# SPIN STABILILIZATION by chenmeixiu

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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
axis rule for spin stabilization.
ATS-5 Satellite - 1969
Examples of Flexibility and/or Dissipation Effects

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

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