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

2. Spin stabilization H   H X Y Z

3. Single Spinners
Dual Spinners

4. x y z,p H  x y z x y z H, ,p H  Pure rotation Conning Nutation
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 x y
z,p H  x y z x y z
H, ,p H 
Pure rotation
Conning
Nutation

5. Torque-free motion dm x y z O

6. Spin stabilization with passive/active control

7. 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

8. Where 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.

9. 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)

10. 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.

11. ATS-5 Satellite

12. Examples of Flexibility and/or Dissipation Effects
Year
Satellite
Control
System
Adverse
Effect
Probable
Cause
1958
Explorer I
Spin
Stabilized
Unstable
Internal Energy
dissipation
1952
Alouette
Rapid Spin
Decay
Solar Torque on
Thermally Deformed
1964
Explorer XX
1969
ATS-5
Spin Stabilized
with active
Nutation Control
Dissipation

13. Momentum precession and spin thrusters locationsF R

14. SACI-1: Spin Stabilized with Geomagnetic Control
Nutation Damper
Torque
coil

15. SCD-1: Spin Stabilized
Partially Filled Ring Nutation Damper
Torque Coil

16. SACI-2 Spin stabilized with geomagnetic control Partially filled ring
Nutation Damper
Spin plane coils
Nutation damper

17. Mathematical model: Satellite With a Partially Filled Ring
Nutation Damper to Prevent Nutation Motion

18. Computer Simulation HT H Hx Hy Hz  x y z

20. 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