1 

Automatic and fast generation of suboptimal and feasible lowthrust trajectories using a boundaryvalue pseudospectral method
Some problems in Astrodynamics, such as the ones posed in the several editions of the Global Trajectory Optimisation Competition, include both a combinatorial and a trajectory optimisation problem. The combinatorial problem consists of finding the sequence of a fixed number of asteroids that will allow to find the optimal trajectory. The trajectory optimisation problem is aimed at finding the optimal rendezvous trajectories connecting the asteroids of the selected sequence. To quickly assess the optimality of the possible sequences it would be interesting to have a fast algorithm that generates a good initial guess. If no limitations on the thrust or constraints on the departure and arrival velocity are considered, this 2Point Boundary Value Problem is analytically solved by the Lambert Problem. This analytic solution has a ballistic arc in between impulsive manoeuvres and sometimes this trajectory is no good approximation for an optimal lowthrust trajectory.
The method developed here, describes the shape of the 3dimensional trajectory with expansions in power series. These expressions contain a number of unknown coefficients or Degrees of Freedom. Substitution of the Boundary Conditions leads to conditions that guarantee the satisfaction of the Boundary Conditions. The remaining Degrees of Freedom then act as optimisation variables. During the optimisation process the propellant mass is minimised for 8 selected test cases. It is shown that the method works very well for relatively short transfers. This new and fast algorithm provides a trajectory that is close to the optimum one, has a small error in final mass and allows to derive the structure of the optimal thrusting profile.

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2 

On the integralconservative numerical solution of fewbody gravitational problems: with applications to capture trajectories
On the design and implementation of integralconservative numerical integration schemes for fewbody problems in astrodynamics. Focuses on exact and approximate energy and angularmomentum integrals in the Jacobi 3body problem, and related Jacobitype integrals in the circular restricted 3body problem and a 4body model for ballistic lunar capture. Includes a selfcontained discussion of necessary astrodynamics and mathematics background, as well as a discussion of the application of these techniques to ballistic lunar capture trajectories for small satellites.

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3 

Analytical representations of lowthrust trajectories

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4 

Fishing on Europe: dynamics of the Jovian moon and its subsurface ocean
The interior of Europa, one of the moons in the Jovian system, is still mainly unknown. There are, however, indications that below an icy outer layer a subsurface ocean is present. Moreover, it has been estimated that in total the ice and ocean are between 80 and 170 kilometers thick. Concerning the thickness of the ice layer, there exist two hypotheses: some believe this layer is relatively thin (up to approximately ten kilometers), whereas others think the ice layer will be much thicker. Since it is expected that the global deformation rate of Europa, caused by the gravity pull of Jupiter, gives insight in the interior of this moon, it is of great interest to investigate this by means of computational models. The main question to be answered in this thesis is: how does the subsurface ocean of Europa deform, due to the tidal pull of Jupiter? To answer this question, the tidal forcing by Jupiter is determined. This tidal potential can be subdivided in a constant tidal potential and a time varying part. Only the latter results in an exchange in tidal energy and timevarying deformation and is, therefore, of interest. The global deformation of Europa due to this timevarying forcing is studied by means of the normal mode analysis. For this analysis, it is assumed that Europa consists of four coupled homogeneous layers; the core, the mantle, the ocean and the sea ice layer. From the normal mode analysis it followed that the radial deformation of Europa in the absence of an ocean, is less than one meter, whereas this deformation is approximately 20 meters if an ocean is present. From these results it can be concluded that by measuring the actual global deformation, for instance by means of future satellite measurements, the presence of an ocean can be determined. The next step is to model the ocean by means of the MIT General Circulation Model (MITgcm), a model that was originally developed for Earth. In this model, the ocean is no longer assumed to be homogeneous. Without sea ice, an ocean of 100 kilometers deep radially deforms approximately 20 meters due to the timevarying tidal potential. In case of an ocean with a depth of 100 kilometers and a sea ice layer with a thickness of ten kilometers, the Europan surface still radially deforms approximately 20 meters, from which it follows that the sea ice layer does not reduce the ocean deformation, i.e. the sea ice acts fluidly. This was also obtained from the normal mode analysis. Furthermore, it follows that the tidal forcing disturbs the geostrophic balance in the ocean and that the ocean dynamics, due to the tidal forcing are driven by the vertical velocities. Since the mantle is also subject to tidal deformation, heat will also be generated in this layer. On Io, for instance, volcanoes are present and it is therefore reasonable to assume that volcanoes are also present on the ocean floor of Europa. These volcanoes release the tidal heat from the mantle in the ocean. Consequently, the sea ice experiences extra heating, which leads to additional melting. This may be a strong argument for the thin sea ice hypothesis. In addition, it is shown that the shallower the ocean, the higher the ocean velocities. Thus, the presence of subsurface volcanoes and, for example, ridges will locally result in higher ocean velocities. It may well be the case that these disturbances in the velocity field and the heat released by volcanoes result in melt troughs and produce the characteristic cracks visible on the Europan surface.

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5 

Geoid anomalies due to
lowviscosity zones in glacial
isostatic adjustment modeling

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6 

A comparative analysis of project management and systems engineering techniques in Cubesat projects
Since the start of CubeSat development different universities and organisations have succeeded in launching and operating their own satellites. Each of these institutes has their own ways in which these projects are organised.Furthermore each project has its own design philosophy and heritage that influence the project. What all these projects do share is a common set of standard CubeSat requirements and similar handbooks on Project Management and Systems Engineering (PMSE). Furthermore the general development time and workforce behind the project are also similar for all institutes. With this in mind it is interesting to investigate where the resulting projects and CubeSats differ and learning opportunities arrise.

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7 

Impact of the space and satellite environment on the optical path differences of Darwin
ESA's space interferometry mission Darwin will make use of optical delay lines (ODL) to help control the optical path differences (OPD) between the satellites to the nanometer level. In order to determine the required ODL control bandwidth, this study investigates the order of magnitude of the highfrequency (> 1 Hz) disturbance forces, and their effects on the OPD. The internal disturbance forces are examined for the three subsystems which are believed to cause most mechanical vibrations. The frequencydependence of the external disturbance forces is determined in LEO for a precursor interferometry demonstration mission,
by Fouriertransforming the accelerometer data of the GRACE mission. These results, together with a literature survey on the space environment in L2, lead to an overall view on the order of magnitude of the highfrequency disturbance forces that can be expected on Darwin. In addition the micrometeoroid impacts
are studied. The internal disturbance forces are found to be dominating. Their highfrequency component remains small but has still the same order of magnitude as the OPDrequirement of 5 nmRMS, for a 1 Hz control bandwidth. Also the micrometeoroid environment shows a possible threat for Darwin.

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8 

Earthquake slip distribution inversions using Synthetic Aperture Radar Interferometry
The research presented in this M.Sc. thesis focuses on the inversion of earthquake slip distributions using Synthetic Aperture Radar Interferometry (InSAR). This spaceborne remote sensing technique enables one to observe surface deformation caused by earthquakes. These observations can be used to estimate earthquake slip distributions. A slip distribution shows the variable amount of displacement on a fault plane that caused the earthquake. Slip distributions can be used to point out areas of potential earthquake hazard.

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9 

Glacier Surface Analysis. Airborne Laser Scanning for monitoring glaciers and crevasses

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10 

Use of global ionospheric maps for precise point positioning: developing an optimised procedure in using Global Ionospheric Maps for singlefrequency standalone positioning with GPS
GPStransmitted waves are affected by the Earth's atmosphere resulting in a decrease of the measured position accuracy. The highest region of the atmosphere, known as the ionosphere, is the main cause of this accuracy degradation. Due to the dispersive nature of the ionosphere for GPSsignals, the induced delay can be measured or eliminated if a dualreceiver is used. (By constructing the Geometry/Ionospherefree Linear Combination, respectively). If a singlefrequency receiver is used instead, one is obliged to account for the ionospheric delay in other ways. In this thesis is investigated how Global Ionospheric Maps (GIMs) can be used to correct for the ionospheric delay. Because these GIMs provide vertical ionospheric delays on given gridpoints and at discrete timeepochs, several processing steps have to be carried out: a spatial and temporalinterpolation has to be performed to obtain an ionospheric delay estimate at the desired location and time and, subsequently, a mapping function has to be applied to transform the (interpolated) vertical value into the desired slant value.
The objective of this research is to investigate the contribution of these processing steps to be able to develop an optimised procedure in using GIMs.With a stochastic analysis, in which GIMbased ionospheric delay estimates are compared with real measured ionospheric delays, a bestsuited procedure in using GIMs is found. This optimised procedure is finally implemented into a singlefrequency Precise Point Positioning (PPP) concept. Static observations reveal a position accuracy at the threedecimetre level horizontally and at the fivedecimetre level vertically, for the European region.

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11 

Interval analysis applied to reentry flight trajectory optimization
Trajectory optimization is an essential part of space plane mission design. One important
aspect of trajectory optimization for reentry vehicles is to minimize the total heat load at the
surface when it returns and the heat flux should remain below certain limit, meanwhile, the
vehicle should land at the desired point. The methods used for reentry trajectory
optimization is quite successful by now. However, if the model is nonlinear, such as the reentry
vehicle, by using the classical optimization method, we can only find the local
minimum and the global minimum is never guaranteed. An innovative way of finding the
global minimum heat load for the trajectory design is introduced, namely the interval
analysis for global optimization.
In this thesis, the basic concept of the interval arithmetic is introduced. The main idea of the
interval arithmetic is to use small intervals for the calculation instead of numbers. As the
interval algorithm has a characteristics to check all the numbers within the interval and
contain all the feasible solutions, guaranteed global optimum can be found eventually.
In this report, interval method is used in both static global optimization and dynamic global
optimization problem. The application to interval analysis to static optimization problem is
very successful. However, although the application to interval analysis to dynamic system
can successfully find the global optimum, the interval global optimization method still suffer
greatly for the dependency problem, the wrapping effect, and huge number of feasible
solutions.
We apply the interval algorithm to find a guaranteed global minimum total heat load for reentry
flight trajectory design, find the difficulties and give recommendations for
improvements.
This thesis serves as a feasibility study using interval analysis for nonlinear trajectory
optimization of reentry vehicles.

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12 

A comparative study of longterm
polar motion of terrestrial bodies

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13 

Development and Testing of a Water Microresistojet
Delft University of Technology (TUDelft) is investigating the use of resistance heaters as a means to increase the specific impulse of cold nitrogen gas thrusters. There are currently envisaged for use on micro and nanosized spacecraft. To this effect, TUDelft developed the Delft University Resistojet (DUR) thruster with the purpose to heat cold nitrogen gas up to 1000 K. Present interest though is in liquid propellants as a mean to reduce storage volume. This thesis presents the design and performances of the new DUR and adapted DUR 1.0H2O, capable of producing standard atmosphere thrust level up to 20 mN, with an electric power up to 150 W, using water as propellant.
In the theoretical study, the design, analysis and model prediction of a resistance heater, using water as propellant, are presented. The goal is to optimize the DUR thruster for this purpose and to predict experimental power levels, temperatures and pressure drop. Heater and thruster tests are performed on ground in the TUDelft Rocket Test Stand (DARTS) with DUR 1.0 and a nozzle with a throat diameter of 0.4 mm. Measured parameters are thrust, pressure, temperature, mass flow, current and voltage.

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14 

3D temperature modeling for the South China Sea using remote sensing data
The South China Sea's (SCS) seasonal, largescale temperature cycle is governed to a large extend by the monsoon. This phenomenon modulates the largescale circulation, transport and mixing as well as the exchange processes with the Pacific Ocean and the East China Sea. Also, significant variations in net surface heat flux will contribute to the largescale, seasonal temperature cycle. As a result, a seasonal mixed layer temperature cycle of over 6oC occurs in the northern SCS regions and between 2oC and 4oC in the southern regions. Over the central SCS temperature stratification is observed throughout the year, while over the shallow northern and southern regions atmospheric forcing and largescale transport will attribute to a seasonal breakdown of the stratified system.
The objective of this study is to assess the largescale threedimensional temperature cycle of the SCS and to develop a corresponding hydrodynamic model that is resolving the monsoonal response. Due to the significant spatial and temporal scales, sea level anomalies observed by satellite altimetry and Sea Surface Temperature (SST) observed by satellite radiometer play an essential role in this study, both to assess the SCS physical system and for modelling applications. The model is setup using the Delft3DFLOW hydrodynamic modelling package and applies an orthogonal sphericalcurvilinear and boundary fitted grid in the horizontal. In the vertical a sigmalayer approach is applied. In the deep SCS regions the model depth is truncated based on a reduced depth approach. For surface heating the socalled Ocean heat flux model of Delft3DFLOW is used. At the open model boundaries water level and lateral transport forcing is applied. The model does not resolve tidal forcing. An extensive sensitivity analysis is performed, with model forcing and validation data both for a climatological year and for the year 2000. The models temperature accuracy is subsequently improved by assimilating remotely sensed SST data using a nudging method. On seasonal scales, the model represents the largescale transport, surface heating and stratification with reasonable accuracy. Without SST nudging a mean difference of 1.75oC is observed with respect to validation data. By nudging SST the mean difference decreases with 15% to 1.5oC.

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15 

Terminal area energy management trajectory optimization using interval analysis

file embargo until: 20160601

16 

Europan tidal deformation: providing a theoretical framework for altimetry data to determine ocean presence

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17 

Orbit Simulation and Design and Verification of the Electrical Power System of the DelfiC3 Nanosatellite
DelfiC3 is a nanosatellite developed by MSc students of the Faculty of Aerospace Engineering and Electrical Engineering, Mathematics and Computer Science at the Delft University of Technology. It will serve as an inorbit test bed for three innovative technologies. DelfiC3 is scheduled for launch in August 2007 by an Indian PSLV launcher.
This report focuses on the design process of the electrical power system. Because DelfiC3 applies a constant voltage power bus, a power conversion system is introduced to transport power from the solar arrays to the power bus. Additional conversion systems are designed for power supply to the various electronics boards. Furthermore, designs are made for interfaces between the electrical power system and the other subsystems. These designs will be presented and discussed in this report.
Because electrical power is a scarce resource in spaceflight, a power budget has been generated and maintained throughout the complete DelfiC3 project. Interface control is applied to ensure efficient cooperation between the various subsystems. In this report, the power budget and interface control process will be presented.
A second focus in this report is the simulation and verification process of the electrical systems of DelfiC3. To generate an adequate impression of the behaviour of the DelfiC3 spacecraft in orbit, several orbit simulations are performed. As simulation output, the orbital position is calculated. In addition, the control and disturbance torques are used to reconstruct the attitude profile of the spacecraft. These parameters are subsequently used to calculate the incoming solar power. It will be shown that the incoming solar power is sufficient to supply DelfiC3 with electrical power.
Electrical system verification is part of the spacecrafts testing process. It has to be verified whether the electrical power system is successful in converting solar array power to bus power. The power distribution system has to be tested to guarantee that power arrives at every subsystem in the correct conditions. It will be shown that the electrical power system performs in accordance with requirements and is qualified for spaceflight.

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18 

An H1(Ph)Coercive Discontinuous Galerkin Formulation for The Poisson Problem: 1D Analysis
Discontinuous Galerkin (DG) methods are finite element techniques for the solution of partial differential equations. They allow shape functions which are discontinuous across interelement edges. In principle, DG methods are ideally suited for hpadaptivity, as they handle nonconforming meshes and varyinginspace polynomialdegree approximations with ease.
Recently, DG formulations for elliptic problems have been put in a general framework of analysis. Although clarifying basic properties, the analysis does not warrant a clear preference. Specifically, none of the conventional DG formulations possesses a bilinear form that is coercive (and continuous) on an infinitedimensional broken Sobolev space. Rather, bilinear forms are only weakly coercive or defined on subspaces only and employ stabilization parameters that typically increase unboundedly as the subspace is expanded, e.g., if the polynomial degree is increased. For hpadaptation, coercivity is a fundamental property: By the classical LaxMilgram theorem, any conforming discretization of a coercive formulation is stable, i.e., discrete approximations are wellposed and have a unique solution, irrespective of the specifics of the underlying approximation space.
In this thesis we consider the onedimensional Poisson problem and present a generic consistent conventional DG formulation. We show that conventional DG formulations are necessarily noncoercive. Moreover, we presents a new symmetric DG formulation which contains nonconventional edge terms based on element Green's functions and the data local to the edges. We show that the new DG formulation is coercive on H1(Ph), the space of functions that are piecewise in the H1 Sobolev space. Furthermore, we show that the new DG formulation and the classical Galerkin formulation are equivalent, that is, in the infinitedimensional case they yield the same solution.

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19 

Tidal deformation of Europa and
Phobos: implications on their structure and history

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20 

The transformation of GPS into NAP heights: Combining NAP, GPS and geoid heights to compute a height reference surface for the Netherlands
GPS is used more and more for height determination. Resulting ellipsoidal heights don't give information about how the water flows. Therefore traditional height systems are used. In the Netherlands this is the NAP. To perform a transformation between both height system a geoid model is needed. This theses looks at the following issues, regarding the determination of this geoid model:
 Comparison between EGM96 and EIGENCG03C for the Dutch geoid
 Computation of a height reference surface out of GPS/levelling data only
 The use of variance component estimation for computation of a height reference surface out of NAP, GPS and geoid heights

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