This thesis pioneers the application of nonlinear dynamics to spacecraft power systems. Two areas of general interest are addressed. On the one hand, the fundamental dynamics of space power systems were investigated from a nonlineax dynamics perspective, and on the other, nonlinear dynamics concepts were used to realise a practical engineering application. The former examines four simple but relevant space power system models. The study revealed a variety of bifurcations, coexisting attractors and chaotic behaviour that could potentially shed light on some familiar but poorly understood effects in space power systems operations, including bus voltage collapse, spurious oscillations, and chaotic 'noise'. Because such behaviour manifests itself in nonlinear systems but could not be exposed by customary linear systems theory, potential anomalies may remain unpredicted which could lead to catastrophic consequences. As such, these results have important implications to reliability issues, critical in space. The exposition of the concepts and tools used in this thesis would serve the practising engineer by providing the basis and pave the way for studying larger and more complex systems, in the quest for improved system performance and reliability. In the course of this work, an algorithm to compute the maximum Lyapunov exponent from differential equations with discontinuities was required to confirm chaos. Although the concepts and tools for investigating smooth equations are well established, dynamics of non-smooth systems have not been extensively studied. Here, the algorithm proposed by Miiller to cope with the discontinuities in mechanics was reviewed and was found to be applicable to power electronics in general. As a confirmation, this algorithm was applied successfully to a well known Buck DC-DC converter. Although the exploitation of nonlinear dynamics to engineer direct practical applications is still in its infancy, one is presented in this thesis. A maximum power point tracker was synthesised via nonlinear dynamics principles, simulated and experimentally verified. Excellent static and dynamic performance were exhibited. In addition, a two-dimensional stroboscopic map was derived which adequately described the fundamental dynamics of the system. This is confirmed from the good agreement between the simulated and experimental return maps. Via this map and further bifurcation study, preliminary design guidelines were established.

Retrieval and analysis of space-exposed surfaces from Low Earth Orbit (LEO) can lead to an improved understanding of the space debris and micrometeoroid particulate environment. A large volume of data has been accumulated from analysis of space-exposed ductile materials, including the LDEF satellite. The Hubble Space Telescope (HST) and EURECA solar arrays provide a large, new source of information on the LEO particulate flux. Below a certain crater diameter, these solar arrays are equivalent to semi-infinite brittle material targets and thus the impact crater fluxes are analogous to impact fluxes on returned lunar rocks and Apollo/Gemini windows. An extensive shot programme has been executed onto glass, aluminium and spacecraft honeycomb (used as exterior spacecraft wall and solar array support structure). The data supplement the large database of brittle material hypervelocity impact tests used in this thesis. These data have been used to (i) develop new, target-dependent, empirically-determined brittle material damage equations, (ii) derive a conversion factor between the brittle material ,) conchoidal diameter( D, and the ballistic limit in aluminium for a particular exposure and shielding history (Fmax)a, nd (iii) investigatet he ballistic limit of spacecrafth oneycomb. In addition, the response of brittle materials to, hypervelocity impact has been explored via hydrocode modelling, including the implementation and validation of the Johnson-Holmquist brittle material model at velocities beyond the experimental calibration regime. The converted semi-infinite brittle material fluxes from the HST and EURECA solar arrays have been directly compared with both an experimentally-measured LDEF mean flux and a modelled flux prediction for meteoroids (excluding space debris). The solar array fluxes are in good agreement with the LDEF data and modelling results for F. greater than 20-30 μm. Below this value of F,,,, the data do not reproduce the space debris flux enhancement shown by LDEF. ll

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