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SPIN STABILILIZATION

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					                 SPIN STABILILIZATION

1. INTRODUCTION                                Z
•Dynamics, Astrodynamics
                                                           z
                                                   x
    •Orbital Dynamics, Attitude Dynamics
•Basic terminology
    •Attitude                                              y
                                           X           Y

            y    Y
      Z
                  z
                        X
x
•Spin stabilization       H
                      

   H
   




                                  Z



                              X       Y
Single Spinners   Dual Spinners
2. The Euler’s Moment Equations
 •Rigidy body dynamics: rotational motion in space
   •Torque-free motion
   •Reference systems:
    •geometrical
    •Angular momentum axis
    •instantaneous rotation axis
    •principal axes


          z H                                       H
                                   H, ,p            


x              y
    Pure rotation         Conning                    Nutation
                             z

                                 dm
                         O

                     x                y




Torque-free motion
Spin stabilization with passive/active control
 Major Axis Rule for Spin Stabilization

 •Stability of rotation about principal axes
 •Consider the the perturbed the steady motion given
 by the Euler’s moment equation for torque-free motion:




Differentating w.r.t. time
and eliminating
Differentating w.r.t. time
and eliminating




Both of these equations represent simple harmonic oscillator
with general solution:

Where

If  is imaginary j will diverge andis unstable.  must be real for
stability. This is satisfied when (Ix-Iy)(Ix-Iz) > 0 . Motion is stable
when Ix>Iy e Ix>Iz or when Ix<Iy e Ix<Iz
Conclusion: motion is stable about major or minor axis but motion
about intermediate axis is unstable .
Internal Energy Dissipation Effects

All real spacecraft have, at least, some nonrigid properties.
These include: elastic structural deflection and sloshing.
Some lessons learned from the past:
• Explorer I (1958)
  Energy dissipation




Since for torque-free motion the angular momentum must be
conserved motion about the major axis corresponds to the
minimum energy state. Conclusion: a semirigid body is stable
only when spinning about the major axis, bringing about the major
axis rule for spin stabilization.
ATS-5 Satellite - 1969
       Examples of Flexibility and/or Dissipation Effects

                      Control            Adverse        Probable
Year    Satellite
                      System             Effect         Cause
1958    Explorer I     Spin              Unstable     Internal Energy
                       Stabilized                     dissipation
                       Spin             Rapid Spin  Solar Torque on
1952     Alouette
                       Stabilized       Decay       Thermally Deformed
                                                    Satellite

1964   Explorer XX    Spin              Rapid Spin Solar Torque on
                      Stabilized        Decay      Thermally Deformed
                                                   Satellite
                     Spin Stabilized                 Internal Energy
1969    ATS-5                            Unstable
                     with active
                                                     Dissipation
                     Nutation Control
Momentum precession and spin thrusters locations



                F
                    R
  SACI-1: Spin Stabilized with Geomagnetic Control
                                        Nutation Damper

Torque
coil
SCD-1: Spin Stabilized
Partially Filled Ring Nutation Damper
Torque Coil
SACI-2

Spin stabilized
with geomagnetic
control
                                      Nutation damper
Partially filled ring
Nutation Damper




                   Spin plane coils
Mathematical model: Satellite With a Partially Filled Ring
Nutation Damper to Prevent Nutation Motion
                      Computer Simulation



         z
    Hz


         
                  H



    Hy
                      Hx

x            HT
                           y
Conclusion

Directional Stability: inertial pointing
Gyroscopic properties of rotating bodies
Major axis rule: rigid body are only idealizations
Single and Dual Spinners
Nutation Dampers: passive and active
Spin stabilization combined with active control