w itl sec2. z 

w :: transverse angular rate,due to 

nutation . 

(~ 

A P ~ )1/2 :: 0.0039 ft-lb-sec 

3-5 

p :: density of fluid 

:: 1. 392. gn; 

cm 

).L :: viscosity of fluid 

:: 0.0134 _g""m __ em sec 

For the present case, 

(1;\t«C:f 

The dissipation rate for one tank is then 

For the vehicle with five tanks, 

If no nutation damper were present on the platform, the nutation amplitude divergence time 

constant due to fuel slosh would be obtained by 

solving Equation 13. 

or 

A A . 0 0 10-2 2 Aww = -r-' T 5 :: r- . 'j) 

s s 

A w:: _0_. 10- 2 w AA s 

The solution of this equation is 

A 

o 10- 2 t A'f" 

w(t) = w e 5 o 

The divergence time constant 

.,. :: 

A 'A, ___ s_ :: 

A. 10- 2 

o 

150,000 seconds'" 41. 5 hours 

Clearly. the wobble buildup is slow. The reason 

for this slow buildup is understood by studying 

Equation 19. It is seen that the dissipation rate 

is proportional to 

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,) 

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(~: r ::(

nutational drivingfre9uenCY~ natural slos hing fr equency J 

when this ratio is much less than unity. For the 

tank location and size analyzed. this ratio is 

(

_6_)4:!o! 10-2 

19.4 

This same frequency relationship holds true for 

a nutation damper. However, a damper's natural frequency is tuned to be close to the nutation 

frequency so that the ratio is nearly unity. Thus, 

a damper requires on the order of 1/100 the 

propellant mass to dissipate energy at this same 

rate. This is, in brief, the reason why a small 

damper can more than overcome large propellant 

loadings. 

VII. TYPICAL DAMPER PARAMETERS 

Rather than estimate the size of nutation 

damper which would just overcome the fuel slosh 

effect, the damper parameters required to provide a I-minute damping time constant will be 

computed. Reference 3 shows that the damping 

time constant due to a simple spring-mass /dash 

pot damper located on the platform is given by 

A T damping = --2-

mho 

(20) 

where 

. m :: damper mass 

ho = damper location above the spacecraft 

. center of mass 

j3 :: dash pot constant 

This expression assumes the damper is tuned to 

be near resonance at A. For the previous 

example. p 

I n 

A =..!...-!.::: 4 rad/ sec p A 

The spring constant. mass relationship required 

of the damper is then 

where 

~ ::: A 2:: 16 (rad! sec)2 m p 

k = spring re sto ring force! deflection -lb! in 

Assuming the damper location is ho :: 3 feet and 

the damper mass is m :; 4 pounds:: O. 125 slug. 

'\" damping:: 60 seconds requires a dash pot 

3-6 

?amping .constant of j3 = 0.07 lb-sec! slug-ft, which 

1S a nomlnal value. easily obtained. The spring 

constant required, 

2 k:: Am::: O. 166 lb/in 

p 

is also a nominal value. representing an easily 

wound spring. These computations illustrate 

that dampe r de sign is not particularly difficult. 

VIII. CONCLUDING REMARKS 

Previous'sections describe preliminary 

analyses performed to establish feasibility and 

practicability of Gyrostat. Not presented are calculations of structural flexing effects. This is 

not dealt with since structural effects are also 

governed by the fourth power frequency relationship. and, for normal structural frequenCies. 

typically greater than 10 cps (62.8 rad/ sec), 

dissipation due to structural effects is several 

order of magnitude less than fuel slosh. 

When the practical nature of Gyrostat was 

established. considerable effort was devoted to 

thoroughly consider all system aspects. Complete dynamic analysis of "real" systems. inclUding an active despin servo loop coupling the 

s~i~er and platform. was performed using a 

d1g1tal compute r simulation specifically des igned 

for Gyrostat (Reference 5). Here, the dynamic 

integrity of a real system was established. 

Further, Reference 5 describes an a.ir -bearing 

supported Gyrostat dynamic model which was 

fabricated and tested (Figure 3). The model corroborated theoretical conclusions. Reference 5 

also compiles a number of analyses which treat 

the case of a Gyrostat with asymmetric platform 

complementing the analyses of References 1 and 3. 

REFERENCES 

1. A. J. lorillo, "Nutation Damping," Hughes 

IDC 2230. 14/69. October 1964. 

2. V. D. Landon and B. Stewart. "Nutational 

Stability of an Axisymmetric Body Containing 

a Rotor." J. Spacecraft and Rockets L 

pp. 682-684. 1964. 

3. A. J. lorillo. "Nutation Damping Dynamics of 

Axisymmetric Rotor Stabilized Satellites. " 

presented to ASME Winter Meeting, Chicago, 

Ill .• November 1965. 

4. D. D. Williams. "Estimates of Energy Dissipation and Nutation Damping Due to Fuel 

Sloshing in a Spherical Tank." Hughes IDC . 

2280. 03/l02. June 1965. 

5. J. R. Velman. Attitude Dynamics of DualSpin Satellites, Hughes Report SSD 60419R, 

September 1966. 

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DESI'UN SECTION 

CONTROL 

ELECTRONICS 

SPUN SECTION 

(2!i.Sdio) 

NUTATION 

DAMPER ASSEMBt Y 

Figure 3. Hughes Gyrostat System Laboratory Model 

3-7 

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PRECISION ASPECTS OF HUGHES GYROSTAT SYSTEM 

ABSTRACT 

A dual-spin satellite configuration is described which has been 

recently developed for application to missions requiring precise pointing of large payloads. 

I. INTRODUCTION 

The subject of this symposium, dual-spin 

satellites, is certainly not new. Yet for many 

years the dual-spin concept was not implemented 

as often as it might have been. Principally, 

because rotating electromechanical assemblies 

required in dual-spin designs were not felt to be 

reliable enough components. This feeling persisted even though an abundance of earth-based 

experience showed that such assemblies, comprising bearing s, brushe 5, and slipring s, can be 

designeci to function indeiinitely. The reason for 

this fairly widespread opinion was lack of welltested space lubrication techniques. Today, 

problems of maintaining long-lived lubrication in. 

a vacuum environment are well understood and 

various solutions are available. Probably the 

best known of these is the Vackote system, 

developed by Ball Brothers Research Corporation, 

which has been demonstrated convincingly in 

their Orbiting Solar Observatory (OSO) satellites. 

Certainly, 050-1 achievements did much to 

encourage our interest in adding a despun oriented platform to the basic 5yncom spinning configuration with its integrated attitude, velocity, 

and passive thennal control systems. The simplicity and estimated cost of the resulting dualspin system concept made it an attractive contender for missions requiring the steady pointing 

of payload. 

It was apparent, however, that the nutational 

stability criterion demanding spin about an axis 

of maximum inertia severely restricted "the 

capacity of the concept. The problem was that 

reasonable designs, whose spin diameters were 

booster shroud limited, could not carry large 

payload structures and still meet this inertia 

ratio rule (Reference 1). Recognizing that this 

criterion did not necessarily apply to dual-spin 

systems, an early attempt was made to determine 

specific criteria (Reference 2). Following the 

energy sink method used by Thompson, this analysis was confined to the special case of a system 

in which one of the bodies is rigid. It was shown 

that inertia constraints. could be circumvented by 

using a rigid spinning member; i. e .• a flywheel. 

The concurrent Hughes attempt to solve the 

problem focused on the dynamics of specific nonrigid elements within nutating dual-spin systems 

and their reaction effects on gross system motion. 

Restricted in scope, this effort nonetheless provided some understanding of the roles which 

various parameters play during nutation. Finally, 

by informal reconstruction of the energy-sink 

method to cope with the excess variables of the 

general case which had caused prior confinement 

"~o special cases, criteria for nonrigid systems 

we re obtained. Though lacking rigorous proof, 

the criteria were entirely consistent with the 

previously develop.ed view of the physical process. 

The result indicated that disSipation mechanisms, 

such as propellant sloshing and structural flexing 

within a rotor, do cause destabilizing forces if 

the rotor spin inertia is not larger than configuration transverse inertias; however, similar 

mechanisms on the non-spinning plat:Corm always 

contribute stabilizing forces. Through detailed 

analysis of typical designs, it was discovered 

that normal structural flexing and sloshing of 

several hundred pounds of propellant within a 

rotor could be adequately compensated by a lightweight passive damper on the platform at 

arbitrarily small inertia ratios. Subsequent 

laboratory experiments and digital computer 

solution of exact equations of motion corroborated 

these findings (Reference 3). 

The important conclusion of this work is that 

spinners should not be relegated to missions 

requiring small oriented payload as commonly 

assumed in system comparisons (Reference 4). 

but rather that their cap.acity can be made virtually unlimited quite easily. Further study of 

configurations with inertia ratios less than unity 

revealed another interesting property which is 

that they lend themselves naturally to precision 

pointing capability (Reference 5). 

Current large spinner desig;ns. with or without despun platforms, have inertia ratios marginally greater than unity in an attempt to package 

as much as possible into diameter-limited 

envelopes. The Application Technology Satellites 

for example have inertia ratios of 1. 04, a nearly 

spherical inertial distribution. Consequently. 

they are difficult to dynamically balance with 

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preCl510n. As a result, a despun platform on 

these vehicles experiences wobble of the order 01 

0.05 degree. Reasonably, this value has been 

assumed to be a practical limit of pointing 

accuracy for large spinners (Reference 4). 

When freed of the inertia ratio constraint, 

there is an understandable tendency to design 

satellites which follow shroud volume forms, 

lTlUch longer than wide. Typical designs then 

have inertia ratios of 0.5 and lower. Since unbalance wobble is inversely proportional to the 

deviation from spherical symmetry, an order of 

magnitude improvement over current spinners is 

automatically realized. By adjusting satellite 

elements such that the overall transverse inertia 

is large, wobble can be reduced further to the 

arcsecond level. With the rotor so well 

balanced, satellite pointing capability is limited 

principally by factors common to any configuration such as sensor accuracy, overall alignment, 

and servo technology in general. 

Based on the analyses referred to above, it 

was concluded that the concept pursued was not 

only inherently simpler but as capable as fully 

stabilized de signs. 

The first implementation of the system is the 

Tactical Communications Satellite presently under 

development (Figure 1). The satellite cnmprises 

a massive, oriented payload and a rotor which 

carries control and power systems as well as 

serving as a spinning sun--shield for electronics. 

The satellite may be des'cribed as either a spinner 

with a despun platform stabilized abvut an axis-of 

Figure 1. Tactical Communications Satellite 

least inertia or a vehicle stabilized by a nonrigid 

rotor. In any event, this configuration is called 

the Hughes Gyrostat System (patent pending). 

This note describes typical Gyrostat systems 

and discusses their performance as orbiting 

platforms. 

II. SYSTEM DESCRIPTION 

Several Gyrostat configurations are illustrated (Figures 2 and 3). The first is designed 

for a synchronous orbit mission and launch by 

an Atlas-Agena. The second is designed for a 

Titan launch. The common elements of these 

configurations are an oriented payload platform, 

a rotor which houses control and power subsystems, and a rotating interface for power 

and signal transfer as well as relative motion. 

Before describing the various SUbsystems. a 

typical mission profile is presented to' fix 

ideas concerning functions which they must 

perform, Figure 4. The Atlas -Agena design 

is used fo"r illustration because it fully exercises the various capabilities of the system. 

Injected into a transfer orbit with perigee at 

about 100 n. mi. and apogee at synchronous 

altitude, the satellite is released with a conventional separation system and, almost simultaneously. the rotor is spun up with a one-shot propulsion system, either gas or solid. The des:pin 

servo keeps the' platform from being dragged by 

bearing friction and acts to keep the platform at 

a low inertial rate required for nutation damper 

eiiectiveness. Stabilized by spin, the vehicle 

coasts to synchronous altitude. Gross velocity 

and attitude errors remnant from the injection 

phase can be corrected by ground command of a 

liquid propellant jet system. At apogee the kick 

motor is fired to form synchronous orbit. A 

maneuver is then ground commanded to precess 

the vehicle to an attitude normal to the or bit 

plane. The platform despin servo is then commanded to an earth-seeking mode and the mission 

can begin. Additional velocity errors are corrected to trim the orbit. (Exc ept for despin 5 ervo 

.operation, this same profile has been performed 

by all Syncom family satellites. All have been 

their own last stages. For Titan launches, a 

typical profile begins in synchronous orbit. The 

functions of achieving circular orbit and orienting the satellite along the north-south axis are 

accomplished before separation.) 

The reaction system consists of three jets for 

attitude and velocity control. Mounted on the 

rotor, two jets are aligned parallel to the spin axis 

and the other normal to the spin axis along a rotor 

radius. When fired over a complete spin cycle, 

an axial jet provide s north-south thrust without 

affecting attitude. When pulsed over a sector of 

a spin cycle. it causes a precessional control 

torque. The radial jet thrust acts through the 

vehicle center of mas s and thus no torque re sults. 

Pulsed over a sector, it provides velocity control 

in any radial direction. (This same velocity and 

attitude control system concept has been used in 

all Hughes earth satellites.) Normally, the jet 

system is commanded at weekly intervals for 

stationkeeping and attitude trim maneuvers. 

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UPl'fR EQUIPMENT PlATfORM 

RADIAL JET 

SOlAJl RADIATION aAIUIlEI 

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AXIAL JET 

lOWl:R eOUIPMENT 

PLATFORM 

There are several distinct attitude-sensing 

functions. The platform control servo requires 

an angle error signal, and the ground operator 

or computer "requires knowledge of satellite 

attitude to compute the sense and magnitude of 

reaction jet torquing commands. Further, 

satellite attitude data is required to process 

payload data. 

EQUIPMENT 

PlATFORM 

RADIAL JET 

AFT RADIATION SAARIER 

ROTATING ASSEMBLY 

SOlAJl PANEL 

CYLINDER 

STAR SCANNeR 

AXIAL JET 

Figure 2. Typical Titan-Class Gyrostat 

Configuration 

APOGEE MOTOR 

Figure 3. Typical Atlas-Agena-Class Gyrostat 

Configuration 

Figure 4. Typical Mission Profile 

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A single sensor, rigidly mounted to the 

rotor and thus scanned by spin. is all that is 

required to fulfill these needs. During the interval of one spin cycle. satellite attitude drift is 

less than 0.01 arcseconds. By scanning two or 

more inertial targets and by obtaining angular 

alignment relative to thes e tar gets. rotor attitude 

is determined in one cycle. Then to determine 

the inertial attitude of the platform, a measure of 

platform orientation relative to the rotor about 

the spin axis is necessary. Due to the considerable inertias of both platform and rotor. the 

relative motion between them remains constant 

enough to use a simple shaft encoder for measuring the relative angle. (Even for a 5-to 10-arcsecond system. a magnetic pip coil will usually 

suffice for this function.) 

The outputs of both scanner and the pip coil 

are transmitted directly to ground for attitude 

determination and are also processed on board to 

derive a s pin angle error for des pin servo 

control. 

For missions requiring nominal pointing 

accuracies of 0.20 degrees, a Tiros-type earth 

sensor can be used as the scanner for the despin 

loop, augmented by a simple sun sensor for 

complete determination. 

For precision missions, a single star scanner is used for both despin control and attitude 

determination. A chevron-masked phototube and 

a lens system, (Figure S) is effective as a star 

scanner. The geometry of star measurements is 

illustrated in Figure' 6. Note that since the· 

inertial attitude of the rotor is constant, the same 

stars, typically five in number. are scanned 

every spin cycle. No catalog or involved processing is reqUired. A simple gating circuit is 

used to isolate the desired star pulse for the 

despin servo system. 

The only active control system on board is 

the despin 5 ervo system whos e principal elements 

are: 

I) 

2) 

3) 

The scanning sensor and pip coil 

Processing electronics 

A servo motor 

A typical system is illustrated in Figure 7. It iii 

a fairly standard sampled data system with a rate 

loop for stable pointing and a supervision loop for 

directed pointing. 

In the designs shown, electrical power is 

deriv.ed from solar panels which form the rotor 

cylinder and is continuously generated without 

active sun-pointing. Not a necessary feature of 

Gyrostat systems, rotor-mounted panels are 

generally preferred when the power required is 

consistent with a reasonable cylinder· size and 

weight even though they are not as efficient as 

oriented panels. For missions with large power 

requirements, oriented panels (or other power 

sources) may be required. The system then 

would be a multi-spin configuration with a rotor, 

an earth-oriented platform, and a sun-oriented 

platform. 

SPIN AXIS 

SIGNAl. 

PROCESSING 

ELECTRONICS CONDENSING LENS 

-;-__ STAll MOTION 

CHEVRON PATTERN 

PttOTOMULTIPLIER EMR-541-E 

FIELD OF VIEW 4 d.g 

FOCAL LENGTH 10 in. 

APERTURE DIAMETER 4 ino 

RETICLE SLIT WIDTH 0.15 ... , 

BLUR DIAMETER 0.075 m, SENSITIVITY +2.6 MAGNITUDE 

MINIMUM SIN 14db 

PULSE STABILITY :l:S an:seconds 

Figur e 5. Star Scanner 

CELESTIAL SPHERE 

ALPHERATZ 

jnAURI 

POLLUX 

"CORONAE 

/3 Pt!GASI 

1.51 

00.77 

115.57 

-126.75 

.14.23 

28.119 

28.58 

28.12 

26.114 

V.88 

Figure 6. Target Star Geometry 

2.00 

1.6<4 

LIS 

2.23 

2.61 

The rotating assembly consists of an outer housing. a pair of ball-bearings. a servo motor, a 

shaft, and a slipring-brush unit. The shaft 

protrudes through a labyrinth seal arrangement. 

Ten to twenty power slip rings are used both for 

redundancy and to keep the current flow per unit 

area at low levels. Signals for control and telemetry are crossed in a multiplexed digital bit 

stream through two rings. 

m. SYSTEM PERFORMANCE CAPABILITY 

Analyses are presented which are confined 

to aspects of system design that do not depend 

heavily on payload specification. Hence, structural, thermal control and power system analyses 

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SENSED 

SPIN 

REFERENCE 

DIGITAL 

fREQUENCY 

lOCI( lOOP 

SHAFT ENCODER 

INDex JllJLSf 

MOTOR 

DRIVE 

if TORQUEI I r---'I 

I I 1E~itr'i~D r-1 se~:~R I I 

L __ -l L_t_.-J I 

..J I -= __ -.J 

PLATfORM 

DYNAMICS 

Figure 7. Platform Despin Control System 

are not discussed. Rather, topics related to system performance as an orbiting payload bus which 

are not readily available elsewhere are considered. For brevity and current interest. high altitude missions are considered. 

Nutational Stability 

The stability criterion for nonrigid symmetric 

dual-spin systems is given by 

(1) 

where 

TR , Tp;' rates of energy dissipation in 

rotor and platform respectively. (always negative) 

Ia0R + !pOp 

>"P :: II - Op 

TABLE 1. TYPICAL PARAMETERS 

Parameter 

Rotor spin inertia, I

R, slug-ft 

Rotor tranverse inertia, I

TR, 

slug-ftZ 

Configuration transverse inertia 

, slug-ftZ ' 

spin inertia, Ip ' 

Rotor spin rate, OR' rpIn 

PlatforIn rate, Op, rpm 

600 

100 

.. 

450 

ZOOO 

zoo 

For the cas e of a platform with low inertial rates 

(of the order of orbital rate). the momentum of 

the rotor is much lar gel" than that of the platform. 

Hence, for practical purposes, the criterion 

becomes 

T 

+ r;-< 0 • (2) 

IT 

The reduction of this criterion to the special 

cases of pure spinners and flywheel.-stabilized 

designs is accomplished by letting Tp and tR go 

to zero, respectively. For gyrostat systems, 

IT> Ia' thus stability 1" equires 

(3) 

For example. at a ratio of 0.5. the dissipation 

rate on the platform must be greater than the 

dissipation rate within the rotor. 

The principal rotor dissipation mechanism 

in the designs shown ill the sloshing of propellant. 

Figure 8 illustrates dissipation due to sloshing 

within a single tank for several values of rotor 

spin. In a multitank system, these values are 

multiplied by the number of tanks. The contribution of structural flexing is normally an order 

of magnitude smaller than the peak slosh 

contribution. 

It may be noted that the sloshing dissipation 

is low relative to the capability of nutation dampers normally used on spinners. Like the structural flexing mechanism, the natural frequency 

of slosh is typically greater than the nutation 

frequency which 'drives the motion by a factor of 

4 or more. A damper is designed to be near 

resonance of the nutation frequency. Since the 

dissipation rate is proportional to 

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IS.61lh - WEIGHT OF LIQUID/TANI( 1.392 um! •• -DENSITY OF LIQUID 0.013 (um!cm __ l - YISCOSITY OF LIQUID 

45 in. -DISTANCE TO SPHERE CENTER FROM SIC CENTER 0.5 -INERTIA RATIO 

~ 0.151--f-I---t---t---+---t---+---! o 

id w'" 

d~ 

~:! 

"'~ 

~£ ~Q 

",w 

~3 

as a.lol-+-f--.:\--t---t---t---t---+----! 

~~ "' .... ~~ ... 0 ~'" 

~~ ~\i; 

<C~ 

'" 0.05 HI--4---".-

l:! 

o 0.1 0.2 0.3 0." 0.5 0.6 

FRACTION FILL. 

Figure 8. Energy Dissipation in Propellant 

Tank Versus Alnount of Fluid in 

Tank For Differ.ent Spin Rates 

(

>"R)4 =' (nutational driving freQUency )4 wN . natural frequency 

the slosh effect is expectedly low relative to an 

efficient dalnper. 

0.7 

For the designs shown, the destabilizing forces due to propellant slosh, if not compens ated. 

cause nutation divergence time constants of 10 to 

40 hours. A nutation damper. such as the pendulum damper on OSO-I. is designed to prOvide 

damping time constants of 5 to 20 minute s, which 

are more than sufficient to merely satisfy 

condition 3. 

The stability criterion displayed here is for 

a.xisymlnetric vehicles. For systems wherein 

the rotor is symmetric and the configuration is. 

asymmetric, the average transverse inertia 

should be used (Reference 6). . 

Momentuln Sizing 

Typical system inertias are fallouts of structural and other system considerations. The spin 

rate is the only really free variable. Factorl!! 

which influence spin rate s election are as follows: 

• 

• 

Desired resistance to exterior torques 

(attitude correction frequency) , 

Required containment of motor thrust 

malalignment and axial jet offset 

• Desired stiffness during possible payload slewing maneuver s 

• Wearout life of bearings, brushes, and 

sliprings 

• Energy required to create lnOlnentum 

(weight) 

Depending on the lnission, the lninilnUIn acceptable spin rate is from 5 to lO rpm. Normally 60 

rpm satisfies all objectivel!l. Wearout life of the 

rotating assembly then is measured in tens of 

years. 

With a lnOmentUIn of isoo to 2400 ft-lb-sec, 

the system is quite stiff. For high altitude lnissions, the largest exterior torque is due to solar 

pressure unbalance. Large systeln designs present average capture areas of the order of 200 tt2. 

The resultant solar thrust is about2xlO-Spounds • 

.An attelnpt is lnade to lninilnize the distance 

between the av.erage thrust center and the center 

of lnass. However,.a residual moment ar:m. of 2 

feet usually results. Hence, the drift rate induced 

is about 0.10 deg/day. Without correction, the 

attitude drift is in the forln of a coning motion 

with a yearly period and lnaximUIn amplitude of 

13 degrees. The drift over a spin cycle (one 

second) is less than 0.003 arcseconds. The 

nutation about this precession is of the same 

order. Short-terln pointing stability is thus not 

lilnited by the rotor momentuln capacity. 

In missions that can tolerate a O. 5-degree 

pointing error, the drift is corrected weekly and 

the attitude is biased so that during the week the 

drift goes from +0. 5 to -0.5 degree. For an 

absolute pointing accuracy of 10 arc seconds, a 

correction pulse every half hour is required. 

After drift calibration, maneuvers can be programmed onboard. 

As an exalnple of payload slewing effects J 

consider rotating a 10-foot diameter des pun 

antenna 17 degrees (fro= the south pole to the 

north pole) in 1 minute. A typical antenna weighs 

30 pounds including the feed and has an elevation 

inertia of about 10 slug-ftZ. The wobble or precession alnplitude caused by the slewing is less 

than 0.002 degree. To decrease this effect an 

order of lnagnitude, a lO-minute tilne to cross 

the earth could be selected. Thus, reasonable 

lnass lnotions on the despun platforln are well 

contained by the rotor mOlnentUln. 

Total weight of a cold gas blowdown s ys t em 

required for initial spin up is about 20 pounds, 

not unreasonable in a nominal 1500-pound design. 

Reaction J et Sys teln Sizing 

Reaction jet systeln sizing consists of selecting jet thrus t lnagnitudes and det erlnining the 

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amount of propellant required for velocity and 

attitude control. 

To precess the system 1 degree with an axial 

jet at a nommal5-foot moment arm requires an 

8-lb-sec total impulse. For the Titan clau 

design. l500 pounds, this may be expressed as 

an equivalent tN of 0.16 ft/sec/deg. To correct 

attitude drifts at the rate of 0.10 degree/day then 

requires about 6 ft/ sec/year. This velocity 

increment is roughly equal to that required for 

in-plane stationkeeping in synchronous orbit, 

7 ft/sec/year. (The velocity increment required 

to prevent orbit north-south precession is much 

larger at about 180 ft/ sec/year.) Residual velocity errors at orbital injection are usually measured in hundreds of feet per second. Thus. even 

including spare attitude maneuver capability, 

attitude control requirements are small relative 

to velocity requirements. 

J.et thrust level is governed chiefly by attitude correction resolution requirements. For 

normal missions, a 5 -pound axial thrust at 5 feet 

suffices, giving a 0.03-degree-per-pulse resolution. For missions with a lO-arcsecond absolute pointing requirement, O.l-pound thrust is 

needed at the 5 -foot moment arm. Higher thrust 

levels could be used at lesser moment arms. In 

practice, a precision system might have large 

axial and radial jet thrustors for velocity control 

and a small additional axial jet for precision 

torquing. In any event, thrust size presents no 

special difficulty arid common propellants may be 

used. 

A detailed description" of a typical system is 

presented in Reference 7. 

Platform Wobble 

This discussion presents sources of platform 

wobble and preliminary analyses intended to 

illustrate the feasibility of precision designs. 

Attention is focused on wobble due to unbalance, 

malalignment. imperfection of the rotating interface, and thermal deformation. 

In essence, the platform is a stationary body 

to which a rotor is attached. Upbalance and malalignment of the rotor (Figure 9) cause wobble 

amplitude given by/' 

where 

Ixz = rotor product of inertia 

m = rotor mass. 

(4) 

£ = rotor center of mass displacement 

from total system center of mass 

x = rotor center of mass deviation 

from spin axi s 

~OTOR PIIODUCT--..,... .. ROTOR CENTER 

OF MASS OF INERTIA 

IMPERFECT 

ROTATING INTERFACE ---l------e+:l 

PLATFORM 

Figure 9. Platform Wobble Forces 

Equation 4 is understood in terms of balancing 

procedures by noting that the torque measured 

with a rotor balancing machine is 

where 

torque ::: (~z + mx h) 0 2 

f.I = rotor spin rate during balancing 

h = rotor center of mass height above 

balancing machine torque reading 

instrumentation 

For rotors less than 3000 pounds, spinning at 

100 rpm, commercial equipment has a torque 

sensitivity of 0.2 ft-lb. which is equivalent to 

2 x 10-3 slug-ft2 of unbalance. 

Assuming the rotor center of mass displacement from the satellite center of mass is equal 

to the rotor center of mass height above the 

balancing table transdUcers, the residual unbalance results in 

For the Atlas Agena class. 

e ~ 1.2 arc seconds 

For the Titan class, 

e < 0.3 arc second 

Another source of platform wobble is shaft 

runout in the rotating interlace. Due principally 

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to ball asymmetries and bearing race ellipticity. 

the center of rotation of a ball bearing is not fb;ed 

with respect to the outer housing. In bearings 

suited for precision application (typically 4-inch 

ball bearings) the center of rotation deviation is 

less than 20 x 10-6 inches. (This value is quoted 

as a nonspecia1 tolerance by bearing manufacturers. With special ball selection procedures. it can 

be held to Sx 10-6 inches.) For a bearing pair 

spaced 10 inches apart. this effect will caUSe runout of the order of 1 arcsecond. Manufacturing 

tolerance and alignment error buildups will also 

contribute to runout. A prototype rotating assembly was fabricated and SUbjected to vibration 

testing. Measurements were then made. The 

assembly demonstrated runout of the order of 3 

arcseconds. 

Due to thermal gradients within the rotol', 

balance and aligrunent are affected once in orbit 

(Figure 10). To illustrate the effect of thermally 

induced structural deformation, a sinlple model is 

analyzed. The rotor is assumed to be a hollow 

aluminum cylinder, 10 feet long and 10 feet in 

diameter. A constant temperature gradientof2.S" C 

is assumed to exist across a diameter. (A 2.5 0 C 

gradient is a conservative upper bound fOr a rotor 

designed with minimization of internal gradients ~) 

The effects of the gradient are as follows: the 

center ofmass is displaced from the shaft axis, and 

inertial symmetry about the axis is destreyed. The 

unbalance torque seen by the platform is 

The wobble is ,correspondingly given by 

(IR - ITR) V + mH 

e 1!! .....:;~-.;...:.:.::--::----

IR - IT 

\- LIT ·1 

I 

I 

I ROTOR 

-1 ., SHIFT 

... I 

Figure 10. Rotor Deformation Due to 

Radial Thermal Gradient 

\ 

(5) 

(6) 

where 

I.jJ = eHective rotation of rotor prinCipal 

axis from shaft axis 

m :: rotor mas s :3! 15 slugs 

£:, :: rotor mass displacement 

i. = rotor mass axial distance from configuration center of maSS:3! 1 foot 

The quantities £:, and I.jJ are given approximately 

by 

where 

K = coefficiect of thermal expansion :: 

30 x 10- inch/inch/oC 

AT ::: thermal gradient 

D :: rotor diameter :3! 10 feet 

L :: rotor length :3! 10 feet 

The wobble induced is 1.7 arcseconds for the 

• 

Agena design and 0.4 arcsecond for the Titan design. 

The rotating interface will also experience 

thermal gradients. Due"to the relative compactness of this unit, the gradient it experiences 

is small and its distortion does not cause significant malalignrnent or increase in bearing 

loading. This assertion has been checked in a 

vacuum thermal test using a prototype unit. 

Structural relaxation in 0 g is computed to be 

less than the thermal effect for typical rotor constructions. (The l-g relaxation is small relative to 

the 5 -g centrifugal load which exists during balancing 

as wellas in-orbit. Further. relaxation is axial and 

does not tend to distort radial symmetry. ) 

Care in matching propellant tank volu:mes 

and tank locations is required. Errors in tank 

location and differences in tank volume s cause 

unbalance with fluid utilization. Figure 11 

illustrates mal aligned, mismatched tank geometry. 

Asswning that deviations from nominal parameters are uncorrelated, the center of mass of a 

fluid in these tanks after a wet balancing procedure deviates from the spin axis an amount 

given by 

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Reasonable errors after careful tank. selection 

are 

5R :::: 0.001 inch, ElL 0.001 inch 

about the following nominal values 

Ro :::: 12 inches, Lo :::: 24 inches 

The fluid center of mass deviation is thus 

d ;l! 4 x 10- 3 inches 

For a nominal initial propellant load of l7 pounds 

per tank, the mass unbalance which exists after 

propellant is totally expended is 2 oz-in. 

Typical tank center of mass separation from the 

configuration center of mass is 3 feet, with a 

resultant mass unbalance of 10- 3 slug-ft2 , 

or wobble of 0.6 arcsecond for the ATLAS design 

and 0.15 arc second for the Titan design. Rotor 

inertial asymmetry due to this effect caus es an 

order of magnitude less wobble. 

Platform Despin Control and.Calibration 

The purpose of previous computations was to 

demonstrate the dynamic character of typical 

.larg.e systems. To the several arcsecond level, 

the rotor induc es no significant platform wobble. 

Further, momentum is so large that attitude 

drift rate is extremely small. 

Working on such a stable base, platform 

despin control can be effected to quite precise 

limits. In the stady-state condition, the principal function of a servo loop is to keep the r elative rotation between rotor and platform constant. 

As in the case of wobble, the large inertias 

involved make this a relatively easy task. The 

principal disturbance affecting loop performance 

is drive motor and friction torque fluctuations. 

_______________ ~=============;-ROTOR 

I" SPIN AXIS 

WHERE 12 Z RO + n 

L

2 -Lo+U 

Figure 11. Mismatched, Malaligned 

Tank· Geom etry 

ROTOR 

eg PLANE 

Measurements with a prototype running at 55 rpm 

indicate that torque fluctuations are less. than 

0.025 ft-lb with frequencies greater than spin 

rate. Typical platforms with inertias of lOO to 

200 slug-ft2 respond with less than 2-arcsecond 

jitter amplitudes to thes e fluctuations even if they 

were at spin-rate. 

Although pointing stability to the 5 -arc second 

level is readily achieved, static pOinting errors 

less than 0.02 degree are difficult to realize even 

with the star scanner. The principal limitation is 

system alignment. For missions which require 

precise absolute pointing, in-orbit calibration and 

adjustment is planned. 

Here, "the payload itself is used. Since optical payload (including many 1R devices) can 

detect stars, natural calibration sourCes are the 

knowr: star targets beyond the earth horizon. By 

slewing the platform away from the earth into the 

sta r field. it is found that at mos t wavelengths, 

dozens of stars can be detected in a single day. 

By comparing attitude determination system data 

with calibration data, malalignments and their 

variation can be determined and corrected through 

commanded adjustment of servo-loop parameters 

and the jet thrusting programmer. RF pa.·yload 

can be us ell for calibration by scanning :!<hown 

ground-based transmitters or receivers. In 

either case, system absolute pointing accuracy 

can normally be calibrated to the resolution of 

the payload requiring the accuracy. 

IV. CONCLUDING REMARKS 

We have attempted to stress several features 

of Gyrostat systems. Any size payload can be 

carried. By virtue of inertia and momentum, 

exceptional stabilization is afforded. And, using 

a relatively simple sensor, payloads can be 

pointed with extreme accuracy after in-orbit 

calibration and adjustment. 

No active elements of the system are novel. 

The rotating interface, including motor drive, is 

patterned after OSO systems which have neither 

failed nor degraded in nearly 3 years of accumulated orbital life. The spinning reaction jet 

system concept has been used successfully on all 

Hughes satellites. The star-sensor phototube is 

similar :1:0 that still operating as a spinning 

meteorological camera on ATS-I. (Even the 

balancing equipment sensitivity cited was realized 

in the ATS program. ) 

Combined with the ability to use the passive 

thermal control concept and spinning power systems which have functioned perfectly in 10 years 

of accumulated Sync om family life, the Gyrostat 

system is believed to be inherently tnore reliable 

than any systetn yet advanced with comparable 

performance potential. 

REFERENCES 

(1) W. T. Thomson and G. S. Reiter, "Attitude 

Drift of Space Vehicles," Journal of Astronautical Sciences, Vol 7, 1960, pp. 29-34. 

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(2) 

(3) 

(4) 

• 

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V. D. Landon and B. Stewart, "Nutational 

Stability of an Axisymmetric Body Containing a Rotor," J. Spacecraft and Rockets I, 

(1964) pp. 682-684. 

A. J. 10 rillo. "DevelopITlent of Hughe s' Gyrostat SysteITl," Hughes Aircraft Company 

SSD 70012R, January 1967. 

H. Perkel, "Stabilite, A Three Axis Attitude Control Syste= Utilizing a Single Reaction 

Wheel, AIAA Paper No. 66-307, May 2 

. through 4,. 1966. 

(5) "Precision Capability of Hughes' Gyrostat 

Systems," Hughes Aircraft Company SSD 

70045R, February 1967. 

(6) J. R. VelITlan, "Attitude Dynamics of DualSpin Satellites. " Hughes Aircraft Company 

SSD 60419R, September 1966. 

(7) R. J. McElvain and W .. W. Porter, "Design 

Considerations for Spin Axis Control of 

Dual-Spin Spacecraft. " presented at the 

Sy=posiu= on Attitude Stabilization and Control of Dual-Spin Spacecraft, EI Segundo, 

California, 1-2 August 1967 . 

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