On dynamic stiffness of spacecraft flexible appendages in deployment phase

Deployment inertial effects of a spacecraft appendage on its flexible dynamics are investigated. The Euler-Bernoulli beam theory and the actual deployment profile, in which appendage axial motion accelerates from static state and then decelerates to end at zero velocity and acceleration, are employed. The study is concentrated on the arm dynamic stiffness introduced by inertial effects of the arm deployment, and the resultant effects on the arm flexible motions. Lagrange's equations and some appropriate shape functions in the series approximation method are employed to study the arm lateral elastic displacements. Finally a system of ordinary differential equations with time varying coefficients governing the system dynamics is developed. Solving the equations of motion reveals the importance of dynamic stiffness effects in precise positioning of appendages tip-payloads. The results indicate that the effects of deployment dynamic stiffness, however, vary significantly with the payload mass and arm deployment time. This investigation can help designers to understand in-depth the effects of axial inertial forces during arm deployment for trajectory planning and designing efficient deploying profile to increase the performance of the control devices.