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

Spin stabilization H   H X Y Z

Single Spinners Dual Spinners

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

Torque-free motion dm x y z O

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

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.

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 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

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 Partially filled ring Nutation Damper Spin plane coils Nutation damper

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

Computer Simulation HT H Hx Hy Hz  x y z

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