Libration

Vibratory motion superimposed upon locked rotatory motion of a satellite is called libration. In order to obtain a basic understanding of the libration behavior of satellites, we shall investigate a few simple special cases. Because it exhibits strong sensitivity to the gravity gradient, among all possible satellite configurations, we select a one-dimensional rod satellite, with an inertia tensor of, say,(3.1)$$\left[ I \right] = \left[ {\begin{array}{*{20}{c}} 0 & {amp;0} & {amp;0} \\ 0 & {amp;B} & {amp;0} \\ 0 & {amp;0} & {amp;B} \\ \end{array} } \right]$$ We assume that the satellite is very small, i.e., $$B \ll m\rho_C^2$$.