Abstract
We derive the dynamic equations of attitude, orbit and flexible modes of a generic satellite. We will follow the Lagrangian approach, and the equations will be set in a form specifically suitable for attitude and orbit control. After the derivation of the flexible body Lagrangian equations we treat some specific complements that are useful for space applications: momentum management systems, generalized forces due a central gravitational field, first invariants of motion in a central gravitational field, transformations to uncouple orbital and attitude equations and methods to linearize the equations around a reference orbital and attitude trajectory. We close the chapter by presenting a typical linear model of a flexible satellite as used in practical linear control engineering design.
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