Orbital Dynamics in the Gravitational Field of Small Bodies by Yang Yu

Author:Yang Yu
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

3.3 Stability of the Equilibrium Points

This section checks for the stability of the equilibrium points in the body-fixed frame Oxyz, or that of the stationary orbit in the inertia frame . Defining the position vector of arbitrary equilibrium point , the state of disturbed equilibrium point is , , and the disturbed form of motion equation near the equilibrium point is

(3.6)

where is the gradient matrix of gravity, is the skew-symmetric matrix of the angular velocity vector , defined as

(3.7)

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