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Analytical representations of low-thrust trajectories
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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 time-varying deformation and is, therefore, of interest. The global deformation of Europa due to this time-varying 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 time-varying 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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Geoid anomalies due to
low-viscosity zones in glacial
isostatic adjustment modeling
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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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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 high-frequency (> 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 frequency-dependence of the external disturbance forces is determined in LEO for a precursor interferometry demonstration mission,
by Fourier-transforming 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 high-frequency 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 high-frequency component remains small but has still the same order of magnitude as the OPD-requirement of 5 nmRMS, for a 1 Hz control bandwidth. Also the micrometeoroid environment shows a possible threat for Darwin.
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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 space-borne 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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Glacier Surface Analysis. Airborne Laser Scanning for monitoring glaciers and crevasses
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Use of global ionospheric maps for precise point positioning: developing an optimised procedure in using Global Ionospheric Maps for single-frequency standalone positioning with GPS
GPS-transmitted 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 GPS-signals, the induced delay can be measured or eliminated if a dual-receiver is used. (By constructing the Geometry/Ionosphere-free Linear Combination, respectively). If a single-frequency 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 time-epochs, several processing steps have to be carried out: a spatial- and temporal-interpolation 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 GIM-based ionospheric delay estimates are compared with real measured ionospheric delays, a best-suited procedure in using GIMs is found. This optimised procedure is finally implemented into a single-frequency Precise Point Positioning (PPP) concept. Static observations reveal a position accuracy at the three-decimetre level horizontally and at the five-decimetre level vertically, for the European region.
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Interval analysis applied to re-entry flight trajectory optimization
Trajectory optimization is an essential part of space plane mission design. One important
aspect of trajectory optimization for re-entry 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 re-entry trajectory
optimization is quite successful by now. However, if the model is non-linear, 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 non-linear trajectory
optimization of re-entry vehicles.
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[Abstract]
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A comparative study of long-term
polar motion of terrestrial bodies
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Automatic and fast generation of sub-optimal and feasible low-thrust trajectories using a boundary-value pseudo-spectral 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 2-Point 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 low-thrust trajectory.
The method developed here, describes the shape of the 3-dimensional 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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On the integral-conservative numerical solution of few-body gravitational problems: with applications to capture trajectories
On the design and implementation of integral-conservative numerical integration schemes for few-body problems in astrodynamics. Focuses on exact and approximate energy and angular-momentum integrals in the Jacobi 3-body problem, and related Jacobi-type integrals in the circular restricted 3-body problem and a 4-body model for ballistic lunar capture. Includes a self-contained 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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Development and Testing of a Water Microresistojet
Delft University of Technology (TU-Delft) 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 nano-sized spacecraft. To this effect, TU-Delft 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 TU-Delft 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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3D temperature modeling for the South China Sea using remote sensing data
The South China Sea's (SCS) seasonal, large-scale temperature cycle is governed to a large extend by the monsoon. This phenomenon modulates the large-scale 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 large-scale, 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 large-scale transport will attribute to a seasonal breakdown of the stratified system.
The objective of this study is to assess the large-scale three-dimensional 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 Delft3D-FLOW hydrodynamic modelling package and applies an orthogonal spherical-curvilinear and boundary fitted grid in the horizontal. In the vertical a sigma-layer approach is applied. In the deep SCS regions the model depth is truncated based on a reduced depth approach. For surface heating the so-called Ocean heat flux model of Delft3D-FLOW 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 large-scale 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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Terminal area energy management trajectory optimization using interval analysis
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Europan tidal deformation: providing a theoretical framework for altimetry data to determine ocean presence
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Buckled precompressed elements: a new class of control actuators for subscale UAVs
This thesis presents the use of a new class of flight control actuators employing Post-Buckled Precompressed (PBP) piezoelectric elements in morphing wing Uninhabited Aerial Vehicles (UAVs). The new actuator relies on axial compression to amplify deflections and control forces simultaneously. Two designs employing morphing wing panels based on PBP actuators were conceived. One design relied on a change in curvature of the actuators to control the camber of the airfoil. Axial compression of the actuators was ensured by means of rubber bands and increased end rotation levels with almost a factor of two up to +/- 13.6deg peak-to-peak, with excellent correlation between theory and experiment. Wind tunnel tests quantitatively proved that wing morphing induced roll acceleration levels in excess of 1500deg/sˆ2. A second design employed PBP actuators in a wing panel with significant thickness, relying on a highly compliant Latex skin to allow for shape deformation and at the same time induce an axial force on the actuators. Bench tests showed that due to the axial compression provided by the skin end rotations were increased with more than a factor of two up to +/- 15.8deg peak-to-peak up to a break frequency of 34Hz. Compared to conventional electromechanical servoactuaters, the PBP actuators showed a net reduction in flight control system weight, slop and power consumption for minimal part count. Both morphing wing concepts showed that PBP piezoelectric actuators have significant benefits over conventional actuators and can be successfully applied to induce aircraft control.
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Weak capture and the weak stability boundary: an investigation into the restricted problem of three bodies
Weak capture in the restricted problem of three bodies refers to transitory motion between the primaries. Such behavior has interesting applications in space mission design, notably, in finding optimal transfer trajectories that surpass the performance of traditional Hohmann transfers. The Weak Stability Boundary (WSB) is a mathematical set that describes the collection of points in phase space that support such motion. Two definitions exist for the WSB region: a numerical algorithmic definition and an analytical definition. The numerical algorithmic definition is the most accurate description of the WSB region; however it cumbersome to use in practice and does not provide insight into the underlying dynamics of the 3-Body Problem (3BP). An analytical definition has recently been developed to circumvent the need to integrate trajectories to establish the WSB region in phase space. This definition consists of intersections of a number of different mathematical sets. Though this definition can be implemented easily, it is inaccurate in describing the WSB region: it overestimates the region in phase space and includes regions consisting of invariant tori around the two primaries that do not permit transit.
The aim of this study is to investigate a possible improvement of the analytical definition and to visualize the internal structure of the WSB region. The internal structure of the WSB region is probed by using extended-Poincarections, which are Poincarections with an additional dimension indicating orbital stability with respect to one of the primaries. The WSB region is investigated in the Planar Circular Restricted 3-Body Problem (PCR3BP), which is a simplified 3BP model. The existence of the WSB region and its internal structure are sketched for a number of different Jacobi energy values. From these results, a number of poignant conclusions can be drawn about the underlying dynamics of the PCR3BP. The methodology presented to visualize the internal structure of the WSB region is proposed as a robust framework to study other dynamical systems in astrodynamics, such as the three-dimensional Circular Restricted 3-Body Problem (CR3BP) and the Elliptic Restricted 3-Body Problem (ER3BP), which are interesting for space mission design.
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Design and realization of a setup for mechanical tests on a MEMS based micro gravity-gradiometer
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Development of a generic inflatable de-orbit device for CubeSats
New space debris mitigation guidelines require satellites in low Earth orbit to de-orbit within 25 years after end of life. This effectively limits the orbital altitude of conventional CubeSat satellites to 400-700 km. For CubeSats employing the generic inflatable de-orbit device discussed here, this range is extended to 910 km by increasing the frontal surface area of the satellite. The device essentially is of the attached ballute type and consists of a thin membrane covering an inflatable structure, which is chemically rigidized after deployment. Coatings are applied to the structure to provide protection against the hostile low Earth orbit environment and to manipulate the temperature of the inflatable. The inflation gas is stored in solid form inside a so-called Cool Gas Generator.
A preliminary design of the pyramid-shaped device is performed for a 1-unit CubeSat of 1 kg mass, with focus on ease of integration.
Initial results of the physical development of the structure are shown. A development model of a flexible connector piece is constructed to which five inflatable tubes are attached at right angles in a leak-tight manner. The method used to bond the tubes to the connector piece as well as attachment of the membranes to the inflatable structure is outlined. Lastly, stowage and deployment of the inflatable structure are discussed. The results indicate that the mass and stowed volume of the complete de-orbit system remain within 9.4% and 10.3% of the CubeSats' total mass and volume.
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