State Equations for a Spacecraft With Maneuvering Flexible Appendages in Terms of Quasi-Coordinates

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Abstract
This paper is concerned with the derivation of the state equations of motion for a spacecraft consisting of a main rigid platform and a given number of flexible appendages changing the orientation relative to the main body. The equations are derived by means of Lagrange’s equations in terms of quasi-coordinates. Assuming that the appendages represent distributed-parameter members, the state equations of motion are hybrid. Moreover, they are nonlinear. Following spatial discretization and truncation, the hybrid equations reduce to a system of nonlinear discretized state equations, which are more practical for numerical calculations and control design. To illustrate the effect of nonlinearity on the dynamic response during reorientation, a numerical example involving spacecraft with a membrane-like antenna is presented.

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