Gravity Gradient - Stability Conditions, Frequencies, Torque Equilibrium Angle, Space Station

This lecture examines gravity-gradient attitude stability for spacecraft using Euler rigid-body equations and small-deviation approximations. It covers pitch, roll, and yaw stability, torque equilibrium angles, oscillation frequencies, environmental torques, and application to the International Space Station.

Syllabus

Space Vehicle Dynamics Lecture 26: Gravity gradient, part 3. Euler rigid body equations with gravity gradient torque. Dynamics in terms of Euler angles, in small deviation approximation. ☞ CORRECTIONS: Should be ^4 in last term at 26:00, should be ^2 under square-root at .
Summary of gravity gradient attitude equilibrium.
Euler equations with gravity gradient torque.
Dynamics in terms of Euler angles, in small deviation approximation.
Condition for stability in pitch.
Space environment forces and torques.
Torque equilibrium angle (TEA).
Roll and yaw conditions for stability.
Oscillation frequencies in roll and yaw.
Gravity gradient stability chart.
Condition for gravity gradient stabilization.
Application to International Space Station (ISS).