General Dynamics for Single- and Dual-Axis Rotating Rigid Spacecraft Components

Deriving and propagating a spacecraft's equations of motion is fundamental to describing its behavior accurately. These equations of motion depend on the spacecraft's configuration, which includes any physical subsystem such as attitude control devices, solar panels, gimbals, etc. Prior work introduced the backsubstitution method to yield a modular and scalable formulation to develop complex spacecraft dynamics specific to rotating components attached to a rigid hub as effectors. This paper relaxes assumptions made in deriving effector components in prior work, such as mass properties and frame definitions. This produces a general architecture that uses common equations of motion for physically equal parts. The result is an analytical solution of a set of general rotating effector equations of motion that greatly expand the configuration space of spacecraft that can be simulated with the backsubstitution method. In contrast to prior work where the rotations are highly constrained, rigid-body components can rotate about one or two general axes, and the component mass distribution can be general, no longer requiring the component's principal axis to align with the center of mass or hinge axis. A numerical software solution demonstrates and verifies how these effectors can mimic a range of dynamic spacecraft components.