Dynamics of satellites during deployment and retraction of flexible appendages

This thesis investigates the dynamical behavior of spinning and/or axially moving beams.An analysis of the effect of appendage root offsets (distance between the mounting point and system center of mass) on the dynamics of constant length spinning appendages is carried out. The stability and response characteristics of the system configuration are investigated taking into account the role played by the non-linear axial shortening effect, when the system is undergoing a steady spin, spin-up or angular slew maneuvers. It is observed that due to the root offset, large static deflections of the beams may result during steady spin of the system. Stability of elastic oscillations around non-trivial steady state configuration is examined and it is seen that, the axial shortening effect increases the stiffness during rotation. A positive offset along the beam causes similar effects on the stiffness matrix increasing the natural frequencies of vibrations. On the other hand, angular acceleration has a destabilizing effect. This destabilizing effect vanishes in the absence of offsets and is greater for larger offset. At some critical value of angular acceleration the frequency becomes zero for a given offset; beyond that the appendage buckles. Also the stability regions in the spin rate-spin acceleration plane are obtained.The axially moving beams may represent appendages in the process of deployment (retrieval) from (into) a spacecraft or a prismatic joint in a flexible manipulator. It is shown analytically that when the length L changes, the transverse vibrations vary, in general, as L$ sp{1/2}$. Thus, the vibrations increase during extension and reduce during retraction. This is in sharp contrast to vibrations of tethered systems which vary as L$ sp{-1/4}$, hence, decrease during deployment and increase during retrieval. The vibratory displacements, in addition to depending on the length, also depend on the type of extension (or retraction). The dynamical behavior for various deployment (retrieval) schemes--uniform deployment rate, exponential extension, uniform variation of the square of the length and harmonic extension is studied. It is seen that uniform and exponential extension lead to larger vibratory displacements compared to the other two schemes. An optimal deployment scheme is devised. It is noted that the optimal scheme is far superior to the uniform or exponential scheme, but has only marginal advantage over harmonic extension or uniform variation of the square of the length. Harmonic extension is recommended, since in this scheme, the axial velocity changes reasonably slowly and is zero at the end of deployment