The possibility of using electrodynamic forces to control pendular oscillations during the retrieval of a subsatellite is investigated. The use of the tether for transferring payloads between orbits is studied

Arnold, D. A.

Colombo, G.

Dobrowolny, M.

Grossi, M. D.

English

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INVESTIGATION OF ELECTRODYNAMIC STABILIZATION AND 
C~WS~ROL @F LON6 ORBITING TETHERS 
Contract NAS8-33691 
Interim Report 
For the period 1 March 1980 through 31 August 1980 
Principal Investigator 
Dr. Giuseppe Colombo 
(IASA-CR-161584) INVESTIGATION O F  N80-3.374 8 
ELECTRODYYAHIC STABILIZATION A N D  CONTROL OF 
LONG ORBITING TETdERS I n t e r i a  Heport ,  1 
Mar. - 31 Aug. 1980 ( S a i t h s o n i a n  Unclas 
Astrophysical Observatory) 8 p ~ ~ * ~ o r l N f * ~ 0 ~ ~ 3 , 3 1  2901 9 
August 1980 
Smi thsonian Insti tution 
Astrophysical Observatory 
Cambridge, Massachusetts 02138 
are members o f  the 
Center for Astrophysics 
I h iy RECEIVED 
N ' - NASA SII FACILITY, Efi ACCESS Dm. .b 
INVESTIGATION OF ELECTRODYNAMIC STABILIZATION AND 
CONTROL OF LONG ORBITING TETHERS 
Contract NAS8-33691 
Inter im Report 
For the period 1 March 1980 through 31 August :986 
Principal Investigator 
Dr. G i  useppe Co1 ombo 
Co-Investiqators 
Dr. Mario D. Grossi 
Dr. Marion Dobrowol ny 
M r .  David A.  Arnold 
INVESTIGATION OF ELECTRODYNAMIC STABILIZATION AND 
CONTRM OF LON6 ORBITING TETHERS 
Interim Report 
Introduction 
This report covers work done during the period 15 February 1980 through 
15 August 1980. During the f i r s t  h a l f  o f  t h i s  period an investigation was done 
on the poss ib i l i t y  o f  using electrodynamic forces t o  control pendular osc i l la -  
t ions during the re t r ieva l  o f  a subsatell ite. During the l a s t  ha l f  o f  the period, 
work was shi f ted to studying the use o f  the tether f o r  transferr ing payloads 
between orbits. Detafled resul ts o f  the re t r ieva l  study a n  presented i n  Monthly 
Progress Report No. 5-7 and resul ts on the launcher study are given i n  Monthly 
Reports No. 8 and 9. This report contains a sumnar: o f  the work done on each 
project during the l as t  s i x  months. 
Study of Electrodmmlcal lu Control 1 lna Tether Q c i  1 la t ions Durina Retrieval 
- 
I The heur ist ic  study o f  using electrodynamic forces t o  control tether 
osci l lat ions was done wi th a small computer program tha t  integrates the in-  
$lane ( 9 )  and out-of-plane ( 4 )  angles vs. time using expressions va l id  for 
small angles. To study re t r ieva l ,  the general equations o f  motion including 
I 
t the radia l  variable r e r e  derived and added to the program. The integrat ion 
, 
of the rad ia l  variable can be done using e i ther  a tension o r  a ra te  control law. 
I There i s  strong coupling between the rad la i  variable and the in-plane angle 
t because the in-plane angular velcci ty I s  para l le l  t o  the o rb i t a l  angular veloci ty b which i s  always i n  the same direct ion and nearly constant i n  magnitude. This 
f allows good control o f  the in-plane behavior using tension or  ra te  control laws. 
, I 
f The pr inc ip le  problem i n  re t r ieva l  i s  control o f  the out-of-plane angle since 
the coupling between the rad ia l  and out-of-plane variable i s  weak. The study 
used electrodynamic forces t o  control the out-of-plane angle and a rate control 
law t o  control the i n-plane angle. The rate control law consisted of three 
terms; a term proportional t o  the rad ia l  distance which would maintain a 
constant re t r ieva l  angle i n  the absence of any perturbations o r  out-of-plane 
osci l lat ions; a damping term t o  reduce any osc i l l a t i o r r  of the in-plane angle; 
and a restoring term t o  keep the in-plane angle near the desired re t r ieva l  
angle set by the f i r s t  term. The restoring term was included t o  counteract 
atmospheric drag which becomes increasingly important as the tether length 
decreases. Decreasing the tether length causes a cor io l  i s  acceleration which 
i s  t o  the rear f o r  downward deployment, and i n  the forward directfor, for up- 
ward deployment. I n  order t o  counteract drag, the restoring term must decrease 
the re t r ieva l  rate f o r  downward deployment, and increase the re t r ieva l  rate for 
upward deployment. I n  runs done f o r  downward deployment, the restoring term 
hal ts the re t r ieva l  a few hundred meters from the Shuttle. For the up~ard  
deployment case, drag can be counteracted longer, but the dynamics eventually 
becomes unstable. For e i ther case, a l ternat ive techniques w s t  be used to 
control the subsatel l i te close t o  the Shuttle. Reasonable values of current 
i I n  the wire (a f rac t ion o f  an ampere) appear t o  be capable of control 1 ing the 
t 
1 out-of-pl ane osc i l  lat ions i n  an i n c l  ined orb1 t. Special considerations apply 
r 
I 
i t o  equatorial orb i ts  o r  orb i ts  passing near the magnetic pole. 
t 
i 
i 
f 
t Study of Using the Tether f o r  Transferrina Payloads Between Orbits \ .  
As requested by the NASA program Mnager the continuatioil phase o f  t h i s  
contract dealing w i  t h  the use o f  the tether as a launcher was begun imnedi a te ly  
I 
upon receipt o f  the contract extension. The study o f  tether dynamics resul t ing 
from electrodynamic control has been postponed u n t i l  a f t e r  the 1 auncher phase. 
The f f r s t  task addressed was the inclusion i n  the Skyhook program o f  a thruster 
mbdel f o r  accelerat ir~g the subsatel 1 1 te. It was decided t o  i nc l  ade thrusters 
i n  the direct:ons o f  tk. Inl-plane angle ( 0 )  the out-of-plane angle ( 4 )  and the 
radial  variable ( r ) .  This choice allows convenient study o f  in-plane and out- 
o f  -plane launches. The radial  thruster was included f o r  generality. A f a c i l  i t y  
has been added t o  the program f o r  specifying the three thrust components during 
two time periods t o  allow f o r  aczeleration and deceleration o f  the subsatel l i tc. 
Various tes t  runs have been done wi th the program t o  gain an understanding 
o f  the dynamics o f  the system, par t icu lar ly  when the subsatell i t e  i s  accelerated 
by thrusters. One of  the most important problems that  needs t o  be studied i s  
potential  i n s tab i l i t i e s  or  breakage o f  the tether. The in1 t l a l  e f fo r t s  have 
concentratcd on developing theoretical models and approxinate analyt ical formu! as 
f o r  describing the behavior o f  the system. 
One possibility for avoiding large ten$ ions in the wire when thrusters 
are used is to fire the thruster in such a direction that the wire goes sltck. 
Unfortunately, the Skyhook program is not well suited to studying a slack tether 
because the wire is represented by a set of discrete points. Whiplaah effects 
are artifical ly exaggerated as discrete points come into tension. 
There are various motions of the tether-subsatel.lite system that result in 
variations of wire tension, such as transverse wire oscil lations, long1 tudional 
oscillations cf the subsatellite at the end of the elastic tether, and rotational 
motions of the wire and subsatellite about the Shuttle resulting in coriolis 
forces. All of these motions can be excited by the use of thrusters on the 
subsatellite. The natural frequencies of the motions will depend on the system 
parlatneters. Approximate analytic expressions have been derived for the tension 
variations resulting from these three types of motion. The values calculated 
from these formulas are being compared to the ciata obtained in the test runs of 
the Skyhook program for various cases. 
Transverse wire oscillations cause tension variations by changing the 
distance between the ends of the wire so tnat there is a radial acceleration of 
the subsatel 1 i te. The analytic expression assumes that the tension variations 
are small compared to the total tension. Stretching of the wfre is also ignored. 
and the period o f  longitudinal oscil1ations of the subsatellite at the end of 
the elastic wire is small compared to the period of the transverse wire oscilla- 
tions. Another approach has also been used to understand the tension variations 
particularly when the transverse oscillations are large. A small program has 
been written to compute the radial acceleration of the subsatell ite by numerical 
differentiation of the output data from the Skyhook program. This makes it 
possible to identify how much of the tension variations is from wire dynamics 
and how much is due to coriol is forces. 
4. 
1 r 
i i * i The fol lowing approximate expression f o r  the wire tension has been obtained 
t by simplifying the general equation of motion f o r  the rad ia l  var iable. 
. . 
'r -T a m(; -3mrt2 -r;2 - r e 2  -2rey) 
I f  r. e, and 4 are constant. the e q u i l i b r i u n  tension i s  T = hrCz where C 
i s  the o r b i t a l  angular veloc I ty.  In-plane and out-of-plane 1 aunches d i f f e r  
because of the l a s t  term which causes the tension LO be la rger  for in-plane 
launches. The e f fec ts  o f  transverse wire o s c i l  l a t i ons  o r  long1 tudinal  osci  1 l a -  
t ions  o f  the end mass show up as rad ia l  accelerations r. 
I n  a long te ther  the c o r i o l i s  forces are smaller for  a f i xed  l i n e a r  ve loc i t y  
because the angular ve loc i ty  i s  smaller. The dynamic range o f  tension var iat ions 
i s  smaller f o r  the above reason plus the f a c t  t ha t  the equi l ibr ium tension i s  
larger.  I f  the accelerat ion and deceleration occur over a f i xed  distance, the 
angular amp1 i tude of the induced transverse w i re  o s c i l  l a t i  on decreases w i th  wire 
lenqth. An addi t ional  problem i n  short  tethers i s  t ha t  a f t e r  deceleration o f  
the subsate l l i te ,  there i s  l i t t l e  remaining tension i n  the wire t o  res t ra in  the 
forward movement o f  the wire. 
When a payload i s  released from the end of a tether,  the system i s  no longer 
i n  tension equil ibrium, so tha t  the remaining mass reco i l s  t o  an extent determined 
by the r a t i o  o f  the masses before and a f t e r  release. The reco i l  could be avoided 
by having the subsate l l i te  release some wire a t  the launch po in t  whi le keeping 
the tension a t  the equi l ibr ium value fo r  the remaining mass. Jn t h i s  way the 
energy stored i n  the stretched te ther  i s  absorbed by the subsatel 1 i t e  i n t e r n a l l y  
instead o f  being converted t o  k i n e t i c  energy. Such a system i s  i n  e f f e c t  a 
damper. A damper w i th  a 1 inear res tor ing  force and ve loc i t y  dependent f r i c t i o n  
would also absorb the energy, but less e f f i c i en t l y .  There could be loss o f  
tension i n  the wire. Depending on the propagation ve loc i t y  f o r  stress along the 
f 
i. wire, the wlre tenslon could also be rel ieved a t  the Shuttle end o f  the system. 
Also, a tension control law could perhaps be used f o r  cont ro l l ing other problems 
such as 1 arge amp1 1 tude transverse wlre o s c i l l  ations. 
I n  the standard Skyh.~., *ware package, the connection between each mass 
point i s  modelled as a spring wi th a l inear  stress-strain relat ionship and a 
damping force proportional t o  the ra te  o f  change o f  distance between the mass 
points. The damping coef f ic ient  f o r  each wire segment fs  specified on input. 
The only exception t o  t h i s  model occurs during daployinent and re t r ieva l  when the 
tension between the Shuttle and the nearest mass polnt i s  specified by control 
laws, Some program modifications would be necessary i n  order t o  implement 
special control laws a t  e i ther  end o f  the wire. 
The development o f  modcls and approximate analyt ical formulas f o r  describing 
the dynamics o f  the system i s  continuing a t  the present t ime.  The form~las are 
compared t o  resul ts o f  tes t  runs wi th the Skyhook program. These models and 
formulas w i l l  be used f o r  designing systems and specifying system parameters 
f o r  performing various types o f  launches. 


Investigation of electrodynamic stabilization and control of long orbiting tethers

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